https://wiki.math.wisc.edu/api.php?action=feedcontributions&user=Ccheng&feedformat=atomUW-Math Wiki - User contributions [en]2024-03-28T14:43:12ZUser contributionsMediaWiki 1.39.5https://wiki.math.wisc.edu/index.php?title=Graduate_Algebraic_Geometry_Seminar&diff=21029Graduate Algebraic Geometry Seminar2021-03-22T15:25:47Z<p>Ccheng: </p>
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<div>'''<br />
'''When:''' Thursday 5:00-6:00 PM CST<br />
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'''Where:''' https://uwmadison.zoom.us/j/92877740706?pwd=OVo0QmxRVEdUQ3RnUWpoWmFRRUI3dz09<br />
[[Image:cat.jpg|thumb|220px| | Lizzie the OFFICIAL mascot of GAGS!!]]<br />
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'''Who:''' All undergraduate and graduate students interested in algebraic geometry, commutative algebra, and related fields are welcome to attend.<br />
<br />
'''Why:''' The purpose of this seminar is to learn algebraic geometry and commutative algebra by giving and listening to talks in a informal setting. Talks are typically accessible to beginning graduate students and take many different forms. Sometimes people present an interesting paper they find. Other times people give a prep talk for the Friday Algebraic Geometry Seminar. Other times people give a series of talks on a topic they have been studying in-depth. Regardless the goal of GAGS is to provide a supportive and inclusive place for all to learn more about algebraic geometry and commutative algebra.<br />
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'''How:''' If you want to get emails regarding time, place, and talk topics ('''which are often assigned quite last minute''') add yourself to the gags mailing list: gags@lists.wisc.edu. The list registration page is [https://admin.lists.wisc.edu/index.php?p=11&l=gags here].<br />
'''<br />
<br />
== Give a talk! ==<br />
We need volunteers to give talks this semester. If you're interested contact [mailto:cwcrowley@wisc.edu Colin] or [mailto:drwagner@math.wisc.edu David], or just add yourself to the list (though in that case we might move your talk later without your permission). Beginning graduate students are particularly encouraged to give a talk, since it's a great way to get your feet wet with the material.<br />
<br />
== Being an audience member ==<br />
The goal of GAGS is to create a safe and comfortable space inclusive of all who wish to expand their knowledge of algebraic geometry and commutative algebra. In order to promote such an environment in addition to the standard expectations of respect/kindness all participants are asked to following the following guidelines:<br />
* Do Not Speak For/Over the Speaker: <br />
* Ask Questions Appropriately: <br />
<br />
== Spring 2021 ==<br />
<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#E0E0E0"| February 4<br />
| bgcolor="#C6D46E"| Asvin Gothandaraman<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 4| A Bertini type theorem via probability]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 25<br />
| bgcolor="#C6D46E"| Colin Crowley<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 25| TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 11<br />
| bgcolor="#C6D46E"| Roufan Jiang<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 11| TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 18<br />
| bgcolor="#C6D46E"| Alex Hof<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 18| An Introduction to the Deformation Theory of Complete Intersection Singularities]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 25<br />
| bgcolor="#C6D46E"| Chiahui (Wendy) Cheng<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 25| Explicit Bound on Collective Strength of Regular Sequences of Three Homogeneous Polynomials]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 1<br />
| bgcolor="#C6D46E"| Erika Pirnes<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 1| Reconstruction conjecture in graph theory]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 8<br />
| bgcolor="#C6D46E"| Caitlyn Booms<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 8| TBD]]<br />
|}<br />
</center><br />
<br />
== February 4 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Asvin Gothandaraman'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: A Bertini type theorem via probability<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: I will prove that most hyperplane slices are irreducible over any field by reducing to finite fields and applying probabilistic arguments. The talk will be very elementary! <br />
|} <br />
</center><br />
== February 25 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Colin Crowley'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: TDB <br />
|} <br />
</center><br />
== March 11 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Roufan Jiang'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: TBD <br />
|} <br />
</center><br />
== March 18 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Alex Hof'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: An Introduction to the Deformation Theory of Complete Intersection Singularities<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: Essentially what it says in the title; I'll give a fairly laid-back overview of some of the basic definitions and results about deformations of complete intersection singularities, including the Kodaira-Spencer map and the existence of versal deformations in the isolated case. If time permits, I'll discuss Morsification of isolated singularities. Very little background will be assumed.<br />
|} <br />
</center><br />
<br />
== March 25 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Chiahui (Wendy) Cheng'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Explicit Bound on Collective Strength of Regular Sequences of Three Homogeneous Polynomials<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: Let f_1,...,f_r in k[x_1,...,x_n] be homogeneous polynomial of degree d. Ananyan and Hochster (2016) proved that there exists a bound N=N(r,d) where if collective strength of f_1,...,f_r is greater than or equal to N, then f_1,...,f_r are regular sequence. In this paper, we study the explicit bound N(r,d) when $r=3$ and d=2,3 and show that N(3,2)=2 and N(3,3)>2.<br />
|} <br />
</center><br />
== April 1 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Erika Pirnes'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Reconstruction conjecture in graph theory<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: The deck of a graph with n vertices is a multiset of n unlabeled graphs, each obtained from the original graph by deleting a vertex (and the edges incident to it). The reconstruction conjecture says that if two finite simple graphs with at least three vertices have the same deck, then they are isomorphic. The talk is going to focus on examples, and does not assume previous knowledge about graph theory.<br />
|} <br />
</center><br />
<br />
== April 8 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Caitlyn Booms'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: TBD<br />
|} <br />
</center><br />
<br />
<br />
== Fall 2020 ==<br />
<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#E0E0E0"| September 30<br />
| bgcolor="#C6D46E"| Asvin Gothandaraman<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#September 30| Title]]<br />
|-<br />
| bgcolor="#E0E0E0"| October 5<br />
| bgcolor="#C6D46E"| Yifan Wei<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#October 5| On the Analytic Side (GAGA)]]<br />
|-<br />
| bgcolor="#E0E0E0"| October 14<br />
| bgcolor="#C6D46E"| Owen Goff<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#October 14| The Magic and Comagic of Hopf Algebras]]<br />
|-<br />
| bgcolor="#E0E0E0"| October 21<br />
| bgcolor="#C6D46E"| Roufan Jiang<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#October 21| TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| October 28<br />
| bgcolor="#C6D46E"| Erika Pirnes<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#October 28| Introduction to representation theory via an example]]<br />
|-<br />
| bgcolor="#E0E0E0"| November 4<br />
| bgcolor="#C6D46E"| Alex Mine<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#November 4| The Internal Language of the Category of Sheaves]]<br />
|-<br />
| bgcolor="#E0E0E0"| November 11<br />
| bgcolor="#C6D46E"| John Cobb<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#November 11| Introduction to Boij-Söderberg Theory]]<br />
|-<br />
| bgcolor="#E0E0E0"| November 18<br />
| bgcolor="#C6D46E"| Yunfan He<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#November 18| Introduction to mixed Hodge structure]]<br />
|-<br />
| bgcolor="#E0E0E0"| November November 25<br />
| bgcolor="#C6D46E"| Maya Banks<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#November 25| TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| December 2<br />
| bgcolor="#C6D46E"| Peter Wei<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#December 2| K3 Surfaces and Their Moduli]]<br />
|-<br />
| bgcolor="#E0E0E0"| December 9<br />
| bgcolor="#C6D46E"| Wendy Cheng<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#December 9| TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| December 16<br />
| bgcolor="#C6D46E"| Caitlyn Booms<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#December 16| Characteristic Dependence of Syzygies of Random Monomial Ideals]]<br />
|}<br />
</center><br />
<br />
== Spring 2020 ==<br />
<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#A6B658" width="300" align="center"|'''Speaker'''<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title (click to see abstract)'''<br />
|-<br />
| bgcolor="#E0E0E0"| January 29<br />
| bgcolor="#C6D46E"| Colin Crowley<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#January 29| Lefschetz hyperplane section theorem via Morse theory]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 5<br />
| bgcolor="#C6D46E"| Asvin Gothandaraman<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 5| An Introduction to Unirationality]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 12<br />
| bgcolor="#C6D46E"| Qiao He<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 12| Title]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 19<br />
| bgcolor="#C6D46E"| Dima Arinkin<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 19| Blowing down, blowing up: surface geometry]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 26<br />
| bgcolor="#C6D46E"| Connor Simpson<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 26| Intro to toric varieties]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 4<br />
| bgcolor="#C6D46E"| Peter<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 4| An introduction to Grothendieck-Riemann-Roch Theorem]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 11<br />
| bgcolor="#C6D46E"| Caitlyn Booms<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 11| Intro to Stanley-Reisner Theory]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 25<br />
| bgcolor="#C6D46E"| Steven He<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 25| Braid group action on derived categories]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 1<br />
| bgcolor="#C6D46E"| Vlad Sotirov<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 1| Title]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 8<br />
| bgcolor="#C6D46E"| Maya Banks<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 8| Title]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 15<br />
| bgcolor="#C6D46E"| Alex Hof<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 15| Embrace the Singularity: An Introduction to Stratified Morse Theory]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 22<br />
| bgcolor="#C6D46E"| Ruofan<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 22| Birational geometry: existence of rational curves]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 29<br />
| bgcolor="#C6D46E"| John Cobb<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 29| Title]]<br />
|}<br />
</center><br />
<br />
== January 29 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Colin Crowley'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Lefschetz hyperplane section theorem via Morse theory<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: Morse theory allows you to learn about the topology of a manifold by studying the critical points of a nice function on the manifold. This perspective produces a nice proof of the theorem in the title, which concerns the homology of smooth projective varieties over C. I'll explain what the theorem says, say something about what Morse theory is and why it's related, and then finish with a neat example. I'm aiming to make this understandable to someone who's taken algebraic geometry 1 and topology 1.<br />
|} <br />
</center><br />
<br />
== February 5 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Asvin Gothandaraman '''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: An introduction to unirationality<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: I will introduce the notion of unirationality and show that cubic hypersurfaces are unirational (following Kollar). If time permits, I will also show that unirational varieties are simply connected. <br />
|} <br />
</center><br />
<br />
== February 12 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Qiao He'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: <br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== February 19 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Dima Arinkin'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Blowing down, blowing up: surface geometry<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract:A big question in algebraic geometry is how much one can change a variety without affecting it `generically'. More precisely, if two varieties are birational, how far can they be from being isomorphic?<br />
<br />
The question is trivial for (smooth projective) curves: they are birational if and only if they are isomorphic. In higher dimension, the<br />
situation is much more interesting. The most fundamental operation are the `blowup', which is a kind of alteration of a variety within its birational isomorphism class, and its opposite, the blowdown.<br />
<br />
In my talk, I will introduce blowups and discuss their properties. Then (time permitting) I would like to look deeper at the case<br />
of surfaces, where the combination of blowups and intersection theory provides a complete and beautiful picture. (If we do get to this point, I won't assume any knowledge of intersection theory: to an extent, this talk is my excuse to introduce it.) <br />
|} <br />
</center><br />
<br />
== February 26 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Connor Simpson'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Intro to Toric Varieties<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: A brief introduction to toric varieties: how to build them, formulas for computing topological data, toric blow-ups, and more.<br />
|} <br />
</center><br />
<br />
== March 4 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Peter Wei'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: An introduction to Grothendieck-Riemann-Roch Theorem<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: The classical Riemann-Roch theorem tells you about how topological (genus) and analytical (through line bundle) properties on compact Riemann surface (i.e. smooth projective curve) relate to each other. Moreover, this theorem can be generalized to any vector bundles (or coherent sheaves) over any smooth projective varieties. Eventually, Grothendieck “relativized” this theorem as a property of a morphism between two projective varieties. In this talk I will introduce basic notions to formulate this theorem. If time permitting, enough examples will be given appropriately.<br />
|} <br />
</center><br />
<br />
== March 11 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Caitlyn Booms'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Intro to Stanley-Reisner Theory<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: Stanley-Reisner theory gives a dictionary between combinatorial objects (simplicial complexes) and algebraic objects (Stanley-Reisner rings). In this talk, I will introduce the main objects of study in this theory, describe this dictionary with several examples, and discuss how Stanley-Reisner theory can help us investigate algebra-geometric questions.<br />
|} <br />
</center><br />
<br />
== March 25 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Steven He'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Braid group action on derived category<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: In this talk, I will define spherical object and A_m-configuration in derived category of coherent sheaves, and say a few words about the motivation coming from the homological mirror symmetry.<br />
|} <br />
</center><br />
<br />
== April 1 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Vlad Sotirov'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: <br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== April 8 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Maya Banks'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: <br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== April 15 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Alex Hof'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Embrace the Singularity: An Introduction to Stratified Morse Theory<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: Early on in the semester, Colin told us a bit about Morse<br />
Theory, and how it lets us get a handle on the (classical) topology of<br />
smooth complex varieties. As we all know, however, not everything in<br />
life goes smoothly, and so too in algebraic geometry. Singular<br />
varieties, when given the classical topology, are not manifolds, but<br />
they can be described in terms of manifolds by means of something called<br />
a Whitney stratification. This allows us to develop a version of Morse<br />
Theory that applies to singular spaces (and also, with a bit of work, to<br />
smooth spaces that fail to be nice in other ways, like non-compact<br />
manifolds!), called Stratified Morse Theory. After going through the<br />
appropriate definitions and briefly reviewing the results of classical<br />
Morse Theory, we'll discuss the so-called Main Theorem of Stratified<br />
Morse Theory and survey some of its consequences.<br />
|} <br />
</center><br />
<br />
== April 22 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Ruofan'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Birational geometry: existence of rational curves<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: Rational curves on a variety control its birational geometry. It thus is important to determine whether they exist. People didn’t know how to do this systematically, before Mori discovered a deformation lemma which detect their existence, and bound their degree if they exist. I will briefly introduce Mori’s insight. <br />
|} <br />
</center><br />
<br />
== April 29 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''John Cobb'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: <br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
<br />
== Organizers' Contact Info ==<br />
<br />
[https://sites.google.com/view/colincrowley/home Colin Crowley]<br />
<br />
[http://www.math.wisc.edu/~drwagner/ David Wagner]<br />
<br />
==The List of Topics that we Made February 2018==<br />
<br />
On February 21st of the Month of February of The 2018th Year of the Seventh Age of The Sun, the People Present at GAGS Compiled Ye Followinge Liste of Topics They Wished to Hear Aboute:<br />
<br />
Feel free to edit the list and/or add references to learn this stuff from. Since then, we've succeeded in talking about some of these, which doesn't mean there shouldn't be another talk. Ask around or look at old semester's websites.<br />
<br />
* Schubert Calculus, aka how many lines intersect four given lines in three-dimensional space? The answer to this question is prettiest when you think about it as a problem of intersecting subvarieties in the Grassmanian. ''What is the Grassmanian, you say?'' That's probably a talk we should have every year, so you should give it!<br />
<br />
* Kindergarten GAGA. GAGA stands for Algebraic Geometry - Analytic Geometry. Serre wrote a famous paper explaining how the two are related, and you could give an exposition suitable to kindergardeners.<br />
<br />
* Katz and Mazur explanation of what a modular form is. What is it?<br />
<br />
* Kindergarten moduli of curves.<br />
<br />
* What is a dualizing sheaf? What is a dualizing complex? What is Serre duality? What is local duality? Can local duality help us understand Serre duality?<br />
<br />
* Generalizations of Riemann - Roch. (Grothendieck - Riemann - Roch? Hirzebruch - Riemann - Roch?)<br />
<br />
* Hodge theory for babies<br />
<br />
* What is a Néron model?<br />
<br />
* What is a crystal? What does it have to do with D-modules? [http://www.math.harvard.edu/~gaitsgde/grad_2009/SeminarNotes/Nov17-19(Crystals).pdf Here's an encouragingly short set of notes on it].<br />
<br />
* What and why is a dessin d'enfants?<br />
<br />
* DG Schemes.<br />
<br />
==Ed Dewey's Wish List Of Olde==__NOTOC__<br />
<br />
Back in the day Ed and Nathan made this list of topics they wanted to hear. They all sound super duper cool, but it's also true that they had many years of AG behind their backs, so this list might not be very representative of what the GAGS audience wants to hear bout.<br />
<br />
Here are the topics we're '''DYING''' to learn about! Please consider looking into one of these topics and giving one or two GAGS talks.<br />
<br />
===Specifically Vague Topics===<br />
* D-modules 101: basics of D-modules, equivalence between left and right D-modules, pullbacks, pushforwards, maybe the Gauss-Manin Connection. Claude Sabbah's introduction to the subject could be a good place to start.<br />
<br />
* Sheaf operations on D-modules (the point is that then you can get a Fourier-Mukai transform between certain O-modules and certain D-modules, which is more or less how geometric Langlands is supposed to work)<br />
<br />
===Interesting Papers & Books===<br />
* ''Symplectic structure of the moduli space of sheaves on an abelian or K3 surface'' - Shigeru Mukai.<br />
<br />
* ''Residues and Duality'' - Robin Hatshorne.<br />
** Have you heard of Serre Duality? Would you like to really understand the nuts and bolts of it and its generalizations? If so this book is for you. (You wouldn't need to read the whole book to give a talk ;).)<br />
<br />
* ''Coherent sheaves on P^n and problems in linear algebra'' - A. A. Beilinson.<br />
** In this two page paper constructs the semi-orthogonal decomposition of the derived category of coherent sheaves on projective space. (This topic is very important, and there are a ton of other resources for this result and the general theory of derived categories.)<br />
<br />
* ''Frobenius splitting and cohomology vanishing for Schubert varieties'' - V.B. Mehta and A. Ramanathan.<br />
** In characteristic p the fact that (x+y)^p=x^p+y^p means that one has the Frobenius morphism, which sends f to f^p. In this paper the authors introduce the notion of what it means for a variety to be Frobenius split, and use this to prove certain cohomologcal vanishing results for Schubert varieties. Since then Frobenius splitting -- and its related cousins (F-regularity, strong F-regularity, F-purity, etc.) have played large roles in geometry and algebra in characteristic p. This is a good place to get a sense for what kicked all this stuff off! <br />
<br />
* ''Schubert Calculus'' - S. L. Kleiman and Dan Laksov.<br />
** An introduction to Schubert calculus suitable for those of all ages. I am told the paper essentially only uses linear algebra!<br />
<br />
* ''Rational Isogenies of Prime Degree'' - Barry Mazur.<br />
** In this paper Mazur classifies all isogenies of rational elliptic curves of prime order. As a result of this he deduces his famous result that the torsion subgroup of an elliptic curve (over Q) is one of 15 abelian groups. This definitely stares into the land of number theory, but certainly would still be of interest to many.<br />
<br />
* ''Esquisse d’une programme'' - Alexander Grothendieck.<br />
** Originating from a grant proposal in the mid 1980's this famous paper outlines a tantalizing research program, which seeks to tie numerous different areas of math (algebraic geometry, Teichmuller theory, Galois theory, etc.) together. This is where Grothendieck introduced his famous Lego game and dessin d'enfant. While just a research proposal this paper has seemingly inspired a ton of cool math, and will allow you to "blow peoples’ minds". (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Géométrie algébraique et géométrie analytique'' - J.P. Serre.<br />
** A projective variety X over the complex numbers has two lives, an algebraic and an analytic, depending on which topology one wishes to work with. That is one can think about X as a complex manifold and work with holomorphic functions or as an algebraic variety and work with regular functions. Hence to any complex projective variety we have two sheaf theories and as a result two cohomology theories. In this famous paper Serre compares these two and shows they are in fact the same. (''Note: This is a super fundamental result that is used all the time; normally in the following way: Uhh... What do you mean by cohomology? Well by GAGA or something it doesn't really mater.) (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Limit linear series: Basic theory''- David Eisenbud and Joe Harris.<br />
** One of the more profitable tools -- especially when studying moduli spaces -- in a geometers tool box is the theory of degenerations. However, sometimes we care about more than just the variety we are degenerating and want to keep track of things like vector/line bundles. In this paper Eisenbud and Harris develop the theory of degenerating a curve together with a linear series. From this they prove a ton of cool results: M_g is of general type for g>24, Brill-Noether theory, etc.<br />
<br />
* ''Picard Groups of Moduli Problems'' - David Mumford.<br />
** This paper is essentially the origin of algebraic stacks.<br />
<br />
* ''The Structure of Algebraic Threefolds: An Introduction to Mori's Program'' - Janos Kollar<br />
** This paper is an introduction to Mori's famous ``minimal model'' program, which is a far reaching program seeking to understand the birational geometry of higher dimensional varieties. <br />
<br />
* ''Cayley-Bacharach Formulas'' - Qingchun Ren, Jürgen Richter-Gebert, Bernd Sturmfels.<br />
** A classical result we all learn in a first semester of algebraic geometry is that 5 points in the plane (in general position) determine a unique plane conic. One can similarly show that 9 (general) points in the plane determine a unique plane cubic curve. This paper tries to answer the question: ``What is equation for this cubic curve?''.<br />
<br />
* ''On Varieties of Minimal Degree (A Centennial Approach)'' - David Eisenbud and Joe Harris.<br />
** Suppose X is a projective variety embedded in projective space so that X is not contained in any hyperplane. By projecting from general points one can see that the degree of X is at least codim(X)+1. This paper discusses the classification of varieties that achieve this lower degree bound i.e. varieties of minimal degree. This topic is quite classical and the paper seems to contain a nice mixture of classical and modern geometry.<br />
<br />
* ''The Gromov-Witten potential associated to a TCFT'' - Kevin J. Costello.<br />
** This seems incredibly interesting, but fairing warning this paper has been described as ''highly technical'', which considering it uses A-infinity algebras and the derived category of a Calabi-Yau seems like a reasonable description. (This paper may be covered in Caldararu's Spring 2017 topics course.)<br />
<br />
<br />
== Past Semesters ==<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2019 Fall 2019]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2019 Spring 2019]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2018 Fall 2018]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2018 Spring 2018]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2017 Fall 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2017 Spring 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2016 Fall 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2016 Spring 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_(Fall_2015) Fall 2015]</div>Cchenghttps://wiki.math.wisc.edu/index.php?title=Graduate_Algebraic_Geometry_Seminar&diff=21028Graduate Algebraic Geometry Seminar2021-03-22T15:24:26Z<p>Ccheng: </p>
<hr />
<div>'''<br />
'''When:''' Thursday 5:00-6:00 PM CST<br />
<br />
'''Where:''' https://uwmadison.zoom.us/j/92877740706?pwd=OVo0QmxRVEdUQ3RnUWpoWmFRRUI3dz09<br />
[[Image:cat.jpg|thumb|220px| | Lizzie the OFFICIAL mascot of GAGS!!]]<br />
<br />
'''Who:''' All undergraduate and graduate students interested in algebraic geometry, commutative algebra, and related fields are welcome to attend.<br />
<br />
'''Why:''' The purpose of this seminar is to learn algebraic geometry and commutative algebra by giving and listening to talks in a informal setting. Talks are typically accessible to beginning graduate students and take many different forms. Sometimes people present an interesting paper they find. Other times people give a prep talk for the Friday Algebraic Geometry Seminar. Other times people give a series of talks on a topic they have been studying in-depth. Regardless the goal of GAGS is to provide a supportive and inclusive place for all to learn more about algebraic geometry and commutative algebra.<br />
<br />
'''How:''' If you want to get emails regarding time, place, and talk topics ('''which are often assigned quite last minute''') add yourself to the gags mailing list: gags@lists.wisc.edu. The list registration page is [https://admin.lists.wisc.edu/index.php?p=11&l=gags here].<br />
'''<br />
<br />
== Give a talk! ==<br />
We need volunteers to give talks this semester. If you're interested contact [mailto:cwcrowley@wisc.edu Colin] or [mailto:drwagner@math.wisc.edu David], or just add yourself to the list (though in that case we might move your talk later without your permission). Beginning graduate students are particularly encouraged to give a talk, since it's a great way to get your feet wet with the material.<br />
<br />
== Being an audience member ==<br />
The goal of GAGS is to create a safe and comfortable space inclusive of all who wish to expand their knowledge of algebraic geometry and commutative algebra. In order to promote such an environment in addition to the standard expectations of respect/kindness all participants are asked to following the following guidelines:<br />
* Do Not Speak For/Over the Speaker: <br />
* Ask Questions Appropriately: <br />
<br />
== Spring 2021 ==<br />
<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#E0E0E0"| February 4<br />
| bgcolor="#C6D46E"| Asvin Gothandaraman<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 4| A Bertini type theorem via probability]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 25<br />
| bgcolor="#C6D46E"| Colin Crowley<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 25| TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 11<br />
| bgcolor="#C6D46E"| Roufan Jiang<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 11| TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 18<br />
| bgcolor="#C6D46E"| Alex Hof<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 18| An Introduction to the Deformation Theory of Complete Intersection Singularities]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 25<br />
| bgcolor="#C6D46E"| Chiahui (Wendy) Cheng<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 25| Explicit Bound on Collective Strength of Regular Sequences of Three Homogeneous Polynomials<br />
|-<br />
| bgcolor="#E0E0E0"| April 1<br />
| bgcolor="#C6D46E"| Erika Pirnes<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 1| Reconstruction conjecture in graph theory]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 8<br />
| bgcolor="#C6D46E"| Caitlyn Booms<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 8| TBD]]<br />
|}<br />
</center><br />
<br />
== February 4 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Asvin Gothandaraman'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: A Bertini type theorem via probability<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: I will prove that most hyperplane slices are irreducible over any field by reducing to finite fields and applying probabilistic arguments. The talk will be very elementary! <br />
|} <br />
</center><br />
== February 25 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Colin Crowley'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: TDB <br />
|} <br />
</center><br />
== March 11 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Roufan Jiang'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: TBD <br />
|} <br />
</center><br />
== March 18 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Alex Hof'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: An Introduction to the Deformation Theory of Complete Intersection Singularities<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: Essentially what it says in the title; I'll give a fairly laid-back overview of some of the basic definitions and results about deformations of complete intersection singularities, including the Kodaira-Spencer map and the existence of versal deformations in the isolated case. If time permits, I'll discuss Morsification of isolated singularities. Very little background will be assumed.<br />
|} <br />
</center><br />
<br />
== March 25 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Chiahui (Wendy) Cheng'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Explicit Bound on Collective Strength of Regular Sequences of Three Homogeneous Polynomials<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: Let f_1,...,f_r in k[x_1,...,x_n] be homogeneous polynomial of degree d. Ananyan and Hochster (2016) proved that there exists a bound N=N(r,d) where if collective strength of f_1,...,f_r is greater than or equal to N, then f_1,...,f_r are regular sequence. In this paper, we study the explicit bound N(r,d) when $r=3$ and d=2,3 and show that N(3,2)=2 and N(3,3)>2.\\<br />
|} <br />
</center><br />
== April 1 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Erika Pirnes'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Reconstruction conjecture in graph theory<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: The deck of a graph with n vertices is a multiset of n unlabeled graphs, each obtained from the original graph by deleting a vertex (and the edges incident to it). The reconstruction conjecture says that if two finite simple graphs with at least three vertices have the same deck, then they are isomorphic. The talk is going to focus on examples, and does not assume previous knowledge about graph theory.<br />
|} <br />
</center><br />
<br />
== April 8 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Caitlyn Booms'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: TBD<br />
|} <br />
</center><br />
<br />
<br />
== Fall 2020 ==<br />
<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#E0E0E0"| September 30<br />
| bgcolor="#C6D46E"| Asvin Gothandaraman<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#September 30| Title]]<br />
|-<br />
| bgcolor="#E0E0E0"| October 5<br />
| bgcolor="#C6D46E"| Yifan Wei<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#October 5| On the Analytic Side (GAGA)]]<br />
|-<br />
| bgcolor="#E0E0E0"| October 14<br />
| bgcolor="#C6D46E"| Owen Goff<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#October 14| The Magic and Comagic of Hopf Algebras]]<br />
|-<br />
| bgcolor="#E0E0E0"| October 21<br />
| bgcolor="#C6D46E"| Roufan Jiang<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#October 21| TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| October 28<br />
| bgcolor="#C6D46E"| Erika Pirnes<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#October 28| Introduction to representation theory via an example]]<br />
|-<br />
| bgcolor="#E0E0E0"| November 4<br />
| bgcolor="#C6D46E"| Alex Mine<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#November 4| The Internal Language of the Category of Sheaves]]<br />
|-<br />
| bgcolor="#E0E0E0"| November 11<br />
| bgcolor="#C6D46E"| John Cobb<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#November 11| Introduction to Boij-Söderberg Theory]]<br />
|-<br />
| bgcolor="#E0E0E0"| November 18<br />
| bgcolor="#C6D46E"| Yunfan He<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#November 18| Introduction to mixed Hodge structure]]<br />
|-<br />
| bgcolor="#E0E0E0"| November November 25<br />
| bgcolor="#C6D46E"| Maya Banks<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#November 25| TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| December 2<br />
| bgcolor="#C6D46E"| Peter Wei<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#December 2| K3 Surfaces and Their Moduli]]<br />
|-<br />
| bgcolor="#E0E0E0"| December 9<br />
| bgcolor="#C6D46E"| Wendy Cheng<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#December 9| TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| December 16<br />
| bgcolor="#C6D46E"| Caitlyn Booms<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#December 16| Characteristic Dependence of Syzygies of Random Monomial Ideals]]<br />
|}<br />
</center><br />
<br />
== Spring 2020 ==<br />
<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#A6B658" width="300" align="center"|'''Speaker'''<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title (click to see abstract)'''<br />
|-<br />
| bgcolor="#E0E0E0"| January 29<br />
| bgcolor="#C6D46E"| Colin Crowley<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#January 29| Lefschetz hyperplane section theorem via Morse theory]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 5<br />
| bgcolor="#C6D46E"| Asvin Gothandaraman<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 5| An Introduction to Unirationality]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 12<br />
| bgcolor="#C6D46E"| Qiao He<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 12| Title]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 19<br />
| bgcolor="#C6D46E"| Dima Arinkin<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 19| Blowing down, blowing up: surface geometry]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 26<br />
| bgcolor="#C6D46E"| Connor Simpson<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 26| Intro to toric varieties]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 4<br />
| bgcolor="#C6D46E"| Peter<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 4| An introduction to Grothendieck-Riemann-Roch Theorem]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 11<br />
| bgcolor="#C6D46E"| Caitlyn Booms<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 11| Intro to Stanley-Reisner Theory]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 25<br />
| bgcolor="#C6D46E"| Steven He<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 25| Braid group action on derived categories]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 1<br />
| bgcolor="#C6D46E"| Vlad Sotirov<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 1| Title]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 8<br />
| bgcolor="#C6D46E"| Maya Banks<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 8| Title]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 15<br />
| bgcolor="#C6D46E"| Alex Hof<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 15| Embrace the Singularity: An Introduction to Stratified Morse Theory]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 22<br />
| bgcolor="#C6D46E"| Ruofan<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 22| Birational geometry: existence of rational curves]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 29<br />
| bgcolor="#C6D46E"| John Cobb<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 29| Title]]<br />
|}<br />
</center><br />
<br />
== January 29 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Colin Crowley'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Lefschetz hyperplane section theorem via Morse theory<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: Morse theory allows you to learn about the topology of a manifold by studying the critical points of a nice function on the manifold. This perspective produces a nice proof of the theorem in the title, which concerns the homology of smooth projective varieties over C. I'll explain what the theorem says, say something about what Morse theory is and why it's related, and then finish with a neat example. I'm aiming to make this understandable to someone who's taken algebraic geometry 1 and topology 1.<br />
|} <br />
</center><br />
<br />
== February 5 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Asvin Gothandaraman '''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: An introduction to unirationality<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: I will introduce the notion of unirationality and show that cubic hypersurfaces are unirational (following Kollar). If time permits, I will also show that unirational varieties are simply connected. <br />
|} <br />
</center><br />
<br />
== February 12 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Qiao He'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: <br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== February 19 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Dima Arinkin'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Blowing down, blowing up: surface geometry<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract:A big question in algebraic geometry is how much one can change a variety without affecting it `generically'. More precisely, if two varieties are birational, how far can they be from being isomorphic?<br />
<br />
The question is trivial for (smooth projective) curves: they are birational if and only if they are isomorphic. In higher dimension, the<br />
situation is much more interesting. The most fundamental operation are the `blowup', which is a kind of alteration of a variety within its birational isomorphism class, and its opposite, the blowdown.<br />
<br />
In my talk, I will introduce blowups and discuss their properties. Then (time permitting) I would like to look deeper at the case<br />
of surfaces, where the combination of blowups and intersection theory provides a complete and beautiful picture. (If we do get to this point, I won't assume any knowledge of intersection theory: to an extent, this talk is my excuse to introduce it.) <br />
|} <br />
</center><br />
<br />
== February 26 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Connor Simpson'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Intro to Toric Varieties<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: A brief introduction to toric varieties: how to build them, formulas for computing topological data, toric blow-ups, and more.<br />
|} <br />
</center><br />
<br />
== March 4 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Peter Wei'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: An introduction to Grothendieck-Riemann-Roch Theorem<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: The classical Riemann-Roch theorem tells you about how topological (genus) and analytical (through line bundle) properties on compact Riemann surface (i.e. smooth projective curve) relate to each other. Moreover, this theorem can be generalized to any vector bundles (or coherent sheaves) over any smooth projective varieties. Eventually, Grothendieck “relativized” this theorem as a property of a morphism between two projective varieties. In this talk I will introduce basic notions to formulate this theorem. If time permitting, enough examples will be given appropriately.<br />
|} <br />
</center><br />
<br />
== March 11 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Caitlyn Booms'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Intro to Stanley-Reisner Theory<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: Stanley-Reisner theory gives a dictionary between combinatorial objects (simplicial complexes) and algebraic objects (Stanley-Reisner rings). In this talk, I will introduce the main objects of study in this theory, describe this dictionary with several examples, and discuss how Stanley-Reisner theory can help us investigate algebra-geometric questions.<br />
|} <br />
</center><br />
<br />
== March 25 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Steven He'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Braid group action on derived category<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: In this talk, I will define spherical object and A_m-configuration in derived category of coherent sheaves, and say a few words about the motivation coming from the homological mirror symmetry.<br />
|} <br />
</center><br />
<br />
== April 1 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Vlad Sotirov'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: <br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== April 8 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Maya Banks'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: <br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== April 15 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Alex Hof'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Embrace the Singularity: An Introduction to Stratified Morse Theory<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: Early on in the semester, Colin told us a bit about Morse<br />
Theory, and how it lets us get a handle on the (classical) topology of<br />
smooth complex varieties. As we all know, however, not everything in<br />
life goes smoothly, and so too in algebraic geometry. Singular<br />
varieties, when given the classical topology, are not manifolds, but<br />
they can be described in terms of manifolds by means of something called<br />
a Whitney stratification. This allows us to develop a version of Morse<br />
Theory that applies to singular spaces (and also, with a bit of work, to<br />
smooth spaces that fail to be nice in other ways, like non-compact<br />
manifolds!), called Stratified Morse Theory. After going through the<br />
appropriate definitions and briefly reviewing the results of classical<br />
Morse Theory, we'll discuss the so-called Main Theorem of Stratified<br />
Morse Theory and survey some of its consequences.<br />
|} <br />
</center><br />
<br />
== April 22 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Ruofan'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Birational geometry: existence of rational curves<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: Rational curves on a variety control its birational geometry. It thus is important to determine whether they exist. People didn’t know how to do this systematically, before Mori discovered a deformation lemma which detect their existence, and bound their degree if they exist. I will briefly introduce Mori’s insight. <br />
|} <br />
</center><br />
<br />
== April 29 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''John Cobb'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: <br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
<br />
== Organizers' Contact Info ==<br />
<br />
[https://sites.google.com/view/colincrowley/home Colin Crowley]<br />
<br />
[http://www.math.wisc.edu/~drwagner/ David Wagner]<br />
<br />
==The List of Topics that we Made February 2018==<br />
<br />
On February 21st of the Month of February of The 2018th Year of the Seventh Age of The Sun, the People Present at GAGS Compiled Ye Followinge Liste of Topics They Wished to Hear Aboute:<br />
<br />
Feel free to edit the list and/or add references to learn this stuff from. Since then, we've succeeded in talking about some of these, which doesn't mean there shouldn't be another talk. Ask around or look at old semester's websites.<br />
<br />
* Schubert Calculus, aka how many lines intersect four given lines in three-dimensional space? The answer to this question is prettiest when you think about it as a problem of intersecting subvarieties in the Grassmanian. ''What is the Grassmanian, you say?'' That's probably a talk we should have every year, so you should give it!<br />
<br />
* Kindergarten GAGA. GAGA stands for Algebraic Geometry - Analytic Geometry. Serre wrote a famous paper explaining how the two are related, and you could give an exposition suitable to kindergardeners.<br />
<br />
* Katz and Mazur explanation of what a modular form is. What is it?<br />
<br />
* Kindergarten moduli of curves.<br />
<br />
* What is a dualizing sheaf? What is a dualizing complex? What is Serre duality? What is local duality? Can local duality help us understand Serre duality?<br />
<br />
* Generalizations of Riemann - Roch. (Grothendieck - Riemann - Roch? Hirzebruch - Riemann - Roch?)<br />
<br />
* Hodge theory for babies<br />
<br />
* What is a Néron model?<br />
<br />
* What is a crystal? What does it have to do with D-modules? [http://www.math.harvard.edu/~gaitsgde/grad_2009/SeminarNotes/Nov17-19(Crystals).pdf Here's an encouragingly short set of notes on it].<br />
<br />
* What and why is a dessin d'enfants?<br />
<br />
* DG Schemes.<br />
<br />
==Ed Dewey's Wish List Of Olde==__NOTOC__<br />
<br />
Back in the day Ed and Nathan made this list of topics they wanted to hear. They all sound super duper cool, but it's also true that they had many years of AG behind their backs, so this list might not be very representative of what the GAGS audience wants to hear bout.<br />
<br />
Here are the topics we're '''DYING''' to learn about! Please consider looking into one of these topics and giving one or two GAGS talks.<br />
<br />
===Specifically Vague Topics===<br />
* D-modules 101: basics of D-modules, equivalence between left and right D-modules, pullbacks, pushforwards, maybe the Gauss-Manin Connection. Claude Sabbah's introduction to the subject could be a good place to start.<br />
<br />
* Sheaf operations on D-modules (the point is that then you can get a Fourier-Mukai transform between certain O-modules and certain D-modules, which is more or less how geometric Langlands is supposed to work)<br />
<br />
===Interesting Papers & Books===<br />
* ''Symplectic structure of the moduli space of sheaves on an abelian or K3 surface'' - Shigeru Mukai.<br />
<br />
* ''Residues and Duality'' - Robin Hatshorne.<br />
** Have you heard of Serre Duality? Would you like to really understand the nuts and bolts of it and its generalizations? If so this book is for you. (You wouldn't need to read the whole book to give a talk ;).)<br />
<br />
* ''Coherent sheaves on P^n and problems in linear algebra'' - A. A. Beilinson.<br />
** In this two page paper constructs the semi-orthogonal decomposition of the derived category of coherent sheaves on projective space. (This topic is very important, and there are a ton of other resources for this result and the general theory of derived categories.)<br />
<br />
* ''Frobenius splitting and cohomology vanishing for Schubert varieties'' - V.B. Mehta and A. Ramanathan.<br />
** In characteristic p the fact that (x+y)^p=x^p+y^p means that one has the Frobenius morphism, which sends f to f^p. In this paper the authors introduce the notion of what it means for a variety to be Frobenius split, and use this to prove certain cohomologcal vanishing results for Schubert varieties. Since then Frobenius splitting -- and its related cousins (F-regularity, strong F-regularity, F-purity, etc.) have played large roles in geometry and algebra in characteristic p. This is a good place to get a sense for what kicked all this stuff off! <br />
<br />
* ''Schubert Calculus'' - S. L. Kleiman and Dan Laksov.<br />
** An introduction to Schubert calculus suitable for those of all ages. I am told the paper essentially only uses linear algebra!<br />
<br />
* ''Rational Isogenies of Prime Degree'' - Barry Mazur.<br />
** In this paper Mazur classifies all isogenies of rational elliptic curves of prime order. As a result of this he deduces his famous result that the torsion subgroup of an elliptic curve (over Q) is one of 15 abelian groups. This definitely stares into the land of number theory, but certainly would still be of interest to many.<br />
<br />
* ''Esquisse d’une programme'' - Alexander Grothendieck.<br />
** Originating from a grant proposal in the mid 1980's this famous paper outlines a tantalizing research program, which seeks to tie numerous different areas of math (algebraic geometry, Teichmuller theory, Galois theory, etc.) together. This is where Grothendieck introduced his famous Lego game and dessin d'enfant. While just a research proposal this paper has seemingly inspired a ton of cool math, and will allow you to "blow peoples’ minds". (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Géométrie algébraique et géométrie analytique'' - J.P. Serre.<br />
** A projective variety X over the complex numbers has two lives, an algebraic and an analytic, depending on which topology one wishes to work with. That is one can think about X as a complex manifold and work with holomorphic functions or as an algebraic variety and work with regular functions. Hence to any complex projective variety we have two sheaf theories and as a result two cohomology theories. In this famous paper Serre compares these two and shows they are in fact the same. (''Note: This is a super fundamental result that is used all the time; normally in the following way: Uhh... What do you mean by cohomology? Well by GAGA or something it doesn't really mater.) (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Limit linear series: Basic theory''- David Eisenbud and Joe Harris.<br />
** One of the more profitable tools -- especially when studying moduli spaces -- in a geometers tool box is the theory of degenerations. However, sometimes we care about more than just the variety we are degenerating and want to keep track of things like vector/line bundles. In this paper Eisenbud and Harris develop the theory of degenerating a curve together with a linear series. From this they prove a ton of cool results: M_g is of general type for g>24, Brill-Noether theory, etc.<br />
<br />
* ''Picard Groups of Moduli Problems'' - David Mumford.<br />
** This paper is essentially the origin of algebraic stacks.<br />
<br />
* ''The Structure of Algebraic Threefolds: An Introduction to Mori's Program'' - Janos Kollar<br />
** This paper is an introduction to Mori's famous ``minimal model'' program, which is a far reaching program seeking to understand the birational geometry of higher dimensional varieties. <br />
<br />
* ''Cayley-Bacharach Formulas'' - Qingchun Ren, Jürgen Richter-Gebert, Bernd Sturmfels.<br />
** A classical result we all learn in a first semester of algebraic geometry is that 5 points in the plane (in general position) determine a unique plane conic. One can similarly show that 9 (general) points in the plane determine a unique plane cubic curve. This paper tries to answer the question: ``What is equation for this cubic curve?''.<br />
<br />
* ''On Varieties of Minimal Degree (A Centennial Approach)'' - David Eisenbud and Joe Harris.<br />
** Suppose X is a projective variety embedded in projective space so that X is not contained in any hyperplane. By projecting from general points one can see that the degree of X is at least codim(X)+1. This paper discusses the classification of varieties that achieve this lower degree bound i.e. varieties of minimal degree. This topic is quite classical and the paper seems to contain a nice mixture of classical and modern geometry.<br />
<br />
* ''The Gromov-Witten potential associated to a TCFT'' - Kevin J. Costello.<br />
** This seems incredibly interesting, but fairing warning this paper has been described as ''highly technical'', which considering it uses A-infinity algebras and the derived category of a Calabi-Yau seems like a reasonable description. (This paper may be covered in Caldararu's Spring 2017 topics course.)<br />
<br />
<br />
== Past Semesters ==<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2019 Fall 2019]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2019 Spring 2019]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2018 Fall 2018]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2018 Spring 2018]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2017 Fall 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2017 Spring 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2016 Fall 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2016 Spring 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_(Fall_2015) Fall 2015]</div>Cchenghttps://wiki.math.wisc.edu/index.php?title=Graduate_Algebraic_Geometry_Seminar&diff=17030Graduate Algebraic Geometry Seminar2019-02-22T20:21:23Z<p>Ccheng: </p>
<hr />
<div>'''<br />
'''When:''' Wednesdays 4:25pm<br />
<br />
'''Where:''' Van Vleck B317 (Spring 2019)<br />
[[Image:cat.jpg|thumb|220px| | Lizzie the OFFICIAL mascot of GAGS!!]]<br />
<br />
'''Who:''' All undergraduate and graduate students interested in algebraic geometry, commutative algebra, and related fields are welcome to attend.<br />
<br />
'''Why:''' The purpose of this seminar is to learn algebraic geometry and commutative algebra by giving and listening to talks in a informal setting. Talks are typically accessible to beginning graduate students and take many different forms. Sometimes people present an interesting paper they find. Other times people give a prep talk for the Friday Algebraic Geometry Seminar. Other times people give a series of talks on a topic they have been studying in-depth. Regardless the goal of GAGS is to provide a supportive and inclusive place for all to learn more about algebraic geometry and commutative algebra.<br />
<br />
'''How:''' If you want to get emails regarding time, place, and talk topics ('''which are often assigned quite last minute''') add yourself to the gags mailing list: gags@lists.wisc.edu. The list registration page is [https://admin.lists.wisc.edu/index.php?p=11&l=gags here].<br />
'''<br />
<br />
== Give a talk! ==<br />
We need volunteers to give talks this semester. If you're interested contact [mailto:cbooms@wisc.edu Caitlyn] or [mailto:drwagner@math.wisc.edu David], or just add yourself to the list (though in that case we might move your talk later without your permission). Beginning graduate students are particularly encouraged to give a talk, since it's a great way to get your feet wet with the material.<br />
<br />
== Being an audience member ==<br />
The goal of GAGS is to create a safe and comfortable space inclusive of all who wish to expand their knowledge of algebraic geometry and commutative algebra. In order to promote such an environment in addition to the standard expectations of respect/kindness all participants are asked to following the following guidelines:<br />
* Do Not Speak For/Over the Speaker: <br />
* Ask Questions Appropriately: <br />
<br />
==The List of Topics that we Made February 2018==<br />
<br />
On February 21st of the Month of February of The 2018th Year of the Seventh Age of The Sun, the People Present at GAGS Compiled Ye Followinge Liste of Topics They Wished to Hear Aboute:<br />
<br />
Feel free to edit the list and/or add references to learn this stuff from. Since then, we've succeeded in talking about some of these, which doesn't mean there shouldn't be another talk. Ask around or look at old semester's websites.<br />
<br />
* Schubert Calculus, aka how many lines intersect four given lines in three-dimensional space? The answer to this question is prettiest when you think about it as a problem of intersecting subvarieties in the Grassmanian. ''What is the Grassmanian, you say?'' That's probably a talk we should have every year, so you should give it!<br />
<br />
* Kindergarten GAGA. GAGA stands for Algebraic Geometry - Analytic Geometry. Serre wrote a famous paper explaining how the two are related, and you could give an exposition suitable to kindergardeners.<br />
<br />
* Katz and Mazur explanation of what a modular form is. What is it?<br />
<br />
* Kindergarten moduli of curves.<br />
<br />
* What is a dualizing sheaf? What is a dualizing complex? What is Serre duality? What is local duality? Can local duality help us understand Serre duality?<br />
<br />
* Generalizations of Riemann - Roch. (Grothendieck - Riemann - Roch? Hirzebruch - Riemann - Roch?)<br />
<br />
* Hodge theory for babies<br />
<br />
* What is a Néron model?<br />
<br />
* What is a crystal? What does it have to do with D-modules? [http://www.math.harvard.edu/~gaitsgde/grad_2009/SeminarNotes/Nov17-19(Crystals).pdf Here's an encouragingly short set of notes on it].<br />
<br />
* What and why is a dessin d'enfants?<br />
<br />
* DG Schemes.<br />
<br />
<br />
==Ed Dewey's Wish List Of Olde==<br />
<br />
Back in the day Ed and Nathan made this list of topics they wanted to hear. They all sound super duper cool, but it's also true that they had many years of AG behind their backs, so this list might not be very representative of what the GAGS audience wants to hear bout.<br />
<br />
Here are the topics we're '''DYING''' to learn about! Please consider looking into one of these topics and giving one or two GAGS talks.<br />
<br />
===Specifically Vague Topics===<br />
* D-modules 101: basics of D-modules, equivalence between left and right D-modules, pullbacks, pushforwards, maybe the Gauss-Manin Connection. Claude Sabbah's introduction to the subject could be a good place to start.<br />
<br />
* Sheaf operations on D-modules (the point is that then you can get a Fourier-Mukai transform between certain O-modules and certain D-modules, which is more or less how geometric Langlands is supposed to work)<br />
<br />
===Famous Theorems===<br />
<br />
===Interesting Papers & Books===<br />
* ''Symplectic structure of the moduli space of sheaves on an abelian or K3 surface'' - Shigeru Mukai.<br />
<br />
* ''Residues and Duality'' - Robin Hatshorne.<br />
** Have you heard of Serre Duality? Would you like to really understand the nuts and bolts of it and its generalizations? If so this book is for you. (You wouldn't need to read the whole book to give a talk ;).)<br />
<br />
* ''Coherent sheaves on P^n and problems in linear algebra'' - A. A. Beilinson.<br />
** In this two page paper constructs the semi-orthogonal decomposition of the derived category of coherent sheaves on projective space. (This topic is very important, and there are a ton of other resources for this result and the general theory of derived categories.)<br />
<br />
* ''Frobenius splitting and cohomology vanishing for Schubert varieties'' - V.B. Mehta and A. Ramanathan.<br />
** In characteristic p the fact that (x+y)^p=x^p+y^p means that one has the Frobenius morphism, which sends f to f^p. In this paper the authors introduce the notion of what it means for a variety to be Frobenius split, and use this to prove certain cohomologcal vanishing results for Schubert varieties. Since then Frobenius splitting -- and its related cousins (F-regularity, strong F-regularity, F-purity, etc.) have played large roles in geometry and algebra in characteristic p. This is a good place to get a sense for what kicked all this stuff off! <br />
<br />
* ''Schubert Calculus'' - S. L. Kleiman and Dan Laksov.<br />
** An introduction to Schubert calculus suitable for those of all ages. I am told the paper essentially only uses linear algebra!<br />
<br />
* ''Rational Isogenies of Prime Degree'' - Barry Mazur.<br />
** In this paper Mazur classifies all isogenies of rational elliptic curves of prime order. As a result of this he deduces his famous result that the torsion subgroup of an elliptic curve (over Q) is one of 15 abelian groups. This definitely stares into the land of number theory, but certainly would still be of interest to many.<br />
<br />
* ''Esquisse d’une programme'' - Alexander Grothendieck.<br />
** Originating from a grant proposal in the mid 1980's this famous paper outlines a tantalizing research program, which seeks to tie numerous different areas of math (algebraic geometry, Teichmuller theory, Galois theory, etc.) together. This is where Grothendieck introduced his famous Lego game and dessin d'enfant. While just a research proposal this paper has seemingly inspired a ton of cool math, and will allow you to "blow peoples’ minds". (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Géométrie algébraique et géométrie analytique'' - J.P. Serre.<br />
** A projective variety X over the complex numbers has two lives, an algebraic and an analytic, depending on which topology one wishes to work with. That is one can think about X as a complex manifold and work with holomorphic functions or as an algebraic variety and work with regular functions. Hence to any complex projective variety we have two sheaf theories and as a result two cohomology theories. In this famous paper Serre compares these two and shows they are in fact the same. (''Note: This is a super fundamental result that is used all the time; normally in the following way: Uhh... What do you mean by cohomology? Well by GAGA or something it doesn't really mater.) (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Limit linear series: Basic theory''- David Eisenbud and Joe Harris.<br />
** One of the more profitable tools -- especially when studying moduli spaces -- in a geometers tool box is the theory of degenerations. However, sometimes we care about more than just the variety we are degenerating and want to keep track of things like vector/line bundles. In this paper Eisenbud and Harris develop the theory of degenerating a curve together with a linear series. From this they prove a ton of cool results: M_g is of general type for g>24, Brill-Noether theory, etc.<br />
<br />
* ''Picard Groups of Moduli Problems'' - David Mumford.<br />
** This paper is essentially the origin of algebraic stacks.<br />
<br />
* ''The Structure of Algebraic Threefolds: An Introduction to Mori's Program'' - Janos Kollar<br />
** This paper is an introduction to Mori's famous ``minimal model'' program, which is a far reaching program seeking to understand the birational geometry of higher dimensional varieties. <br />
<br />
* ''Cayley-Bacharach Formulas'' - Qingchun Ren, Jürgen Richter-Gebert, Bernd Sturmfels.<br />
** A classical result we all learn in a first semester of algebraic geometry is that 5 points in the plane (in general position) determine a unique plane conic. One can similarly show that 9 (general) points in the plane determine a unique plane cubic curve. This paper tries to answer the question: ``What is equation for this cubic curve?''.<br />
<br />
* ''On Varieties of Minimal Degree (A Centennial Approach)'' - David Eisenbud and Joe Harris.<br />
** Suppose X is a projective variety embedded in projective space so that X is not contained in any hyperplane. By projecting from general points one can see that the degree of X is at least codim(X)+1. This paper discusses the classification of varieties that achieve this lower degree bound i.e. varieties of minimal degree. This topic is quite classical and the paper seems to contain a nice mixture of classical and modern geometry.<br />
<br />
* ''The Gromov-Witten potential associated to a TCFT'' - Kevin J. Costello.<br />
** This seems incredibly interesting, but fairing warning this paper has been described as ''highly technical'', which considering it uses A-infinity algebras and the derived category of a Calabi-Yau seems like a reasonable description. (This paper may be covered in Caldararu's Spring 2017 topics course.)<br />
__NOTOC__<br />
<br />
== Spring 2019 ==<br />
<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#A6B658" width="300" align="center"|'''Speaker'''<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title (click to see abstract)'''<br />
|-<br />
| bgcolor="#E0E0E0"| February 6<br />
| bgcolor="#C6D46E"| Vlad Sotirov<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 6| Heisenberg Groups and the Fourier Transform]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 13<br />
| bgcolor="#C6D46E"| David Wagner<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 13| DG potpourri]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 20<br />
| bgcolor="#C6D46E"| Caitlyn Booms<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 20| Completions of Noncatenary Local Domains and UFDs]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 27<br />
| bgcolor="#C6D46E"| Sun Woo Park<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 27| Baker’s Theorem]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 6<br />
| bgcolor="#C6D46E"| Connor Simpson<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 6| Mason's Conjectures and Chow Rings of Matroids]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 13<br />
| bgcolor="#C6D46E"| Brandon Boggess<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 13| Dial M_1,1 for moduli]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 27<br />
| bgcolor="#C6D46E"| Solly Parenti<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 27| Title]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 3<br />
| bgcolor="#C6D46E"| Colin Crowley<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 3| Title]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 10<br />
| bgcolor="#C6D46E"| Alex Hof<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 10| Kindergarten GAGA]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 17<br />
| bgcolor="#C6D46E"| Soumya Sankar<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 17| Title]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 24<br />
| bgcolor="#C6D46E"| Wendy Cheng<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 24| Title]]<br />
|-<br />
| bgcolor="#E0E0E0"| May 1<br />
| bgcolor="#C6D46E"| Shengyuan Huang<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#May 1| Orbifold Singular Cohomology]]<br />
|}<br />
</center><br />
<br />
== February 6 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Vladimir Sotirov'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Heisenberg Groups and the Fourier Transform<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: I will discuss the relationship between Fourier transforms and the Heisenberg groups, with a view toward the discussion of line bundles on complex tori that appears in Polishchuk's book Abelian Varieties, Theta functions, and the Fourier transform.<br />
<br />
|} <br />
</center><br />
<br />
== February 13 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''David Wagner'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: DG potpourri<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: I will explain how differential graded categories made their way into AG as a way to solve some of the inadequacies of the ordinary derived category. We will then give examples of the utility of DG techniques. <br />
[[File:Dg-meme.png]]<br />
|} <br />
</center><br />
<br />
== February 20 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Caitlyn Booms'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Completions of Noncatenary Local Domains and UFDs<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: A ring is called catenary if for any pair of prime ideals P contained in Q, all saturated chains of prime ideals between P and Q have the same length.<br />
In this talk, I will introduce the necessary background about noncatenary rings and completions of local (Noetherian) domains, as well as the relevant history. Then, I will give the characterization of completions of noncatenary local domains and noncatenary local UFDs, which I will use to describe examples of very strange rings.<br />
|} <br />
</center><br />
<br />
== February 27 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Sun Woo Park'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Baker's Theorem<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: As a follow up talk to last semester, I will state and prove Baker’s theorem, a classical theorem which uses Newton Polygons to count the genus of a given curve. I will also briefly sketch how one can use Newton polygons to understand resolution of singularities of a given curve over valuation rings.<br />
|} <br />
</center><br />
<br />
== March 6 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Connor Simpson'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Mason's Conjectures and Chow Rings of Matroids<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: A matroid is a combinatorial structure that abstracts many different notions of independence, including linear independence in a vector space. Mason's Conjectures are a series of three increasingly strong inequalities on certain numerical invariants of matroids, the weakest of which resisted proof for over 40 years until its resolution in 2015. However, in the years since, all of Mason's conjectures have become theorems!<br />
<br />
In this talk, we will introduce matroids and the Chow ring of a matroid, the amazing algebraic gadget used to prove Mason's first conjecture. Finally, outline the proof of Mason's second conjecture (work of our very own Botong Wang & coauthors).<br />
|} <br />
</center><br />
<br />
== March 13 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Brandon Boggess'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Dial M_1,1 for moduli<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: We will speculate wildly about what kind of object the moduli space of elliptic curves should be. I don't know what a stack is, and I promise not to try to define one.<br />
|} <br />
</center><br />
<br />
== March 27 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Solly Parenti'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: <br />
|-<br />
| bgcolor="#BCD2EE" | Abstract:<br />
|} <br />
</center><br />
<br />
== April 3 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Colin Crowley'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: <br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== April 10 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Alex Hof'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: <br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== April 17 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Soumya Sankar'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: <br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== April 24 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Name'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: <br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== May 1 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Shengyuan Huang'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Orbifold Singular Cohomology<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== Organizers' Contact Info ==<br />
<br />
[https://sites.google.com/wisc.edu/cbooms/ Caitlyn Booms]<br />
<br />
[http://www.math.wisc.edu/~drwagner/ David Wagner]<br />
<br />
[https://www.math.wisc.edu/~moises/ Moisés Herradón Cueto]<br />
<br />
== Past Semesters ==<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2018 Fall 2018]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2018 Spring 2018]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2017 Fall 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2017 Spring 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2016 Fall 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2016 Spring 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_(Fall_2015) Fall 2015]</div>Cchenghttps://wiki.math.wisc.edu/index.php?title=Reading_Seminar_2018-19&diff=15992Reading Seminar 2018-192018-09-14T21:12:36Z<p>Ccheng: </p>
<hr />
<div>==Overview==<br />
My (Daniel's) experience has been that reading seminars have diminishing returns: they run out of steam after about 8 lectures on a certain book, as everyone starts falling behind, etc. I was thinking aim broader (rather than deeper), covering 3 books, but with fewer lectures. My idea is to partly cover: Beauville's "Complex Algebraic Surfaces"; Atiyah's "K-theory" (1989 edition); and Harris and Morrison's "Moduli of Curves". We would do about 6-8 lectures on each. This allows us to reboot every two months, which I hope will be mentally refreshing and will allow people who have lost the thread of the book to rejoin. Anyways, it's an experiment!<br />
<br />
Some notes:<br />
<ul><br />
<li>Here is lecture notes from Ravi Vakil on Complex Algebraic Surfaces "http://math.stanford.edu/~vakil/02-245/index.html"<br />
<li> Each book will have a co-organizer: Wanlin Li for Beauville's book; Michael Brown for Atiyah's book; and Rachel Davis for Harris and Mumford's book. Thanks!</li><br />
<li>I left some "Makeup" dates in the schedule with the idea that we would most likely take a week off on those dates. But if we need to miss another date (because of a conflict with a special colloquium or some other event), then we can use those as makeup slots.</li><br />
</ul><br />
<br />
We are experimenting with lots of new formats in this year's seminar. If you aren't happy with how the reading seminar is going, please let one of the organizers (Daniel, Wanlin, Michael, or Rachel) know and we will do our best to get things back on a helpful track.<br />
<br />
==Time and Location==<br />
Talks will be on Fridays from 11:45-12:35 in B325. This semester, Daniel is planning to keep a VERY HARD watch on the clock.<br />
<br />
== Talk Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | sections<br />
<br />
|-<br />
|September 7<br />
|Wanlin Li<br />
|Beauville I<br />
|-<br />
|September 14<br />
|Rachel Davis<br />
|Beauville II<br />
|-<br />
|September 21<br />
|Brandon Boggess<br />
|Beauville II and III<br />
|-<br />
|September 28<br />
|??<br />
|Beauville III<br />
|-<br />
|October 5<br />
|Wendy Cheng<br />
|Beauville IV<br />
|-<br />
|October 12<br />
|Soumya Sankar<br />
|Beauville V<br />
|-<br />
|October 19<br />
|??<br />
|Beauville V and VI<br />
|-<br />
|October 26<br />
|Dan Corey<br />
|Beauville VII and VIII<br />
|-<br />
|November 2<br />
|??<br />
|Makeup Beauville<br />
|-<br />
|November 9<br />
|Michael Brown<br />
|Atiyah 1 (Overview of goals of the seminar, Section 2.1) <br />
|-<br />
|November 16<br />
|Asvin Gothandaraman<br />
|Atiyah 2 (Section 2.2)<br />
|-<br />
|November 23<br />
|NO MEETING<br />
|Thanksgiving<br />
|-<br />
|November 30<br />
|Daniel Erman<br />
|Atiyah 3 (Section 2.5)<br />
|-<br />
|SEMESETER BREAK<br />
|No meetings<br />
|<br />
|-<br />
|January 29<br />
|??<br />
|Atiyah 4 (Section 2.3, Part 1)<br />
|-<br />
|February 1<br />
|??<br />
|Atiyah 5 (Section 2.3, Part 2)<br />
|-<br />
|February 8<br />
|??<br />
|Atiyah 6 (Section 2.6)<br />
|-<br />
|February 15<br />
|??<br />
|Atiyah 7 (Section 2.7, up to the Thom Isomorphism Theorem)<br />
|-<br />
|February 22<br />
|??<br />
|Makeup<br />
|-<br />
|March 1<br />
| Juliette Bruce<br />
|Moduli 1<br />
|-<br />
|March 8<br />
|Niudun Wang<br />
|Moduli 2<br />
|-<br />
|March 15<br />
|??<br />
|Moduli 3<br />
|-<br />
|March 22<br />
|??<br />
|Moduli 4<br />
|-<br />
|March 29<br />
|??<br />
|Moduli 5<br />
|-<br />
|April 5<br />
|??<br />
|Moduli 6<br />
|-<br />
|April 12<br />
|??<br />
|Moduli 7<br />
|-<br />
|April 19<br />
|??<br />
|Makeup<br />
|}<br />
<br />
==How to plan your talk==<br />
One key to giving good talks in a reading seminar is to know how to refocus the material that you read. Instead of going through the chapter lemma by lemma, you should ask: What is the main idea in this section? It could be a theorem, a definition, or even an example. But after reading the section, decide what the most important idea is and be sure to highlight early on.<br />
<br />
You will probably need to skip the proofs--and even the statements--of many of the lemmas and other results in the chapter. This is a good thing! The reason someone attends a talk, as opposed to just reading the material on their own, is because they want to see the material from the perspective of someone who has thought it about carefully.<br />
<br />
Also, make sure to give clear examples.<br />
<br />
<br />
==Feedback on talks==<br />
One of the goals for this semester is to help the speakers learn to give better talks. Here is our plan:<br />
<br />
<li> Feedback session: This is like a streamlined version of what creative writing workshops do. Every week, we reserve 15 minutes (12:35-12:50) for the entire audience to critique that week’s speaker. Comments will be friendly and constructive. A key rule is that the speaker is not allowed to speak until the last 5 minutes.</li><br />
<br />
<li> Partner: We assign a “partner” each week (usually the previous week's speaker). The partner will meet for 20-30 minutes with the speaker in advance to:<br />
<ol> Discuss a plan for the talk. Here the speaker can outline what they see as the main ideas, and the partner can share any wisdom gleaned from their experience the previous week. </ol><br />
<ol> Ask the speaker if there are any particular things that the speaker would like feedback on (e.g. pacing, boardwork, clarity of voice, etc.). </ol><br />
The partner would also take notes during the feedback session, to give the speaker a record of the conversation.<br />
</li><br />
<br />
This is very much an experiment, and while it might be intimidating at first, I actually think it could really help everyone (the speakers and the audience members too).</div>Cchenghttps://wiki.math.wisc.edu/index.php?title=Graduate_Algebraic_Geometry_Seminar_Fall_2017&diff=13641Graduate Algebraic Geometry Seminar Fall 20172017-04-10T04:52:16Z<p>Ccheng: /* April 12 */</p>
<hr />
<div>'''<br />
'''When:''' Wednesdays 4:40pm<br />
<br />
'''Where:'''Van Vleck B321 (Spring 2017)<br />
[[Image:cat.jpg|thumb|220px| | Lizzie the OFFICIAL mascot of GAGS!!]]<br />
<br />
'''Who:''' YOU!!<br />
<br />
'''Why:''' The purpose of this seminar is to learn algebraic geometry by giving and listening to talks in a informal setting. Talks are typically accessible to beginning graduate students and take many different forms. Sometimes people present an interesting paper they find. Other times people give a prep talk for the Friday Algebraic Geometry Seminar. Other times people give a series of talks on a topic they have been studying in-depth.<br />
<br />
'''How:'''If you want to get emails regarding time, place, and talk topics ('''which are often assigned quite last minute''') add yourself to the gags mailing list: gags@lists.wisc.edu. The list registration page is [https://admin.lists.wisc.edu/index.php?p=11&l=gags here].<br />
'''<br />
<br />
<br />
<br />
<br />
<br />
== Give a talk! ==<br />
We need volunteers to give talks this semester. If you're interested contact [mailto:djbruce@math.wisc.edu DJ], or just add yourself to the list (though in that case we might move your talk later without your permission). Beginning graduate students are particularly encouraged to give a talk, since it's a great way to get your feet wet with the material.<br />
<br />
<br />
== Wish List ==<br />
Here are the topics we're '''DYING''' to learn about! Please consider looking into one of these topics and giving one or two GAGS talks.<br />
<br />
===Specifically Vague Topics===<br />
* D-modules 101: basics of D-modules, equivalence between left and right D-modules, pullbacks, pushforwards, maybe the Gauss-Manin Connection. Claude Sabbah's introduction to the subject could be a good place to start.<br />
<br />
* Sheaf operations on D-modules (the point is that then you can get a Fourier-Mukai transform between certain O-modules and certain D-modules, which is more or less how geometric Langlands is supposed to work)<br />
<br />
===Famous Theorems===<br />
<br />
===Interesting Papers & Books===<br />
* ''Symplectic structure of the moduli space of sheaves on an abelian or K3 surface'' - Shigeru Mukai.<br />
<br />
* ''Residues and Duality'' - Robin Hatshorne.<br />
** Have you heard of Serre Duality? Would you like to really understand the nuts and bolts of it and its generalizations? If so this book is for you. (You wouldn't need to read the whole book to give a talk ;).)<br />
<br />
* ''Coherent sheaves on P^n and problems in linear algebra'' - A. A. Beilinson.<br />
** In this two page paper constructs the semi-orthogonal decomposition of the derived category of coherent sheaves on projective space. (This topic is very important, and there are a ton of other resources for this result and the general theory of derived categories.)<br />
<br />
* ''Frobenius splitting and cohomology vanishing for Schubert varieties'' - V.B. Mehta and A. Ramanathan.<br />
** In characteristic p the fact that (x+y)^p=x^p+y^p means that one has the Frobenius morphism, which sends f to f^p. In this paper the authors introduce the notion of what it means for a variety to be Frobenius split, and use this to prove certain cohomologcal vanishing results for Schubert varieties. Since then Frobenius splitting -- and its related cousins (F-regularity, strong F-regularity, F-purity, etc.) have played large roles in geometry and algebra in characteristic p. This is a good place to get a sense for what kicked all this stuff off! <br />
<br />
* ''Schubert Calculus'' - S. L. Kleiman and Dan Laksov.<br />
** An introduction to Schubert calculus suitable for those of all ages. I am told the paper essentially only uses linear algebra!<br />
<br />
* ''Rational Isogenies of Prime Degree'' - Barry Mazur.<br />
** In this paper Mazur classifies all isogenies of rational elliptic curves of prime order. As a result of this he deduces his famous result that the torsion subgroup of an elliptic curve (over Q) is one of 15 abelian groups. This definitely stares into the land of number theory, but certainly would still be of interest to many.<br />
<br />
* ''Esquisse d’une programme'' - Alexander Grothendieck.<br />
** Originating from a grant proposal in the mid 1980's this famous paper outlines a tantalizing research program, which seeks to tie numerous different areas of math (algebraic geometry, Teichmuller theory, Galois theory, etc.) together. This is where Grothendieck introduced his famous Lego game and dessin d'enfant. While just a research proposal this paper has seemingly inspired a ton of cool math, and will allow you to "blow peoples’ minds". (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Géométrie algébraique et géométrie analytique'' - J.P. Serre.<br />
** A projective variety X over the complex numbers has two lives, an algebraic and an analytic, depending on which topology one wishes to work with. That is one can think about X as a complex manifold and work with holomorphic functions or as an algebraic variety and work with regular functions. Hence to any complex projective variety we have two sheaf theories and as a result two cohomology theories. In this famous paper Serre compares these two and shows they are in fact the same. (''Note: This is a super fundamental result that is used all the time; normally in the following way: Uhh... What do you mean by cohomology? Well by GAGA or something it doesn't really mater.) (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Limit linear series: Basic theory''- David Eisenbud and Joe Harris.<br />
** One of the more profitable tools -- especially when studying moduli spaces -- in a geometers tool box is the theory of degenerations. However, sometimes we care about more than just the variety we are degenerating and want to keep track of things like vector/line bundles. In this paper Eisenbud and Harris develop the theory of degenerating a curve together with a linear series. From this they prove a ton of cool results: M_g is of general type for g>24, Brill-Noether theory, etc.<br />
<br />
* ''Picard Groups of Moduli Problems'' - David Mumford.<br />
** This paper is essentially the origin of algebraic stacks.<br />
<br />
* ''The Structure of Algebraic Threefolds: An Introduction to Mori's Program'' - Janos Kollar<br />
** This paper is an introduction to Mori's famous ``minimal model'' program, which is a far reaching program seeking to understand the birational geometry of higher dimensional varieties. <br />
<br />
* ''Cayley-Bacharach Formulas'' - Qingchun Ren, Jürgen Richter-Gebert, Bernd Sturmfels.<br />
** A classical result we all learn in a first semester of algebraic geometry is that 5 points in the plane (in general position) determine a unique plane conic. One can similarly show that 9 (general) points in the plane determine a unique plane cubic curve. This paper tries to answer the question: ``What is equation for this cubic curve?''.<br />
<br />
* ''On Varieties of Minimal Degree (A Centennial Approach)'' - David Eisenbud and Joe Harris.<br />
** Suppose X is a projective variety embedded in projective space so that X is not contained in any hyperplane. By projecting from general points one can see that the degree of X is at least codim(X)+1. This paper discusses the classification of varieties that achieve this lower degree bound i.e. varieties of minimal degree. This topic is quite classical and the paper seems to contain a nice mixture of classical and modern geometry.<br />
<br />
* ''The Gromov-Witten potential associated to a TCFT'' - Kevin J. Costello.<br />
** This seems incredibly interesting, but fairing warning this paper has been described as ''highly technical'', which considering it uses A-infinity algebras and the derived category of a Calabi-Yau seems like a reasonable description. (This paper may be covered in Caldararu's Spring 2017 topics course.)<br />
__NOTOC__<br />
<br />
== Spring 2017 ==<br />
<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#A6B658" width="300" align="center"|'''Speaker'''<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title (click to see abstract)'''<br />
|-<br />
| bgcolor="#E0E0E0"| January 25<br />
| bgcolor="#C6D46E"| Nathan Clement<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#January 25 | Hodge to de Rham, part one]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 1<br />
| bgcolor="#C6D46E"| Nathan Clement<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 1 | Hodge to de Rham, part two]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 8 <br />
| bgcolor="#C6D46E"| Dima Arinkin<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 8 | Motivated introduction to geometric Langlands]] <br />
|-<br />
| bgcolor="#E0E0E0"| February 15<br />
| bgcolor="#C6D46E"| No Talk<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 15 | We Failed, We All Failed]] <br />
|-<br />
| bgcolor="#E0E0E0"| February 22<br />
| bgcolor="#C6D46E"| No Talk<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 22 | We Failed, We All Failed Pt. 2]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 1<br />
| bgcolor="#C6D46E"| Brandon Boggess<br />
| bgcolor="#BCE2FE"| [[Graduate Algebraic Geometry Seminar#March 1 | An Introduction to Mori's Program]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 8<br />
| bgcolor="#C6D46E"| David Wagner<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 8| Picard groups of moduli problems]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 15<br />
| bgcolor="#C6D46E"| No Talk<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 15| We Failed, We All Failed Pt. 3]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 22<br />
| bgcolor="#C6D46E"| Spring Break<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 22 | No Seminar. ]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 29<br />
| bgcolor="#C6D46E"| David Wagner<br />
| bgcolor="#BCE2FE"| [[Graduate Algebraic Geometry Seminar#March 29| Picard groups of moduli problems II]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 5<br />
| bgcolor="#C6D46E"| John Wiltshire-Gordon<br />
| bgcolor="#BCE2FE"| [[Graduate Algebraic Geometry Seminar#April 5| Adjoint functors rule your life]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 12<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 12| TBD]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 19<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 19| TBD ]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 26<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 26| TBD ]] <br />
|}<br />
</center><br />
<br />
== January 25 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Nathan Clement'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Hodge to de Rham, part one<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: I will use the magic of differential calculus in positive characteristic to prove an important result in the cohomology of smooth varieties in positive characteristic. The techniques I'll use are mainly elementary, but prior experience with differential forms, the Frobenius homomorphism, and a little homological algebra will help. This is the setup, come back next week for the punchline!<br />
|} <br />
</center><br />
<br />
== February 1 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Nathan Clement'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Hodge to de Rham, part two<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: Having proved an important result in positive characteristic, I'll give a nifty argument to leverage the positive characteristic statement into a characteristic zero result. I'll talk about some cohomology comparison theorems, and we'll see that all this business in positive characteristic provides an alternate proof to the classic Hodge decomposition theorem for cohomology.<br />
|} <br />
</center><br />
<br />
== February 8 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Dima Arinkin'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Motivated introduction to geometric Langlands<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: The Langlands program originated from bold conjectures formulated by Robert Langlands in the late 1960's. The conjectures <br />
combine number theory and representation theory in a highly unexpected way. The geometric Langlands program adds algebro-<br />
geometric methods (and, sometimes, physics) to the mix.<br />
<br />
This interplay of ideas creates a beautiful picture... and a very challenging subject. In my talk, I will suggest one possible <br />
way to approach the area. I plan to focus on questions rather than answers: the goal is to explain how (some of) the questions fit together,<br />
and to tell you the keywords that go into the answers. <br />
|} <br />
</center><br />
<br />
== February 15 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''No Talk'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: We Failed, We All Failed Pt. 1<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: n/a<br />
|} <br />
</center><br />
<br />
== February 22 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''No Talk'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: We Failed, We All Failed Pt. 2<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: n/a<br />
|} <br />
</center><br />
<br />
== March 1 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Brandon Boggess'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: An Introduction to Mori's Program<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: In studying the birational classification of varieties, one plan of attack is to construct a "simplest" variety in each birational equivalence class. We will see how this approach gives a full structure theory for surfaces, and investigate what new challenges arise in the case of threefolds.<br />
<br />
|} <br />
</center><br />
<br />
== March 8 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''David Wagner'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Picard groups of moduli problems<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: In a pastoral traipse, I will discuss some lower bounds on the time it takes an average adult to drink a medium Frosty from Wendy's, including some results of my own about making these bounds sharp. Time permitting, I will also explain how this theory can be extended to study the ingestion of M&M's, a connection previously unkown.<br />
|} <br />
</center><br />
<br />
== March 15 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''No Talk'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: We Failed, We All Failed Pt. 3<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: n/a<br />
|} <br />
</center><br />
<br />
== March 22 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Spring Break'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: No Seminar.<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: n/a<br />
|} <br />
</center><br />
<br />
== March 29 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''David Wagner'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Picard groups of moduli problems II<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: Having discussed Grothendieck topologies and an existence theorem for absolute products of families, we construct <math>\mathfrak{M}_{1,1}</math><br />
and give a convenient characterization of the line bundles on the moduli problem, finally proving that <math>\mathrm{Pic}(\mathfrak{M}_{1,1})=\mathbb Z/12</math><br />
. Our numinous and mystical journey towards this sublime result will make ample use of Grothendieck's generalized Hilbert 90. Facts you knew about sheaf cohomology of schemes will suddenly materialize in the context of sites.<br />
|} <br />
</center><br />
<br />
== April 5 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''John Wiltshire-Gordon'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Adjoint functors rule your life<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: This talk is about adjoint functors. We will do examples!<br />
<br />
|} <br />
</center><br />
<br />
== April 12 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
== April 19 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBA'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center> <br />
<br />
== April 26 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBA'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center> <br />
<br />
== Organizers' Contact Info ==<br />
[http://www.math.wisc.edu/~djbruce DJ Bruce]<br />
<br />
[http://www.math.wisc.edu/~clement Nathan Clement]<br />
<br />
[https://www.math.wisc.edu/~moises Moisés Herradón Cueto]<br />
<br />
== Past Semesters ==<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2016 Fall 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2016 Spring 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_(Fall_2015) Fall 2015]</div>Cchenghttps://wiki.math.wisc.edu/index.php?title=Graduate_Algebraic_Geometry_Seminar_Fall_2017&diff=13640Graduate Algebraic Geometry Seminar Fall 20172017-04-10T04:51:45Z<p>Ccheng: /* Spring 2017 */</p>
<hr />
<div>'''<br />
'''When:''' Wednesdays 4:40pm<br />
<br />
'''Where:'''Van Vleck B321 (Spring 2017)<br />
[[Image:cat.jpg|thumb|220px| | Lizzie the OFFICIAL mascot of GAGS!!]]<br />
<br />
'''Who:''' YOU!!<br />
<br />
'''Why:''' The purpose of this seminar is to learn algebraic geometry by giving and listening to talks in a informal setting. Talks are typically accessible to beginning graduate students and take many different forms. Sometimes people present an interesting paper they find. Other times people give a prep talk for the Friday Algebraic Geometry Seminar. Other times people give a series of talks on a topic they have been studying in-depth.<br />
<br />
'''How:'''If you want to get emails regarding time, place, and talk topics ('''which are often assigned quite last minute''') add yourself to the gags mailing list: gags@lists.wisc.edu. The list registration page is [https://admin.lists.wisc.edu/index.php?p=11&l=gags here].<br />
'''<br />
<br />
<br />
<br />
<br />
<br />
== Give a talk! ==<br />
We need volunteers to give talks this semester. If you're interested contact [mailto:djbruce@math.wisc.edu DJ], or just add yourself to the list (though in that case we might move your talk later without your permission). Beginning graduate students are particularly encouraged to give a talk, since it's a great way to get your feet wet with the material.<br />
<br />
<br />
== Wish List ==<br />
Here are the topics we're '''DYING''' to learn about! Please consider looking into one of these topics and giving one or two GAGS talks.<br />
<br />
===Specifically Vague Topics===<br />
* D-modules 101: basics of D-modules, equivalence between left and right D-modules, pullbacks, pushforwards, maybe the Gauss-Manin Connection. Claude Sabbah's introduction to the subject could be a good place to start.<br />
<br />
* Sheaf operations on D-modules (the point is that then you can get a Fourier-Mukai transform between certain O-modules and certain D-modules, which is more or less how geometric Langlands is supposed to work)<br />
<br />
===Famous Theorems===<br />
<br />
===Interesting Papers & Books===<br />
* ''Symplectic structure of the moduli space of sheaves on an abelian or K3 surface'' - Shigeru Mukai.<br />
<br />
* ''Residues and Duality'' - Robin Hatshorne.<br />
** Have you heard of Serre Duality? Would you like to really understand the nuts and bolts of it and its generalizations? If so this book is for you. (You wouldn't need to read the whole book to give a talk ;).)<br />
<br />
* ''Coherent sheaves on P^n and problems in linear algebra'' - A. A. Beilinson.<br />
** In this two page paper constructs the semi-orthogonal decomposition of the derived category of coherent sheaves on projective space. (This topic is very important, and there are a ton of other resources for this result and the general theory of derived categories.)<br />
<br />
* ''Frobenius splitting and cohomology vanishing for Schubert varieties'' - V.B. Mehta and A. Ramanathan.<br />
** In characteristic p the fact that (x+y)^p=x^p+y^p means that one has the Frobenius morphism, which sends f to f^p. In this paper the authors introduce the notion of what it means for a variety to be Frobenius split, and use this to prove certain cohomologcal vanishing results for Schubert varieties. Since then Frobenius splitting -- and its related cousins (F-regularity, strong F-regularity, F-purity, etc.) have played large roles in geometry and algebra in characteristic p. This is a good place to get a sense for what kicked all this stuff off! <br />
<br />
* ''Schubert Calculus'' - S. L. Kleiman and Dan Laksov.<br />
** An introduction to Schubert calculus suitable for those of all ages. I am told the paper essentially only uses linear algebra!<br />
<br />
* ''Rational Isogenies of Prime Degree'' - Barry Mazur.<br />
** In this paper Mazur classifies all isogenies of rational elliptic curves of prime order. As a result of this he deduces his famous result that the torsion subgroup of an elliptic curve (over Q) is one of 15 abelian groups. This definitely stares into the land of number theory, but certainly would still be of interest to many.<br />
<br />
* ''Esquisse d’une programme'' - Alexander Grothendieck.<br />
** Originating from a grant proposal in the mid 1980's this famous paper outlines a tantalizing research program, which seeks to tie numerous different areas of math (algebraic geometry, Teichmuller theory, Galois theory, etc.) together. This is where Grothendieck introduced his famous Lego game and dessin d'enfant. While just a research proposal this paper has seemingly inspired a ton of cool math, and will allow you to "blow peoples’ minds". (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Géométrie algébraique et géométrie analytique'' - J.P. Serre.<br />
** A projective variety X over the complex numbers has two lives, an algebraic and an analytic, depending on which topology one wishes to work with. That is one can think about X as a complex manifold and work with holomorphic functions or as an algebraic variety and work with regular functions. Hence to any complex projective variety we have two sheaf theories and as a result two cohomology theories. In this famous paper Serre compares these two and shows they are in fact the same. (''Note: This is a super fundamental result that is used all the time; normally in the following way: Uhh... What do you mean by cohomology? Well by GAGA or something it doesn't really mater.) (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Limit linear series: Basic theory''- David Eisenbud and Joe Harris.<br />
** One of the more profitable tools -- especially when studying moduli spaces -- in a geometers tool box is the theory of degenerations. However, sometimes we care about more than just the variety we are degenerating and want to keep track of things like vector/line bundles. In this paper Eisenbud and Harris develop the theory of degenerating a curve together with a linear series. From this they prove a ton of cool results: M_g is of general type for g>24, Brill-Noether theory, etc.<br />
<br />
* ''Picard Groups of Moduli Problems'' - David Mumford.<br />
** This paper is essentially the origin of algebraic stacks.<br />
<br />
* ''The Structure of Algebraic Threefolds: An Introduction to Mori's Program'' - Janos Kollar<br />
** This paper is an introduction to Mori's famous ``minimal model'' program, which is a far reaching program seeking to understand the birational geometry of higher dimensional varieties. <br />
<br />
* ''Cayley-Bacharach Formulas'' - Qingchun Ren, Jürgen Richter-Gebert, Bernd Sturmfels.<br />
** A classical result we all learn in a first semester of algebraic geometry is that 5 points in the plane (in general position) determine a unique plane conic. One can similarly show that 9 (general) points in the plane determine a unique plane cubic curve. This paper tries to answer the question: ``What is equation for this cubic curve?''.<br />
<br />
* ''On Varieties of Minimal Degree (A Centennial Approach)'' - David Eisenbud and Joe Harris.<br />
** Suppose X is a projective variety embedded in projective space so that X is not contained in any hyperplane. By projecting from general points one can see that the degree of X is at least codim(X)+1. This paper discusses the classification of varieties that achieve this lower degree bound i.e. varieties of minimal degree. This topic is quite classical and the paper seems to contain a nice mixture of classical and modern geometry.<br />
<br />
* ''The Gromov-Witten potential associated to a TCFT'' - Kevin J. Costello.<br />
** This seems incredibly interesting, but fairing warning this paper has been described as ''highly technical'', which considering it uses A-infinity algebras and the derived category of a Calabi-Yau seems like a reasonable description. (This paper may be covered in Caldararu's Spring 2017 topics course.)<br />
__NOTOC__<br />
<br />
== Spring 2017 ==<br />
<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#A6B658" width="300" align="center"|'''Speaker'''<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title (click to see abstract)'''<br />
|-<br />
| bgcolor="#E0E0E0"| January 25<br />
| bgcolor="#C6D46E"| Nathan Clement<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#January 25 | Hodge to de Rham, part one]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 1<br />
| bgcolor="#C6D46E"| Nathan Clement<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 1 | Hodge to de Rham, part two]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 8 <br />
| bgcolor="#C6D46E"| Dima Arinkin<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 8 | Motivated introduction to geometric Langlands]] <br />
|-<br />
| bgcolor="#E0E0E0"| February 15<br />
| bgcolor="#C6D46E"| No Talk<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 15 | We Failed, We All Failed]] <br />
|-<br />
| bgcolor="#E0E0E0"| February 22<br />
| bgcolor="#C6D46E"| No Talk<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 22 | We Failed, We All Failed Pt. 2]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 1<br />
| bgcolor="#C6D46E"| Brandon Boggess<br />
| bgcolor="#BCE2FE"| [[Graduate Algebraic Geometry Seminar#March 1 | An Introduction to Mori's Program]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 8<br />
| bgcolor="#C6D46E"| David Wagner<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 8| Picard groups of moduli problems]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 15<br />
| bgcolor="#C6D46E"| No Talk<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 15| We Failed, We All Failed Pt. 3]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 22<br />
| bgcolor="#C6D46E"| Spring Break<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 22 | No Seminar. ]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 29<br />
| bgcolor="#C6D46E"| David Wagner<br />
| bgcolor="#BCE2FE"| [[Graduate Algebraic Geometry Seminar#March 29| Picard groups of moduli problems II]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 5<br />
| bgcolor="#C6D46E"| John Wiltshire-Gordon<br />
| bgcolor="#BCE2FE"| [[Graduate Algebraic Geometry Seminar#April 5| Adjoint functors rule your life]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 12<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 12| TBD]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 19<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 19| TBD ]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 26<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 26| TBD ]] <br />
|}<br />
</center><br />
<br />
== January 25 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Nathan Clement'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Hodge to de Rham, part one<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: I will use the magic of differential calculus in positive characteristic to prove an important result in the cohomology of smooth varieties in positive characteristic. The techniques I'll use are mainly elementary, but prior experience with differential forms, the Frobenius homomorphism, and a little homological algebra will help. This is the setup, come back next week for the punchline!<br />
|} <br />
</center><br />
<br />
== February 1 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Nathan Clement'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Hodge to de Rham, part two<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: Having proved an important result in positive characteristic, I'll give a nifty argument to leverage the positive characteristic statement into a characteristic zero result. I'll talk about some cohomology comparison theorems, and we'll see that all this business in positive characteristic provides an alternate proof to the classic Hodge decomposition theorem for cohomology.<br />
|} <br />
</center><br />
<br />
== February 8 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Dima Arinkin'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Motivated introduction to geometric Langlands<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: The Langlands program originated from bold conjectures formulated by Robert Langlands in the late 1960's. The conjectures <br />
combine number theory and representation theory in a highly unexpected way. The geometric Langlands program adds algebro-<br />
geometric methods (and, sometimes, physics) to the mix.<br />
<br />
This interplay of ideas creates a beautiful picture... and a very challenging subject. In my talk, I will suggest one possible <br />
way to approach the area. I plan to focus on questions rather than answers: the goal is to explain how (some of) the questions fit together,<br />
and to tell you the keywords that go into the answers. <br />
|} <br />
</center><br />
<br />
== February 15 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''No Talk'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: We Failed, We All Failed Pt. 1<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: n/a<br />
|} <br />
</center><br />
<br />
== February 22 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''No Talk'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: We Failed, We All Failed Pt. 2<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: n/a<br />
|} <br />
</center><br />
<br />
== March 1 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Brandon Boggess'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: An Introduction to Mori's Program<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: In studying the birational classification of varieties, one plan of attack is to construct a "simplest" variety in each birational equivalence class. We will see how this approach gives a full structure theory for surfaces, and investigate what new challenges arise in the case of threefolds.<br />
<br />
|} <br />
</center><br />
<br />
== March 8 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''David Wagner'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Picard groups of moduli problems<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: In a pastoral traipse, I will discuss some lower bounds on the time it takes an average adult to drink a medium Frosty from Wendy's, including some results of my own about making these bounds sharp. Time permitting, I will also explain how this theory can be extended to study the ingestion of M&M's, a connection previously unkown.<br />
|} <br />
</center><br />
<br />
== March 15 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''No Talk'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: We Failed, We All Failed Pt. 3<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: n/a<br />
|} <br />
</center><br />
<br />
== March 22 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Spring Break'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: No Seminar.<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: n/a<br />
|} <br />
</center><br />
<br />
== March 29 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''David Wagner'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Picard groups of moduli problems II<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: Having discussed Grothendieck topologies and an existence theorem for absolute products of families, we construct <math>\mathfrak{M}_{1,1}</math><br />
and give a convenient characterization of the line bundles on the moduli problem, finally proving that <math>\mathrm{Pic}(\mathfrak{M}_{1,1})=\mathbb Z/12</math><br />
. Our numinous and mystical journey towards this sublime result will make ample use of Grothendieck's generalized Hilbert 90. Facts you knew about sheaf cohomology of schemes will suddenly materialize in the context of sites.<br />
|} <br />
</center><br />
<br />
== April 5 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''John Wiltshire-Gordon'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Adjoint functors rule your life<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: This talk is about adjoint functors. We will do examples!<br />
<br />
|} <br />
</center><br />
<br />
== April 12 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Wendy Cheng'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Boij-Soderberg Theory<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
== April 19 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBA'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center> <br />
<br />
== April 26 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBA'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center> <br />
<br />
== Organizers' Contact Info ==<br />
[http://www.math.wisc.edu/~djbruce DJ Bruce]<br />
<br />
[http://www.math.wisc.edu/~clement Nathan Clement]<br />
<br />
[https://www.math.wisc.edu/~moises Moisés Herradón Cueto]<br />
<br />
== Past Semesters ==<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2016 Fall 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2016 Spring 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_(Fall_2015) Fall 2015]</div>Cchenghttps://wiki.math.wisc.edu/index.php?title=Graduate_Algebraic_Geometry_Seminar_Fall_2017&diff=13553Graduate Algebraic Geometry Seminar Fall 20172017-03-24T03:10:51Z<p>Ccheng: /* April 12 */</p>
<hr />
<div>'''<br />
'''When:''' Wednesdays 4:40pm<br />
<br />
'''Where:'''Van Vleck B321 (Spring 2017)<br />
[[Image:cat.jpg|thumb|220px| | Lizzie the OFFICIAL mascot of GAGS!!]]<br />
<br />
'''Who:''' YOU!!<br />
<br />
'''Why:''' The purpose of this seminar is to learn algebraic geometry by giving and listening to talks in a informal setting. Talks are typically accessible to beginning graduate students and take many different forms. Sometimes people present an interesting paper they find. Other times people give a prep talk for the Friday Algebraic Geometry Seminar. Other times people give a series of talks on a topic they have been studying in-depth.<br />
<br />
'''How:'''If you want to get emails regarding time, place, and talk topics ('''which are often assigned quite last minute''') add yourself to the gags mailing list: gags@lists.wisc.edu. The list registration page is [https://admin.lists.wisc.edu/index.php?p=11&l=gags here].<br />
'''<br />
<br />
<br />
<br />
<br />
<br />
== Give a talk! ==<br />
We need volunteers to give talks this semester. If you're interested contact [mailto:djbruce@math.wisc.edu DJ], or just add yourself to the list (though in that case we might move your talk later without your permission). Beginning graduate students are particularly encouraged to give a talk, since it's a great way to get your feet wet with the material.<br />
<br />
<br />
== Wish List ==<br />
Here are the topics we're '''DYING''' to learn about! Please consider looking into one of these topics and giving one or two GAGS talks.<br />
<br />
===Specifically Vague Topics===<br />
* D-modules 101: basics of D-modules, equivalence between left and right D-modules, pullbacks, pushforwards, maybe the Gauss-Manin Connection. Claude Sabbah's introduction to the subject could be a good place to start.<br />
<br />
* Sheaf operations on D-modules (the point is that then you can get a Fourier-Mukai transform between certain O-modules and certain D-modules, which is more or less how geometric Langlands is supposed to work)<br />
<br />
===Famous Theorems===<br />
<br />
===Interesting Papers & Books===<br />
* ''Symplectic structure of the moduli space of sheaves on an abelian or K3 surface'' - Shigeru Mukai.<br />
<br />
* ''Residues and Duality'' - Robin Hatshorne.<br />
** Have you heard of Serre Duality? Would you like to really understand the nuts and bolts of it and its generalizations? If so this book is for you. (You wouldn't need to read the whole book to give a talk ;).)<br />
<br />
* ''Coherent sheaves on P^n and problems in linear algebra'' - A. A. Beilinson.<br />
** In this two page paper constructs the semi-orthogonal decomposition of the derived category of coherent sheaves on projective space. (This topic is very important, and there are a ton of other resources for this result and the general theory of derived categories.)<br />
<br />
* ''Frobenius splitting and cohomology vanishing for Schubert varieties'' - V.B. Mehta and A. Ramanathan.<br />
** In characteristic p the fact that (x+y)^p=x^p+y^p means that one has the Frobenius morphism, which sends f to f^p. In this paper the authors introduce the notion of what it means for a variety to be Frobenius split, and use this to prove certain cohomologcal vanishing results for Schubert varieties. Since then Frobenius splitting -- and its related cousins (F-regularity, strong F-regularity, F-purity, etc.) have played large roles in geometry and algebra in characteristic p. This is a good place to get a sense for what kicked all this stuff off! <br />
<br />
* ''Schubert Calculus'' - S. L. Kleiman and Dan Laksov.<br />
** An introduction to Schubert calculus suitable for those of all ages. I am told the paper essentially only uses linear algebra!<br />
<br />
* ''Rational Isogenies of Prime Degree'' - Barry Mazur.<br />
** In this paper Mazur classifies all isogenies of rational elliptic curves of prime order. As a result of this he deduces his famous result that the torsion subgroup of an elliptic curve (over Q) is one of 15 abelian groups. This definitely stares into the land of number theory, but certainly would still be of interest to many.<br />
<br />
* ''Esquisse d’une programme'' - Alexander Grothendieck.<br />
** Originating from a grant proposal in the mid 1980's this famous paper outlines a tantalizing research program, which seeks to tie numerous different areas of math (algebraic geometry, Teichmuller theory, Galois theory, etc.) together. This is where Grothendieck introduced his famous Lego game and dessin d'enfant. While just a research proposal this paper has seemingly inspired a ton of cool math, and will allow you to "blow peoples’ minds". (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Géométrie algébraique et géométrie analytique'' - J.P. Serre.<br />
** A projective variety X over the complex numbers has two lives, an algebraic and an analytic, depending on which topology one wishes to work with. That is one can think about X as a complex manifold and work with holomorphic functions or as an algebraic variety and work with regular functions. Hence to any complex projective variety we have two sheaf theories and as a result two cohomology theories. In this famous paper Serre compares these two and shows they are in fact the same. (''Note: This is a super fundamental result that is used all the time; normally in the following way: Uhh... What do you mean by cohomology? Well by GAGA or something it doesn't really mater.) (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Limit linear series: Basic theory''- David Eisenbud and Joe Harris.<br />
** One of the more profitable tools -- especially when studying moduli spaces -- in a geometers tool box is the theory of degenerations. However, sometimes we care about more than just the variety we are degenerating and want to keep track of things like vector/line bundles. In this paper Eisenbud and Harris develop the theory of degenerating a curve together with a linear series. From this they prove a ton of cool results: M_g is of general type for g>24, Brill-Noether theory, etc.<br />
<br />
* ''Picard Groups of Moduli Problems'' - David Mumford.<br />
** This paper is essentially the origin of algebraic stacks.<br />
<br />
* ''The Structure of Algebraic Threefolds: An Introduction to Mori's Program'' - Janos Kollar<br />
** This paper is an introduction to Mori's famous ``minimal model'' program, which is a far reaching program seeking to understand the birational geometry of higher dimensional varieties. <br />
<br />
* ''Cayley-Bacharach Formulas'' - Qingchun Ren, Jürgen Richter-Gebert, Bernd Sturmfels.<br />
** A classical result we all learn in a first semester of algebraic geometry is that 5 points in the plane (in general position) determine a unique plane conic. One can similarly show that 9 (general) points in the plane determine a unique plane cubic curve. This paper tries to answer the question: ``What is equation for this cubic curve?''.<br />
<br />
* ''On Varieties of Minimal Degree (A Centennial Approach)'' - David Eisenbud and Joe Harris.<br />
** Suppose X is a projective variety embedded in projective space so that X is not contained in any hyperplane. By projecting from general points one can see that the degree of X is at least codim(X)+1. This paper discusses the classification of varieties that achieve this lower degree bound i.e. varieties of minimal degree. This topic is quite classical and the paper seems to contain a nice mixture of classical and modern geometry.<br />
<br />
* ''The Gromov-Witten potential associated to a TCFT'' - Kevin J. Costello.<br />
** This seems incredibly interesting, but fairing warning this paper has been described as ''highly technical'', which considering it uses A-infinity algebras and the derived category of a Calabi-Yau seems like a reasonable description. (This paper may be covered in Caldararu's Spring 2017 topics course.)<br />
__NOTOC__<br />
<br />
== Spring 2017 ==<br />
<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#A6B658" width="300" align="center"|'''Speaker'''<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title (click to see abstract)'''<br />
|-<br />
| bgcolor="#E0E0E0"| January 25<br />
| bgcolor="#C6D46E"| Nathan Clement<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#January 25 | Hodge to de Rham, part one]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 1<br />
| bgcolor="#C6D46E"| Nathan Clement<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 1 | Hodge to de Rham, part two]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 8 <br />
| bgcolor="#C6D46E"| Dima Arinkin<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 8 | Motivated introduction to geometric Langlands]] <br />
|-<br />
| bgcolor="#E0E0E0"| February 15<br />
| bgcolor="#C6D46E"| No Talk<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 15 | We Failed, We All Failed]] <br />
|-<br />
| bgcolor="#E0E0E0"| February 22<br />
| bgcolor="#C6D46E"| No Talk<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 22 | We Failed, We All Failed Pt. 2]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 1<br />
| bgcolor="#C6D46E"| Brandon Boggess<br />
| bgcolor="#BCE2FE"| [[Graduate Algebraic Geometry Seminar#March 1 | An Introduction to Mori's Program]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 8<br />
| bgcolor="#C6D46E"| David Wagner<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 8| Picard groups of moduli problems]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 15<br />
| bgcolor="#C6D46E"| No Talk<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 15| We Failed, We All Failed Pt. 3]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 22<br />
| bgcolor="#C6D46E"| Spring Break<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 22 | No Seminar. ]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 29<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"| [[Graduate Algebraic Geometry Seminar#March 29| TBD]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 5<br />
| bgcolor="#C6D46E"| John Wiltshire-Gordon<br />
| bgcolor="#BCE2FE"| [[Graduate Algebraic Geometry Seminar#April 5| TBD]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 12<br />
| bgcolor="#C6D46E"| Wendy Cheng<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 12| Boij-Soderberg Theory]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 19<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 19| TBD ]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 26<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 26| TBD ]] <br />
|}<br />
</center><br />
<br />
== January 25 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Nathan Clement'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Hodge to de Rham, part one<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: I will use the magic of differential calculus in positive characteristic to prove an important result in the cohomology of smooth varieties in positive characteristic. The techniques I'll use are mainly elementary, but prior experience with differential forms, the Frobenius homomorphism, and a little homological algebra will help. This is the setup, come back next week for the punchline!<br />
|} <br />
</center><br />
<br />
== February 1 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Nathan Clement'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Hodge to de Rham, part two<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: Having proved an important result in positive characteristic, I'll give a nifty argument to leverage the positive characteristic statement into a characteristic zero result. I'll talk about some cohomology comparison theorems, and we'll see that all this business in positive characteristic provides an alternate proof to the classic Hodge decomposition theorem for cohomology.<br />
|} <br />
</center><br />
<br />
== February 8 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Dima Arinkin'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Motivated introduction to geometric Langlands<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: The Langlands program originated from bold conjectures formulated by Robert Langlands in the late 1960's. The conjectures <br />
combine number theory and representation theory in a highly unexpected way. The geometric Langlands program adds algebro-<br />
geometric methods (and, sometimes, physics) to the mix.<br />
<br />
This interplay of ideas creates a beautiful picture... and a very challenging subject. In my talk, I will suggest one possible <br />
way to approach the area. I plan to focus on questions rather than answers: the goal is to explain how (some of) the questions fit together,<br />
and to tell you the keywords that go into the answers. <br />
|} <br />
</center><br />
<br />
== February 15 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''n/a'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: No Talk<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: n/a<br />
|} <br />
</center><br />
<br />
== February 22 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''n/a'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: No Talk<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: n/a<br />
|} <br />
</center><br />
<br />
== March 1 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Brandon Boggess'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: An Introduction to Mori's Program<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: In studying the birational classification of varieties, one plan of attack is to construct a "simplest" variety in each birational equivalence class. We will see how this approach gives a full structure theory for surfaces, and investigate what new challenges arise in the case of threefolds.<br />
<br />
|} <br />
</center><br />
<br />
== March 8 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''David Wagner'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Picard groups of moduli problems<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: In a pastoral traipse, I will discuss some lower bounds on the time it takes an average adult to drink a medium Frosty from Wendy's, including some results of my own about making these bounds sharp. Time permitting, I will also explain how this theory can be extended to study the ingestion of M&M's, a connection previously unkown.<br />
|} <br />
</center><br />
<br />
== March 15 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''n/'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: No Talk<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: n/a<br />
|} <br />
</center><br />
<br />
== March 22 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Spring Break'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: No Seminar.<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: n/a<br />
|} <br />
</center><br />
<br />
== March 29 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBA'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
== April 5 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''John Wiltshire-Gordon'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
== April 12 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Wendy Cheng'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Boij-Soderberg Theory<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
== April 19 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBA'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center> <br />
<br />
== April 26 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBA'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center> <br />
<br />
== Organizers' Contact Info ==<br />
[http://www.math.wisc.edu/~djbruce DJ Bruce]<br />
<br />
[http://www.math.wisc.edu/~clement Nathan Clement]<br />
<br />
[https://www.math.wisc.edu/~moises Moisés Herradón Cueto]<br />
<br />
== Past Semesters ==<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2016 Fall 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2016 Spring 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_(Fall_2015) Fall 2015]</div>Cchenghttps://wiki.math.wisc.edu/index.php?title=Graduate_Algebraic_Geometry_Seminar_Fall_2017&diff=13552Graduate Algebraic Geometry Seminar Fall 20172017-03-24T03:10:03Z<p>Ccheng: /* April 12 */</p>
<hr />
<div>'''<br />
'''When:''' Wednesdays 4:40pm<br />
<br />
'''Where:'''Van Vleck B321 (Spring 2017)<br />
[[Image:cat.jpg|thumb|220px| | Lizzie the OFFICIAL mascot of GAGS!!]]<br />
<br />
'''Who:''' YOU!!<br />
<br />
'''Why:''' The purpose of this seminar is to learn algebraic geometry by giving and listening to talks in a informal setting. Talks are typically accessible to beginning graduate students and take many different forms. Sometimes people present an interesting paper they find. Other times people give a prep talk for the Friday Algebraic Geometry Seminar. Other times people give a series of talks on a topic they have been studying in-depth.<br />
<br />
'''How:'''If you want to get emails regarding time, place, and talk topics ('''which are often assigned quite last minute''') add yourself to the gags mailing list: gags@lists.wisc.edu. The list registration page is [https://admin.lists.wisc.edu/index.php?p=11&l=gags here].<br />
'''<br />
<br />
<br />
<br />
<br />
<br />
== Give a talk! ==<br />
We need volunteers to give talks this semester. If you're interested contact [mailto:djbruce@math.wisc.edu DJ], or just add yourself to the list (though in that case we might move your talk later without your permission). Beginning graduate students are particularly encouraged to give a talk, since it's a great way to get your feet wet with the material.<br />
<br />
<br />
== Wish List ==<br />
Here are the topics we're '''DYING''' to learn about! Please consider looking into one of these topics and giving one or two GAGS talks.<br />
<br />
===Specifically Vague Topics===<br />
* D-modules 101: basics of D-modules, equivalence between left and right D-modules, pullbacks, pushforwards, maybe the Gauss-Manin Connection. Claude Sabbah's introduction to the subject could be a good place to start.<br />
<br />
* Sheaf operations on D-modules (the point is that then you can get a Fourier-Mukai transform between certain O-modules and certain D-modules, which is more or less how geometric Langlands is supposed to work)<br />
<br />
===Famous Theorems===<br />
<br />
===Interesting Papers & Books===<br />
* ''Symplectic structure of the moduli space of sheaves on an abelian or K3 surface'' - Shigeru Mukai.<br />
<br />
* ''Residues and Duality'' - Robin Hatshorne.<br />
** Have you heard of Serre Duality? Would you like to really understand the nuts and bolts of it and its generalizations? If so this book is for you. (You wouldn't need to read the whole book to give a talk ;).)<br />
<br />
* ''Coherent sheaves on P^n and problems in linear algebra'' - A. A. Beilinson.<br />
** In this two page paper constructs the semi-orthogonal decomposition of the derived category of coherent sheaves on projective space. (This topic is very important, and there are a ton of other resources for this result and the general theory of derived categories.)<br />
<br />
* ''Frobenius splitting and cohomology vanishing for Schubert varieties'' - V.B. Mehta and A. Ramanathan.<br />
** In characteristic p the fact that (x+y)^p=x^p+y^p means that one has the Frobenius morphism, which sends f to f^p. In this paper the authors introduce the notion of what it means for a variety to be Frobenius split, and use this to prove certain cohomologcal vanishing results for Schubert varieties. Since then Frobenius splitting -- and its related cousins (F-regularity, strong F-regularity, F-purity, etc.) have played large roles in geometry and algebra in characteristic p. This is a good place to get a sense for what kicked all this stuff off! <br />
<br />
* ''Schubert Calculus'' - S. L. Kleiman and Dan Laksov.<br />
** An introduction to Schubert calculus suitable for those of all ages. I am told the paper essentially only uses linear algebra!<br />
<br />
* ''Rational Isogenies of Prime Degree'' - Barry Mazur.<br />
** In this paper Mazur classifies all isogenies of rational elliptic curves of prime order. As a result of this he deduces his famous result that the torsion subgroup of an elliptic curve (over Q) is one of 15 abelian groups. This definitely stares into the land of number theory, but certainly would still be of interest to many.<br />
<br />
* ''Esquisse d’une programme'' - Alexander Grothendieck.<br />
** Originating from a grant proposal in the mid 1980's this famous paper outlines a tantalizing research program, which seeks to tie numerous different areas of math (algebraic geometry, Teichmuller theory, Galois theory, etc.) together. This is where Grothendieck introduced his famous Lego game and dessin d'enfant. While just a research proposal this paper has seemingly inspired a ton of cool math, and will allow you to "blow peoples’ minds". (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Géométrie algébraique et géométrie analytique'' - J.P. Serre.<br />
** A projective variety X over the complex numbers has two lives, an algebraic and an analytic, depending on which topology one wishes to work with. That is one can think about X as a complex manifold and work with holomorphic functions or as an algebraic variety and work with regular functions. Hence to any complex projective variety we have two sheaf theories and as a result two cohomology theories. In this famous paper Serre compares these two and shows they are in fact the same. (''Note: This is a super fundamental result that is used all the time; normally in the following way: Uhh... What do you mean by cohomology? Well by GAGA or something it doesn't really mater.) (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Limit linear series: Basic theory''- David Eisenbud and Joe Harris.<br />
** One of the more profitable tools -- especially when studying moduli spaces -- in a geometers tool box is the theory of degenerations. However, sometimes we care about more than just the variety we are degenerating and want to keep track of things like vector/line bundles. In this paper Eisenbud and Harris develop the theory of degenerating a curve together with a linear series. From this they prove a ton of cool results: M_g is of general type for g>24, Brill-Noether theory, etc.<br />
<br />
* ''Picard Groups of Moduli Problems'' - David Mumford.<br />
** This paper is essentially the origin of algebraic stacks.<br />
<br />
* ''The Structure of Algebraic Threefolds: An Introduction to Mori's Program'' - Janos Kollar<br />
** This paper is an introduction to Mori's famous ``minimal model'' program, which is a far reaching program seeking to understand the birational geometry of higher dimensional varieties. <br />
<br />
* ''Cayley-Bacharach Formulas'' - Qingchun Ren, Jürgen Richter-Gebert, Bernd Sturmfels.<br />
** A classical result we all learn in a first semester of algebraic geometry is that 5 points in the plane (in general position) determine a unique plane conic. One can similarly show that 9 (general) points in the plane determine a unique plane cubic curve. This paper tries to answer the question: ``What is equation for this cubic curve?''.<br />
<br />
* ''On Varieties of Minimal Degree (A Centennial Approach)'' - David Eisenbud and Joe Harris.<br />
** Suppose X is a projective variety embedded in projective space so that X is not contained in any hyperplane. By projecting from general points one can see that the degree of X is at least codim(X)+1. This paper discusses the classification of varieties that achieve this lower degree bound i.e. varieties of minimal degree. This topic is quite classical and the paper seems to contain a nice mixture of classical and modern geometry.<br />
<br />
* ''The Gromov-Witten potential associated to a TCFT'' - Kevin J. Costello.<br />
** This seems incredibly interesting, but fairing warning this paper has been described as ''highly technical'', which considering it uses A-infinity algebras and the derived category of a Calabi-Yau seems like a reasonable description. (This paper may be covered in Caldararu's Spring 2017 topics course.)<br />
__NOTOC__<br />
<br />
== Spring 2017 ==<br />
<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#A6B658" width="300" align="center"|'''Speaker'''<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title (click to see abstract)'''<br />
|-<br />
| bgcolor="#E0E0E0"| January 25<br />
| bgcolor="#C6D46E"| Nathan Clement<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#January 25 | Hodge to de Rham, part one]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 1<br />
| bgcolor="#C6D46E"| Nathan Clement<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 1 | Hodge to de Rham, part two]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 8 <br />
| bgcolor="#C6D46E"| Dima Arinkin<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 8 | Motivated introduction to geometric Langlands]] <br />
|-<br />
| bgcolor="#E0E0E0"| February 15<br />
| bgcolor="#C6D46E"| No Talk<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 15 | We Failed, We All Failed]] <br />
|-<br />
| bgcolor="#E0E0E0"| February 22<br />
| bgcolor="#C6D46E"| No Talk<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 22 | We Failed, We All Failed Pt. 2]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 1<br />
| bgcolor="#C6D46E"| Brandon Boggess<br />
| bgcolor="#BCE2FE"| [[Graduate Algebraic Geometry Seminar#March 1 | An Introduction to Mori's Program]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 8<br />
| bgcolor="#C6D46E"| David Wagner<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 8| Picard groups of moduli problems]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 15<br />
| bgcolor="#C6D46E"| No Talk<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 15| We Failed, We All Failed Pt. 3]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 22<br />
| bgcolor="#C6D46E"| Spring Break<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 22 | No Seminar. ]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 29<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"| [[Graduate Algebraic Geometry Seminar#March 29| TBD]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 5<br />
| bgcolor="#C6D46E"| John Wiltshire-Gordon<br />
| bgcolor="#BCE2FE"| [[Graduate Algebraic Geometry Seminar#April 5| TBD]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 12<br />
| bgcolor="#C6D46E"| Wendy Cheng<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 12| Boij-Soderberg Theory]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 19<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 19| TBD ]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 26<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 26| TBD ]] <br />
|}<br />
</center><br />
<br />
== January 25 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Nathan Clement'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Hodge to de Rham, part one<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: I will use the magic of differential calculus in positive characteristic to prove an important result in the cohomology of smooth varieties in positive characteristic. The techniques I'll use are mainly elementary, but prior experience with differential forms, the Frobenius homomorphism, and a little homological algebra will help. This is the setup, come back next week for the punchline!<br />
|} <br />
</center><br />
<br />
== February 1 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Nathan Clement'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Hodge to de Rham, part two<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: Having proved an important result in positive characteristic, I'll give a nifty argument to leverage the positive characteristic statement into a characteristic zero result. I'll talk about some cohomology comparison theorems, and we'll see that all this business in positive characteristic provides an alternate proof to the classic Hodge decomposition theorem for cohomology.<br />
|} <br />
</center><br />
<br />
== February 8 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Dima Arinkin'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Motivated introduction to geometric Langlands<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: The Langlands program originated from bold conjectures formulated by Robert Langlands in the late 1960's. The conjectures <br />
combine number theory and representation theory in a highly unexpected way. The geometric Langlands program adds algebro-<br />
geometric methods (and, sometimes, physics) to the mix.<br />
<br />
This interplay of ideas creates a beautiful picture... and a very challenging subject. In my talk, I will suggest one possible <br />
way to approach the area. I plan to focus on questions rather than answers: the goal is to explain how (some of) the questions fit together,<br />
and to tell you the keywords that go into the answers. <br />
|} <br />
</center><br />
<br />
== February 15 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''n/a'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: No Talk<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: n/a<br />
|} <br />
</center><br />
<br />
== February 22 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''n/a'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: No Talk<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: n/a<br />
|} <br />
</center><br />
<br />
== March 1 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Brandon Boggess'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: An Introduction to Mori's Program<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: In studying the birational classification of varieties, one plan of attack is to construct a "simplest" variety in each birational equivalence class. We will see how this approach gives a full structure theory for surfaces, and investigate what new challenges arise in the case of threefolds.<br />
<br />
|} <br />
</center><br />
<br />
== March 8 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''David Wagner'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Picard groups of moduli problems<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: In a pastoral traipse, I will discuss some lower bounds on the time it takes an average adult to drink a medium Frosty from Wendy's, including some results of my own about making these bounds sharp. Time permitting, I will also explain how this theory can be extended to study the ingestion of M&M's, a connection previously unkown.<br />
|} <br />
</center><br />
<br />
== March 15 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''n/'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: No Talk<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: n/a<br />
|} <br />
</center><br />
<br />
== March 22 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Spring Break'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: No Seminar.<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: n/a<br />
|} <br />
</center><br />
<br />
== March 29 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBA'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
== April 5 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''John Wiltshire-Gordon'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
== April 12 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Wendy Cheng'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
== April 19 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBA'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center> <br />
<br />
== April 26 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBA'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center> <br />
<br />
== Organizers' Contact Info ==<br />
[http://www.math.wisc.edu/~djbruce DJ Bruce]<br />
<br />
[http://www.math.wisc.edu/~clement Nathan Clement]<br />
<br />
[https://www.math.wisc.edu/~moises Moisés Herradón Cueto]<br />
<br />
== Past Semesters ==<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2016 Fall 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2016 Spring 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_(Fall_2015) Fall 2015]</div>Cchenghttps://wiki.math.wisc.edu/index.php?title=Graduate_Algebraic_Geometry_Seminar_Fall_2017&diff=13551Graduate Algebraic Geometry Seminar Fall 20172017-03-24T03:08:27Z<p>Ccheng: </p>
<hr />
<div>'''<br />
'''When:''' Wednesdays 4:40pm<br />
<br />
'''Where:'''Van Vleck B321 (Spring 2017)<br />
[[Image:cat.jpg|thumb|220px| | Lizzie the OFFICIAL mascot of GAGS!!]]<br />
<br />
'''Who:''' YOU!!<br />
<br />
'''Why:''' The purpose of this seminar is to learn algebraic geometry by giving and listening to talks in a informal setting. Talks are typically accessible to beginning graduate students and take many different forms. Sometimes people present an interesting paper they find. Other times people give a prep talk for the Friday Algebraic Geometry Seminar. Other times people give a series of talks on a topic they have been studying in-depth.<br />
<br />
'''How:'''If you want to get emails regarding time, place, and talk topics ('''which are often assigned quite last minute''') add yourself to the gags mailing list: gags@lists.wisc.edu. The list registration page is [https://admin.lists.wisc.edu/index.php?p=11&l=gags here].<br />
'''<br />
<br />
<br />
<br />
<br />
<br />
== Give a talk! ==<br />
We need volunteers to give talks this semester. If you're interested contact [mailto:djbruce@math.wisc.edu DJ], or just add yourself to the list (though in that case we might move your talk later without your permission). Beginning graduate students are particularly encouraged to give a talk, since it's a great way to get your feet wet with the material.<br />
<br />
<br />
== Wish List ==<br />
Here are the topics we're '''DYING''' to learn about! Please consider looking into one of these topics and giving one or two GAGS talks.<br />
<br />
===Specifically Vague Topics===<br />
* D-modules 101: basics of D-modules, equivalence between left and right D-modules, pullbacks, pushforwards, maybe the Gauss-Manin Connection. Claude Sabbah's introduction to the subject could be a good place to start.<br />
<br />
* Sheaf operations on D-modules (the point is that then you can get a Fourier-Mukai transform between certain O-modules and certain D-modules, which is more or less how geometric Langlands is supposed to work)<br />
<br />
===Famous Theorems===<br />
<br />
===Interesting Papers & Books===<br />
* ''Symplectic structure of the moduli space of sheaves on an abelian or K3 surface'' - Shigeru Mukai.<br />
<br />
* ''Residues and Duality'' - Robin Hatshorne.<br />
** Have you heard of Serre Duality? Would you like to really understand the nuts and bolts of it and its generalizations? If so this book is for you. (You wouldn't need to read the whole book to give a talk ;).)<br />
<br />
* ''Coherent sheaves on P^n and problems in linear algebra'' - A. A. Beilinson.<br />
** In this two page paper constructs the semi-orthogonal decomposition of the derived category of coherent sheaves on projective space. (This topic is very important, and there are a ton of other resources for this result and the general theory of derived categories.)<br />
<br />
* ''Frobenius splitting and cohomology vanishing for Schubert varieties'' - V.B. Mehta and A. Ramanathan.<br />
** In characteristic p the fact that (x+y)^p=x^p+y^p means that one has the Frobenius morphism, which sends f to f^p. In this paper the authors introduce the notion of what it means for a variety to be Frobenius split, and use this to prove certain cohomologcal vanishing results for Schubert varieties. Since then Frobenius splitting -- and its related cousins (F-regularity, strong F-regularity, F-purity, etc.) have played large roles in geometry and algebra in characteristic p. This is a good place to get a sense for what kicked all this stuff off! <br />
<br />
* ''Schubert Calculus'' - S. L. Kleiman and Dan Laksov.<br />
** An introduction to Schubert calculus suitable for those of all ages. I am told the paper essentially only uses linear algebra!<br />
<br />
* ''Rational Isogenies of Prime Degree'' - Barry Mazur.<br />
** In this paper Mazur classifies all isogenies of rational elliptic curves of prime order. As a result of this he deduces his famous result that the torsion subgroup of an elliptic curve (over Q) is one of 15 abelian groups. This definitely stares into the land of number theory, but certainly would still be of interest to many.<br />
<br />
* ''Esquisse d’une programme'' - Alexander Grothendieck.<br />
** Originating from a grant proposal in the mid 1980's this famous paper outlines a tantalizing research program, which seeks to tie numerous different areas of math (algebraic geometry, Teichmuller theory, Galois theory, etc.) together. This is where Grothendieck introduced his famous Lego game and dessin d'enfant. While just a research proposal this paper has seemingly inspired a ton of cool math, and will allow you to "blow peoples’ minds". (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Géométrie algébraique et géométrie analytique'' - J.P. Serre.<br />
** A projective variety X over the complex numbers has two lives, an algebraic and an analytic, depending on which topology one wishes to work with. That is one can think about X as a complex manifold and work with holomorphic functions or as an algebraic variety and work with regular functions. Hence to any complex projective variety we have two sheaf theories and as a result two cohomology theories. In this famous paper Serre compares these two and shows they are in fact the same. (''Note: This is a super fundamental result that is used all the time; normally in the following way: Uhh... What do you mean by cohomology? Well by GAGA or something it doesn't really mater.) (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Limit linear series: Basic theory''- David Eisenbud and Joe Harris.<br />
** One of the more profitable tools -- especially when studying moduli spaces -- in a geometers tool box is the theory of degenerations. However, sometimes we care about more than just the variety we are degenerating and want to keep track of things like vector/line bundles. In this paper Eisenbud and Harris develop the theory of degenerating a curve together with a linear series. From this they prove a ton of cool results: M_g is of general type for g>24, Brill-Noether theory, etc.<br />
<br />
* ''Picard Groups of Moduli Problems'' - David Mumford.<br />
** This paper is essentially the origin of algebraic stacks.<br />
<br />
* ''The Structure of Algebraic Threefolds: An Introduction to Mori's Program'' - Janos Kollar<br />
** This paper is an introduction to Mori's famous ``minimal model'' program, which is a far reaching program seeking to understand the birational geometry of higher dimensional varieties. <br />
<br />
* ''Cayley-Bacharach Formulas'' - Qingchun Ren, Jürgen Richter-Gebert, Bernd Sturmfels.<br />
** A classical result we all learn in a first semester of algebraic geometry is that 5 points in the plane (in general position) determine a unique plane conic. One can similarly show that 9 (general) points in the plane determine a unique plane cubic curve. This paper tries to answer the question: ``What is equation for this cubic curve?''.<br />
<br />
* ''On Varieties of Minimal Degree (A Centennial Approach)'' - David Eisenbud and Joe Harris.<br />
** Suppose X is a projective variety embedded in projective space so that X is not contained in any hyperplane. By projecting from general points one can see that the degree of X is at least codim(X)+1. This paper discusses the classification of varieties that achieve this lower degree bound i.e. varieties of minimal degree. This topic is quite classical and the paper seems to contain a nice mixture of classical and modern geometry.<br />
<br />
* ''The Gromov-Witten potential associated to a TCFT'' - Kevin J. Costello.<br />
** This seems incredibly interesting, but fairing warning this paper has been described as ''highly technical'', which considering it uses A-infinity algebras and the derived category of a Calabi-Yau seems like a reasonable description. (This paper may be covered in Caldararu's Spring 2017 topics course.)<br />
__NOTOC__<br />
<br />
== Spring 2017 ==<br />
<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#A6B658" width="300" align="center"|'''Speaker'''<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title (click to see abstract)'''<br />
|-<br />
| bgcolor="#E0E0E0"| January 25<br />
| bgcolor="#C6D46E"| Nathan Clement<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#January 25 | Hodge to de Rham, part one]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 1<br />
| bgcolor="#C6D46E"| Nathan Clement<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 1 | Hodge to de Rham, part two]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 8 <br />
| bgcolor="#C6D46E"| Dima Arinkin<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 8 | Motivated introduction to geometric Langlands]] <br />
|-<br />
| bgcolor="#E0E0E0"| February 15<br />
| bgcolor="#C6D46E"| No Talk<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 15 | We Failed, We All Failed]] <br />
|-<br />
| bgcolor="#E0E0E0"| February 22<br />
| bgcolor="#C6D46E"| No Talk<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 22 | We Failed, We All Failed Pt. 2]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 1<br />
| bgcolor="#C6D46E"| Brandon Boggess<br />
| bgcolor="#BCE2FE"| [[Graduate Algebraic Geometry Seminar#March 1 | An Introduction to Mori's Program]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 8<br />
| bgcolor="#C6D46E"| David Wagner<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 8| Picard groups of moduli problems]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 15<br />
| bgcolor="#C6D46E"| No Talk<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 15| We Failed, We All Failed Pt. 3]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 22<br />
| bgcolor="#C6D46E"| Spring Break<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 22 | No Seminar. ]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 29<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"| [[Graduate Algebraic Geometry Seminar#March 29| TBD]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 5<br />
| bgcolor="#C6D46E"| John Wiltshire-Gordon<br />
| bgcolor="#BCE2FE"| [[Graduate Algebraic Geometry Seminar#April 5| TBD]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 12<br />
| bgcolor="#C6D46E"| Wendy Cheng<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 12| Boij-Soderberg Theory]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 19<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 19| TBD ]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 26<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 26| TBD ]] <br />
|}<br />
</center><br />
<br />
== January 25 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Nathan Clement'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Hodge to de Rham, part one<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: I will use the magic of differential calculus in positive characteristic to prove an important result in the cohomology of smooth varieties in positive characteristic. The techniques I'll use are mainly elementary, but prior experience with differential forms, the Frobenius homomorphism, and a little homological algebra will help. This is the setup, come back next week for the punchline!<br />
|} <br />
</center><br />
<br />
== February 1 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Nathan Clement'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Hodge to de Rham, part two<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: Having proved an important result in positive characteristic, I'll give a nifty argument to leverage the positive characteristic statement into a characteristic zero result. I'll talk about some cohomology comparison theorems, and we'll see that all this business in positive characteristic provides an alternate proof to the classic Hodge decomposition theorem for cohomology.<br />
|} <br />
</center><br />
<br />
== February 8 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Dima Arinkin'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Motivated introduction to geometric Langlands<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: The Langlands program originated from bold conjectures formulated by Robert Langlands in the late 1960's. The conjectures <br />
combine number theory and representation theory in a highly unexpected way. The geometric Langlands program adds algebro-<br />
geometric methods (and, sometimes, physics) to the mix.<br />
<br />
This interplay of ideas creates a beautiful picture... and a very challenging subject. In my talk, I will suggest one possible <br />
way to approach the area. I plan to focus on questions rather than answers: the goal is to explain how (some of) the questions fit together,<br />
and to tell you the keywords that go into the answers. <br />
|} <br />
</center><br />
<br />
== February 15 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''n/a'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: No Talk<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: n/a<br />
|} <br />
</center><br />
<br />
== February 22 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''n/a'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: No Talk<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: n/a<br />
|} <br />
</center><br />
<br />
== March 1 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Brandon Boggess'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: An Introduction to Mori's Program<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: In studying the birational classification of varieties, one plan of attack is to construct a "simplest" variety in each birational equivalence class. We will see how this approach gives a full structure theory for surfaces, and investigate what new challenges arise in the case of threefolds.<br />
<br />
|} <br />
</center><br />
<br />
== March 8 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''David Wagner'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Picard groups of moduli problems<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: In a pastoral traipse, I will discuss some lower bounds on the time it takes an average adult to drink a medium Frosty from Wendy's, including some results of my own about making these bounds sharp. Time permitting, I will also explain how this theory can be extended to study the ingestion of M&M's, a connection previously unkown.<br />
|} <br />
</center><br />
<br />
== March 15 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''n/'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: No Talk<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: n/a<br />
|} <br />
</center><br />
<br />
== March 22 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Spring Break'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: No Seminar.<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: n/a<br />
|} <br />
</center><br />
<br />
== March 29 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBA'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
== April 5 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''John Wiltshire-Gordon'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
== April 12 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBA'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center> <br />
<br />
== April 19 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBA'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center> <br />
<br />
== April 26 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBA'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center> <br />
<br />
== Organizers' Contact Info ==<br />
[http://www.math.wisc.edu/~djbruce DJ Bruce]<br />
<br />
[http://www.math.wisc.edu/~clement Nathan Clement]<br />
<br />
[https://www.math.wisc.edu/~moises Moisés Herradón Cueto]<br />
<br />
== Past Semesters ==<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2016 Fall 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2016 Spring 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_(Fall_2015) Fall 2015]</div>Cchenghttps://wiki.math.wisc.edu/index.php?title=Graduate_Algebraic_Geometry_Seminar_Fall_2017&diff=13550Graduate Algebraic Geometry Seminar Fall 20172017-03-24T03:07:50Z<p>Ccheng: </p>
<hr />
<div>'''<br />
'''When:''' Wednesdays 4:40pm<br />
<br />
'''Where:'''Van Vleck B321 (Spring 2017)<br />
[[Image:cat.jpg|thumb|220px| | Lizzie the OFFICIAL mascot of GAGS!!]]<br />
<br />
'''Who:''' YOU!!<br />
<br />
'''Why:''' The purpose of this seminar is to learn algebraic geometry by giving and listening to talks in a informal setting. Talks are typically accessible to beginning graduate students and take many different forms. Sometimes people present an interesting paper they find. Other times people give a prep talk for the Friday Algebraic Geometry Seminar. Other times people give a series of talks on a topic they have been studying in-depth.<br />
<br />
'''How:'''If you want to get emails regarding time, place, and talk topics ('''which are often assigned quite last minute''') add yourself to the gags mailing list: gags@lists.wisc.edu. The list registration page is [https://admin.lists.wisc.edu/index.php?p=11&l=gags here].<br />
'''<br />
<br />
<br />
<br />
<br />
<br />
== Give a talk! ==<br />
We need volunteers to give talks this semester. If you're interested contact [mailto:djbruce@math.wisc.edu DJ], or just add yourself to the list (though in that case we might move your talk later without your permission). Beginning graduate students are particularly encouraged to give a talk, since it's a great way to get your feet wet with the material.<br />
<br />
<br />
== Wish List ==<br />
Here are the topics we're '''DYING''' to learn about! Please consider looking into one of these topics and giving one or two GAGS talks.<br />
<br />
===Specifically Vague Topics===<br />
* D-modules 101: basics of D-modules, equivalence between left and right D-modules, pullbacks, pushforwards, maybe the Gauss-Manin Connection. Claude Sabbah's introduction to the subject could be a good place to start.<br />
<br />
* Sheaf operations on D-modules (the point is that then you can get a Fourier-Mukai transform between certain O-modules and certain D-modules, which is more or less how geometric Langlands is supposed to work)<br />
<br />
===Famous Theorems===<br />
<br />
===Interesting Papers & Books===<br />
* ''Symplectic structure of the moduli space of sheaves on an abelian or K3 surface'' - Shigeru Mukai.<br />
<br />
* ''Residues and Duality'' - Robin Hatshorne.<br />
** Have you heard of Serre Duality? Would you like to really understand the nuts and bolts of it and its generalizations? If so this book is for you. (You wouldn't need to read the whole book to give a talk ;).)<br />
<br />
* ''Coherent sheaves on P^n and problems in linear algebra'' - A. A. Beilinson.<br />
** In this two page paper constructs the semi-orthogonal decomposition of the derived category of coherent sheaves on projective space. (This topic is very important, and there are a ton of other resources for this result and the general theory of derived categories.)<br />
<br />
* ''Frobenius splitting and cohomology vanishing for Schubert varieties'' - V.B. Mehta and A. Ramanathan.<br />
** In characteristic p the fact that (x+y)^p=x^p+y^p means that one has the Frobenius morphism, which sends f to f^p. In this paper the authors introduce the notion of what it means for a variety to be Frobenius split, and use this to prove certain cohomologcal vanishing results for Schubert varieties. Since then Frobenius splitting -- and its related cousins (F-regularity, strong F-regularity, F-purity, etc.) have played large roles in geometry and algebra in characteristic p. This is a good place to get a sense for what kicked all this stuff off! <br />
<br />
* ''Schubert Calculus'' - S. L. Kleiman and Dan Laksov.<br />
** An introduction to Schubert calculus suitable for those of all ages. I am told the paper essentially only uses linear algebra!<br />
<br />
* ''Rational Isogenies of Prime Degree'' - Barry Mazur.<br />
** In this paper Mazur classifies all isogenies of rational elliptic curves of prime order. As a result of this he deduces his famous result that the torsion subgroup of an elliptic curve (over Q) is one of 15 abelian groups. This definitely stares into the land of number theory, but certainly would still be of interest to many.<br />
<br />
* ''Esquisse d’une programme'' - Alexander Grothendieck.<br />
** Originating from a grant proposal in the mid 1980's this famous paper outlines a tantalizing research program, which seeks to tie numerous different areas of math (algebraic geometry, Teichmuller theory, Galois theory, etc.) together. This is where Grothendieck introduced his famous Lego game and dessin d'enfant. While just a research proposal this paper has seemingly inspired a ton of cool math, and will allow you to "blow peoples’ minds". (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Géométrie algébraique et géométrie analytique'' - J.P. Serre.<br />
** A projective variety X over the complex numbers has two lives, an algebraic and an analytic, depending on which topology one wishes to work with. That is one can think about X as a complex manifold and work with holomorphic functions or as an algebraic variety and work with regular functions. Hence to any complex projective variety we have two sheaf theories and as a result two cohomology theories. In this famous paper Serre compares these two and shows they are in fact the same. (''Note: This is a super fundamental result that is used all the time; normally in the following way: Uhh... What do you mean by cohomology? Well by GAGA or something it doesn't really mater.) (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Limit linear series: Basic theory''- David Eisenbud and Joe Harris.<br />
** One of the more profitable tools -- especially when studying moduli spaces -- in a geometers tool box is the theory of degenerations. However, sometimes we care about more than just the variety we are degenerating and want to keep track of things like vector/line bundles. In this paper Eisenbud and Harris develop the theory of degenerating a curve together with a linear series. From this they prove a ton of cool results: M_g is of general type for g>24, Brill-Noether theory, etc.<br />
<br />
* ''Picard Groups of Moduli Problems'' - David Mumford.<br />
** This paper is essentially the origin of algebraic stacks.<br />
<br />
* ''The Structure of Algebraic Threefolds: An Introduction to Mori's Program'' - Janos Kollar<br />
** This paper is an introduction to Mori's famous ``minimal model'' program, which is a far reaching program seeking to understand the birational geometry of higher dimensional varieties. <br />
<br />
* ''Cayley-Bacharach Formulas'' - Qingchun Ren, Jürgen Richter-Gebert, Bernd Sturmfels.<br />
** A classical result we all learn in a first semester of algebraic geometry is that 5 points in the plane (in general position) determine a unique plane conic. One can similarly show that 9 (general) points in the plane determine a unique plane cubic curve. This paper tries to answer the question: ``What is equation for this cubic curve?''.<br />
<br />
* ''On Varieties of Minimal Degree (A Centennial Approach)'' - David Eisenbud and Joe Harris.<br />
** Suppose X is a projective variety embedded in projective space so that X is not contained in any hyperplane. By projecting from general points one can see that the degree of X is at least codim(X)+1. This paper discusses the classification of varieties that achieve this lower degree bound i.e. varieties of minimal degree. This topic is quite classical and the paper seems to contain a nice mixture of classical and modern geometry.<br />
<br />
* ''The Gromov-Witten potential associated to a TCFT'' - Kevin J. Costello.<br />
** This seems incredibly interesting, but fairing warning this paper has been described as ''highly technical'', which considering it uses A-infinity algebras and the derived category of a Calabi-Yau seems like a reasonable description. (This paper may be covered in Caldararu's Spring 2017 topics course.)<br />
__NOTOC__<br />
<br />
== Spring 2017 ==<br />
<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#A6B658" width="300" align="center"|'''Speaker'''<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title (click to see abstract)'''<br />
|-<br />
| bgcolor="#E0E0E0"| January 25<br />
| bgcolor="#C6D46E"| Nathan Clement<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#January 25 | Hodge to de Rham, part one]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 1<br />
| bgcolor="#C6D46E"| Nathan Clement<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 1 | Hodge to de Rham, part two]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 8 <br />
| bgcolor="#C6D46E"| Dima Arinkin<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 8 | Motivated introduction to geometric Langlands]] <br />
|-<br />
| bgcolor="#E0E0E0"| February 15<br />
| bgcolor="#C6D46E"| No Talk<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 15 | We Failed, We All Failed]] <br />
|-<br />
| bgcolor="#E0E0E0"| February 22<br />
| bgcolor="#C6D46E"| No Talk<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 22 | We Failed, We All Failed Pt. 2]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 1<br />
| bgcolor="#C6D46E"| Brandon Boggess<br />
| bgcolor="#BCE2FE"| [[Graduate Algebraic Geometry Seminar#March 1 | An Introduction to Mori's Program]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 8<br />
| bgcolor="#C6D46E"| David Wagner<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 8| Picard groups of moduli problems]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 15<br />
| bgcolor="#C6D46E"| No Talk<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 15| We Failed, We All Failed Pt. 3]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 22<br />
| bgcolor="#C6D46E"| Spring Break<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 22 | No Seminar. ]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 29<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"| [[Graduate Algebraic Geometry Seminar#March 29| TBD]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 5<br />
| bgcolor="#C6D46E"| John Wiltshire-Gordon<br />
| bgcolor="#BCE2FE"| [[Graduate Algebraic Geometry Seminar#April 5| TBD]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 12<br />
| bgcolor="#C6D46E"| Wendy Cheng<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 12| Boij-S<math>\text{\"o}</math>oderberg Theory]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 19<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 19| TBD ]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 26<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 26| TBD ]] <br />
|}<br />
</center><br />
<br />
== January 25 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Nathan Clement'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Hodge to de Rham, part one<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: I will use the magic of differential calculus in positive characteristic to prove an important result in the cohomology of smooth varieties in positive characteristic. The techniques I'll use are mainly elementary, but prior experience with differential forms, the Frobenius homomorphism, and a little homological algebra will help. This is the setup, come back next week for the punchline!<br />
|} <br />
</center><br />
<br />
== February 1 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Nathan Clement'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Hodge to de Rham, part two<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: Having proved an important result in positive characteristic, I'll give a nifty argument to leverage the positive characteristic statement into a characteristic zero result. I'll talk about some cohomology comparison theorems, and we'll see that all this business in positive characteristic provides an alternate proof to the classic Hodge decomposition theorem for cohomology.<br />
|} <br />
</center><br />
<br />
== February 8 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Dima Arinkin'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Motivated introduction to geometric Langlands<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: The Langlands program originated from bold conjectures formulated by Robert Langlands in the late 1960's. The conjectures <br />
combine number theory and representation theory in a highly unexpected way. The geometric Langlands program adds algebro-<br />
geometric methods (and, sometimes, physics) to the mix.<br />
<br />
This interplay of ideas creates a beautiful picture... and a very challenging subject. In my talk, I will suggest one possible <br />
way to approach the area. I plan to focus on questions rather than answers: the goal is to explain how (some of) the questions fit together,<br />
and to tell you the keywords that go into the answers. <br />
|} <br />
</center><br />
<br />
== February 15 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''n/a'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: No Talk<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: n/a<br />
|} <br />
</center><br />
<br />
== February 22 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''n/a'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: No Talk<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: n/a<br />
|} <br />
</center><br />
<br />
== March 1 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Brandon Boggess'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: An Introduction to Mori's Program<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: In studying the birational classification of varieties, one plan of attack is to construct a "simplest" variety in each birational equivalence class. We will see how this approach gives a full structure theory for surfaces, and investigate what new challenges arise in the case of threefolds.<br />
<br />
|} <br />
</center><br />
<br />
== March 8 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''David Wagner'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Picard groups of moduli problems<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: In a pastoral traipse, I will discuss some lower bounds on the time it takes an average adult to drink a medium Frosty from Wendy's, including some results of my own about making these bounds sharp. Time permitting, I will also explain how this theory can be extended to study the ingestion of M&M's, a connection previously unkown.<br />
|} <br />
</center><br />
<br />
== March 15 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''n/'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: No Talk<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: n/a<br />
|} <br />
</center><br />
<br />
== March 22 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Spring Break'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: No Seminar.<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: n/a<br />
|} <br />
</center><br />
<br />
== March 29 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBA'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
== April 5 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''John Wiltshire-Gordon'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
== April 12 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBA'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center> <br />
<br />
== April 19 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBA'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center> <br />
<br />
== April 26 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBA'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center> <br />
<br />
== Organizers' Contact Info ==<br />
[http://www.math.wisc.edu/~djbruce DJ Bruce]<br />
<br />
[http://www.math.wisc.edu/~clement Nathan Clement]<br />
<br />
[https://www.math.wisc.edu/~moises Moisés Herradón Cueto]<br />
<br />
== Past Semesters ==<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2016 Fall 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2016 Spring 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_(Fall_2015) Fall 2015]</div>Cchenghttps://wiki.math.wisc.edu/index.php?title=Graduate_Algebraic_Geometry_Seminar_Fall_2017&diff=13549Graduate Algebraic Geometry Seminar Fall 20172017-03-24T03:06:19Z<p>Ccheng: </p>
<hr />
<div>'''<br />
'''When:''' Wednesdays 4:40pm<br />
<br />
'''Where:'''Van Vleck B321 (Spring 2017)<br />
[[Image:cat.jpg|thumb|220px| | Lizzie the OFFICIAL mascot of GAGS!!]]<br />
<br />
'''Who:''' YOU!!<br />
<br />
'''Why:''' The purpose of this seminar is to learn algebraic geometry by giving and listening to talks in a informal setting. Talks are typically accessible to beginning graduate students and take many different forms. Sometimes people present an interesting paper they find. Other times people give a prep talk for the Friday Algebraic Geometry Seminar. Other times people give a series of talks on a topic they have been studying in-depth.<br />
<br />
'''How:'''If you want to get emails regarding time, place, and talk topics ('''which are often assigned quite last minute''') add yourself to the gags mailing list: gags@lists.wisc.edu. The list registration page is [https://admin.lists.wisc.edu/index.php?p=11&l=gags here].<br />
'''<br />
<br />
<br />
<br />
<br />
<br />
== Give a talk! ==<br />
We need volunteers to give talks this semester. If you're interested contact [mailto:djbruce@math.wisc.edu DJ], or just add yourself to the list (though in that case we might move your talk later without your permission). Beginning graduate students are particularly encouraged to give a talk, since it's a great way to get your feet wet with the material.<br />
<br />
<br />
== Wish List ==<br />
Here are the topics we're '''DYING''' to learn about! Please consider looking into one of these topics and giving one or two GAGS talks.<br />
<br />
===Specifically Vague Topics===<br />
* D-modules 101: basics of D-modules, equivalence between left and right D-modules, pullbacks, pushforwards, maybe the Gauss-Manin Connection. Claude Sabbah's introduction to the subject could be a good place to start.<br />
<br />
* Sheaf operations on D-modules (the point is that then you can get a Fourier-Mukai transform between certain O-modules and certain D-modules, which is more or less how geometric Langlands is supposed to work)<br />
<br />
===Famous Theorems===<br />
<br />
===Interesting Papers & Books===<br />
* ''Symplectic structure of the moduli space of sheaves on an abelian or K3 surface'' - Shigeru Mukai.<br />
<br />
* ''Residues and Duality'' - Robin Hatshorne.<br />
** Have you heard of Serre Duality? Would you like to really understand the nuts and bolts of it and its generalizations? If so this book is for you. (You wouldn't need to read the whole book to give a talk ;).)<br />
<br />
* ''Coherent sheaves on P^n and problems in linear algebra'' - A. A. Beilinson.<br />
** In this two page paper constructs the semi-orthogonal decomposition of the derived category of coherent sheaves on projective space. (This topic is very important, and there are a ton of other resources for this result and the general theory of derived categories.)<br />
<br />
* ''Frobenius splitting and cohomology vanishing for Schubert varieties'' - V.B. Mehta and A. Ramanathan.<br />
** In characteristic p the fact that (x+y)^p=x^p+y^p means that one has the Frobenius morphism, which sends f to f^p. In this paper the authors introduce the notion of what it means for a variety to be Frobenius split, and use this to prove certain cohomologcal vanishing results for Schubert varieties. Since then Frobenius splitting -- and its related cousins (F-regularity, strong F-regularity, F-purity, etc.) have played large roles in geometry and algebra in characteristic p. This is a good place to get a sense for what kicked all this stuff off! <br />
<br />
* ''Schubert Calculus'' - S. L. Kleiman and Dan Laksov.<br />
** An introduction to Schubert calculus suitable for those of all ages. I am told the paper essentially only uses linear algebra!<br />
<br />
* ''Rational Isogenies of Prime Degree'' - Barry Mazur.<br />
** In this paper Mazur classifies all isogenies of rational elliptic curves of prime order. As a result of this he deduces his famous result that the torsion subgroup of an elliptic curve (over Q) is one of 15 abelian groups. This definitely stares into the land of number theory, but certainly would still be of interest to many.<br />
<br />
* ''Esquisse d’une programme'' - Alexander Grothendieck.<br />
** Originating from a grant proposal in the mid 1980's this famous paper outlines a tantalizing research program, which seeks to tie numerous different areas of math (algebraic geometry, Teichmuller theory, Galois theory, etc.) together. This is where Grothendieck introduced his famous Lego game and dessin d'enfant. While just a research proposal this paper has seemingly inspired a ton of cool math, and will allow you to "blow peoples’ minds". (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Géométrie algébraique et géométrie analytique'' - J.P. Serre.<br />
** A projective variety X over the complex numbers has two lives, an algebraic and an analytic, depending on which topology one wishes to work with. That is one can think about X as a complex manifold and work with holomorphic functions or as an algebraic variety and work with regular functions. Hence to any complex projective variety we have two sheaf theories and as a result two cohomology theories. In this famous paper Serre compares these two and shows they are in fact the same. (''Note: This is a super fundamental result that is used all the time; normally in the following way: Uhh... What do you mean by cohomology? Well by GAGA or something it doesn't really mater.) (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Limit linear series: Basic theory''- David Eisenbud and Joe Harris.<br />
** One of the more profitable tools -- especially when studying moduli spaces -- in a geometers tool box is the theory of degenerations. However, sometimes we care about more than just the variety we are degenerating and want to keep track of things like vector/line bundles. In this paper Eisenbud and Harris develop the theory of degenerating a curve together with a linear series. From this they prove a ton of cool results: M_g is of general type for g>24, Brill-Noether theory, etc.<br />
<br />
* ''Picard Groups of Moduli Problems'' - David Mumford.<br />
** This paper is essentially the origin of algebraic stacks.<br />
<br />
* ''The Structure of Algebraic Threefolds: An Introduction to Mori's Program'' - Janos Kollar<br />
** This paper is an introduction to Mori's famous ``minimal model'' program, which is a far reaching program seeking to understand the birational geometry of higher dimensional varieties. <br />
<br />
* ''Cayley-Bacharach Formulas'' - Qingchun Ren, Jürgen Richter-Gebert, Bernd Sturmfels.<br />
** A classical result we all learn in a first semester of algebraic geometry is that 5 points in the plane (in general position) determine a unique plane conic. One can similarly show that 9 (general) points in the plane determine a unique plane cubic curve. This paper tries to answer the question: ``What is equation for this cubic curve?''.<br />
<br />
* ''On Varieties of Minimal Degree (A Centennial Approach)'' - David Eisenbud and Joe Harris.<br />
** Suppose X is a projective variety embedded in projective space so that X is not contained in any hyperplane. By projecting from general points one can see that the degree of X is at least codim(X)+1. This paper discusses the classification of varieties that achieve this lower degree bound i.e. varieties of minimal degree. This topic is quite classical and the paper seems to contain a nice mixture of classical and modern geometry.<br />
<br />
* ''The Gromov-Witten potential associated to a TCFT'' - Kevin J. Costello.<br />
** This seems incredibly interesting, but fairing warning this paper has been described as ''highly technical'', which considering it uses A-infinity algebras and the derived category of a Calabi-Yau seems like a reasonable description. (This paper may be covered in Caldararu's Spring 2017 topics course.)<br />
__NOTOC__<br />
<br />
== Spring 2017 ==<br />
<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#A6B658" width="300" align="center"|'''Speaker'''<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title (click to see abstract)'''<br />
|-<br />
| bgcolor="#E0E0E0"| January 25<br />
| bgcolor="#C6D46E"| Nathan Clement<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#January 25 | Hodge to de Rham, part one]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 1<br />
| bgcolor="#C6D46E"| Nathan Clement<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 1 | Hodge to de Rham, part two]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 8 <br />
| bgcolor="#C6D46E"| Dima Arinkin<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 8 | Motivated introduction to geometric Langlands]] <br />
|-<br />
| bgcolor="#E0E0E0"| February 15<br />
| bgcolor="#C6D46E"| No Talk<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 15 | We Failed, We All Failed]] <br />
|-<br />
| bgcolor="#E0E0E0"| February 22<br />
| bgcolor="#C6D46E"| No Talk<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 22 | We Failed, We All Failed Pt. 2]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 1<br />
| bgcolor="#C6D46E"| Brandon Boggess<br />
| bgcolor="#BCE2FE"| [[Graduate Algebraic Geometry Seminar#March 1 | An Introduction to Mori's Program]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 8<br />
| bgcolor="#C6D46E"| David Wagner<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 8| Picard groups of moduli problems]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 15<br />
| bgcolor="#C6D46E"| No Talk<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 15| We Failed, We All Failed Pt. 3]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 22<br />
| bgcolor="#C6D46E"| Spring Break<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 22 | No Seminar. ]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 29<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"| [[Graduate Algebraic Geometry Seminar#March 29| TBD]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 5<br />
| bgcolor="#C6D46E"| John Wiltshire-Gordon<br />
| bgcolor="#BCE2FE"| [[Graduate Algebraic Geometry Seminar#April 5| TBD]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 12<br />
| bgcolor="#C6D46E"| Wendy Cheng<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 12| Boij-S<math>\"o</math>oderberg Theory]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 19<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 19| TBD ]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 26<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 26| TBD ]] <br />
|}<br />
</center><br />
<br />
== January 25 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Nathan Clement'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Hodge to de Rham, part one<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: I will use the magic of differential calculus in positive characteristic to prove an important result in the cohomology of smooth varieties in positive characteristic. The techniques I'll use are mainly elementary, but prior experience with differential forms, the Frobenius homomorphism, and a little homological algebra will help. This is the setup, come back next week for the punchline!<br />
|} <br />
</center><br />
<br />
== February 1 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Nathan Clement'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Hodge to de Rham, part two<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: Having proved an important result in positive characteristic, I'll give a nifty argument to leverage the positive characteristic statement into a characteristic zero result. I'll talk about some cohomology comparison theorems, and we'll see that all this business in positive characteristic provides an alternate proof to the classic Hodge decomposition theorem for cohomology.<br />
|} <br />
</center><br />
<br />
== February 8 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Dima Arinkin'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Motivated introduction to geometric Langlands<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: The Langlands program originated from bold conjectures formulated by Robert Langlands in the late 1960's. The conjectures <br />
combine number theory and representation theory in a highly unexpected way. The geometric Langlands program adds algebro-<br />
geometric methods (and, sometimes, physics) to the mix.<br />
<br />
This interplay of ideas creates a beautiful picture... and a very challenging subject. In my talk, I will suggest one possible <br />
way to approach the area. I plan to focus on questions rather than answers: the goal is to explain how (some of) the questions fit together,<br />
and to tell you the keywords that go into the answers. <br />
|} <br />
</center><br />
<br />
== February 15 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''n/a'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: No Talk<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: n/a<br />
|} <br />
</center><br />
<br />
== February 22 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''n/a'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: No Talk<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: n/a<br />
|} <br />
</center><br />
<br />
== March 1 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Brandon Boggess'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: An Introduction to Mori's Program<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: In studying the birational classification of varieties, one plan of attack is to construct a "simplest" variety in each birational equivalence class. We will see how this approach gives a full structure theory for surfaces, and investigate what new challenges arise in the case of threefolds.<br />
<br />
|} <br />
</center><br />
<br />
== March 8 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''David Wagner'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Picard groups of moduli problems<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: In a pastoral traipse, I will discuss some lower bounds on the time it takes an average adult to drink a medium Frosty from Wendy's, including some results of my own about making these bounds sharp. Time permitting, I will also explain how this theory can be extended to study the ingestion of M&M's, a connection previously unkown.<br />
|} <br />
</center><br />
<br />
== March 15 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''n/'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: No Talk<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: n/a<br />
|} <br />
</center><br />
<br />
== March 22 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Spring Break'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: No Seminar.<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: n/a<br />
|} <br />
</center><br />
<br />
== March 29 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBA'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
== April 5 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''John Wiltshire-Gordon'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
== April 12 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBA'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center> <br />
<br />
== April 19 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBA'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center> <br />
<br />
== April 26 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBA'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center> <br />
<br />
== Organizers' Contact Info ==<br />
[http://www.math.wisc.edu/~djbruce DJ Bruce]<br />
<br />
[http://www.math.wisc.edu/~clement Nathan Clement]<br />
<br />
[https://www.math.wisc.edu/~moises Moisés Herradón Cueto]<br />
<br />
== Past Semesters ==<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2016 Fall 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2016 Spring 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_(Fall_2015) Fall 2015]</div>Cchenghttps://wiki.math.wisc.edu/index.php?title=Graduate_Algebraic_Geometry_Seminar_Fall_2017&diff=13548Graduate Algebraic Geometry Seminar Fall 20172017-03-24T03:04:50Z<p>Ccheng: </p>
<hr />
<div>'''<br />
'''When:''' Wednesdays 4:40pm<br />
<br />
'''Where:'''Van Vleck B321 (Spring 2017)<br />
[[Image:cat.jpg|thumb|220px| | Lizzie the OFFICIAL mascot of GAGS!!]]<br />
<br />
'''Who:''' YOU!!<br />
<br />
'''Why:''' The purpose of this seminar is to learn algebraic geometry by giving and listening to talks in a informal setting. Talks are typically accessible to beginning graduate students and take many different forms. Sometimes people present an interesting paper they find. Other times people give a prep talk for the Friday Algebraic Geometry Seminar. Other times people give a series of talks on a topic they have been studying in-depth.<br />
<br />
'''How:'''If you want to get emails regarding time, place, and talk topics ('''which are often assigned quite last minute''') add yourself to the gags mailing list: gags@lists.wisc.edu. The list registration page is [https://admin.lists.wisc.edu/index.php?p=11&l=gags here].<br />
'''<br />
<br />
<br />
<br />
<br />
<br />
== Give a talk! ==<br />
We need volunteers to give talks this semester. If you're interested contact [mailto:djbruce@math.wisc.edu DJ], or just add yourself to the list (though in that case we might move your talk later without your permission). Beginning graduate students are particularly encouraged to give a talk, since it's a great way to get your feet wet with the material.<br />
<br />
<br />
== Wish List ==<br />
Here are the topics we're '''DYING''' to learn about! Please consider looking into one of these topics and giving one or two GAGS talks.<br />
<br />
===Specifically Vague Topics===<br />
* D-modules 101: basics of D-modules, equivalence between left and right D-modules, pullbacks, pushforwards, maybe the Gauss-Manin Connection. Claude Sabbah's introduction to the subject could be a good place to start.<br />
<br />
* Sheaf operations on D-modules (the point is that then you can get a Fourier-Mukai transform between certain O-modules and certain D-modules, which is more or less how geometric Langlands is supposed to work)<br />
<br />
===Famous Theorems===<br />
<br />
===Interesting Papers & Books===<br />
* ''Symplectic structure of the moduli space of sheaves on an abelian or K3 surface'' - Shigeru Mukai.<br />
<br />
* ''Residues and Duality'' - Robin Hatshorne.<br />
** Have you heard of Serre Duality? Would you like to really understand the nuts and bolts of it and its generalizations? If so this book is for you. (You wouldn't need to read the whole book to give a talk ;).)<br />
<br />
* ''Coherent sheaves on P^n and problems in linear algebra'' - A. A. Beilinson.<br />
** In this two page paper constructs the semi-orthogonal decomposition of the derived category of coherent sheaves on projective space. (This topic is very important, and there are a ton of other resources for this result and the general theory of derived categories.)<br />
<br />
* ''Frobenius splitting and cohomology vanishing for Schubert varieties'' - V.B. Mehta and A. Ramanathan.<br />
** In characteristic p the fact that (x+y)^p=x^p+y^p means that one has the Frobenius morphism, which sends f to f^p. In this paper the authors introduce the notion of what it means for a variety to be Frobenius split, and use this to prove certain cohomologcal vanishing results for Schubert varieties. Since then Frobenius splitting -- and its related cousins (F-regularity, strong F-regularity, F-purity, etc.) have played large roles in geometry and algebra in characteristic p. This is a good place to get a sense for what kicked all this stuff off! <br />
<br />
* ''Schubert Calculus'' - S. L. Kleiman and Dan Laksov.<br />
** An introduction to Schubert calculus suitable for those of all ages. I am told the paper essentially only uses linear algebra!<br />
<br />
* ''Rational Isogenies of Prime Degree'' - Barry Mazur.<br />
** In this paper Mazur classifies all isogenies of rational elliptic curves of prime order. As a result of this he deduces his famous result that the torsion subgroup of an elliptic curve (over Q) is one of 15 abelian groups. This definitely stares into the land of number theory, but certainly would still be of interest to many.<br />
<br />
* ''Esquisse d’une programme'' - Alexander Grothendieck.<br />
** Originating from a grant proposal in the mid 1980's this famous paper outlines a tantalizing research program, which seeks to tie numerous different areas of math (algebraic geometry, Teichmuller theory, Galois theory, etc.) together. This is where Grothendieck introduced his famous Lego game and dessin d'enfant. While just a research proposal this paper has seemingly inspired a ton of cool math, and will allow you to "blow peoples’ minds". (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Géométrie algébraique et géométrie analytique'' - J.P. Serre.<br />
** A projective variety X over the complex numbers has two lives, an algebraic and an analytic, depending on which topology one wishes to work with. That is one can think about X as a complex manifold and work with holomorphic functions or as an algebraic variety and work with regular functions. Hence to any complex projective variety we have two sheaf theories and as a result two cohomology theories. In this famous paper Serre compares these two and shows they are in fact the same. (''Note: This is a super fundamental result that is used all the time; normally in the following way: Uhh... What do you mean by cohomology? Well by GAGA or something it doesn't really mater.) (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Limit linear series: Basic theory''- David Eisenbud and Joe Harris.<br />
** One of the more profitable tools -- especially when studying moduli spaces -- in a geometers tool box is the theory of degenerations. However, sometimes we care about more than just the variety we are degenerating and want to keep track of things like vector/line bundles. In this paper Eisenbud and Harris develop the theory of degenerating a curve together with a linear series. From this they prove a ton of cool results: M_g is of general type for g>24, Brill-Noether theory, etc.<br />
<br />
* ''Picard Groups of Moduli Problems'' - David Mumford.<br />
** This paper is essentially the origin of algebraic stacks.<br />
<br />
* ''The Structure of Algebraic Threefolds: An Introduction to Mori's Program'' - Janos Kollar<br />
** This paper is an introduction to Mori's famous ``minimal model'' program, which is a far reaching program seeking to understand the birational geometry of higher dimensional varieties. <br />
<br />
* ''Cayley-Bacharach Formulas'' - Qingchun Ren, Jürgen Richter-Gebert, Bernd Sturmfels.<br />
** A classical result we all learn in a first semester of algebraic geometry is that 5 points in the plane (in general position) determine a unique plane conic. One can similarly show that 9 (general) points in the plane determine a unique plane cubic curve. This paper tries to answer the question: ``What is equation for this cubic curve?''.<br />
<br />
* ''On Varieties of Minimal Degree (A Centennial Approach)'' - David Eisenbud and Joe Harris.<br />
** Suppose X is a projective variety embedded in projective space so that X is not contained in any hyperplane. By projecting from general points one can see that the degree of X is at least codim(X)+1. This paper discusses the classification of varieties that achieve this lower degree bound i.e. varieties of minimal degree. This topic is quite classical and the paper seems to contain a nice mixture of classical and modern geometry.<br />
<br />
* ''The Gromov-Witten potential associated to a TCFT'' - Kevin J. Costello.<br />
** This seems incredibly interesting, but fairing warning this paper has been described as ''highly technical'', which considering it uses A-infinity algebras and the derived category of a Calabi-Yau seems like a reasonable description. (This paper may be covered in Caldararu's Spring 2017 topics course.)<br />
__NOTOC__<br />
<br />
== Spring 2017 ==<br />
<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#A6B658" width="300" align="center"|'''Speaker'''<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title (click to see abstract)'''<br />
|-<br />
| bgcolor="#E0E0E0"| January 25<br />
| bgcolor="#C6D46E"| Nathan Clement<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#January 25 | Hodge to de Rham, part one]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 1<br />
| bgcolor="#C6D46E"| Nathan Clement<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 1 | Hodge to de Rham, part two]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 8 <br />
| bgcolor="#C6D46E"| Dima Arinkin<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 8 | Motivated introduction to geometric Langlands]] <br />
|-<br />
| bgcolor="#E0E0E0"| February 15<br />
| bgcolor="#C6D46E"| No Talk<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 15 | We Failed, We All Failed]] <br />
|-<br />
| bgcolor="#E0E0E0"| February 22<br />
| bgcolor="#C6D46E"| No Talk<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 22 | We Failed, We All Failed Pt. 2]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 1<br />
| bgcolor="#C6D46E"| Brandon Boggess<br />
| bgcolor="#BCE2FE"| [[Graduate Algebraic Geometry Seminar#March 1 | An Introduction to Mori's Program]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 8<br />
| bgcolor="#C6D46E"| David Wagner<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 8| Picard groups of moduli problems]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 15<br />
| bgcolor="#C6D46E"| No Talk<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 15| We Failed, We All Failed Pt. 3]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 22<br />
| bgcolor="#C6D46E"| Spring Break<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 22 | No Seminar. ]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 29<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"| [[Graduate Algebraic Geometry Seminar#March 29| TBD]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 5<br />
| bgcolor="#C6D46E"| John Wiltshire-Gordon<br />
| bgcolor="#BCE2FE"| [[Graduate Algebraic Geometry Seminar#April 5| TBD]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 12<br />
| bgcolor="#C6D46E"| Wendy Cheng<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 12| Boij-S\"oderberg Theory]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 19<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 19| TBD ]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 26<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 26| TBD ]] <br />
|}<br />
</center><br />
<br />
== January 25 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Nathan Clement'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Hodge to de Rham, part one<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: I will use the magic of differential calculus in positive characteristic to prove an important result in the cohomology of smooth varieties in positive characteristic. The techniques I'll use are mainly elementary, but prior experience with differential forms, the Frobenius homomorphism, and a little homological algebra will help. This is the setup, come back next week for the punchline!<br />
|} <br />
</center><br />
<br />
== February 1 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Nathan Clement'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Hodge to de Rham, part two<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: Having proved an important result in positive characteristic, I'll give a nifty argument to leverage the positive characteristic statement into a characteristic zero result. I'll talk about some cohomology comparison theorems, and we'll see that all this business in positive characteristic provides an alternate proof to the classic Hodge decomposition theorem for cohomology.<br />
|} <br />
</center><br />
<br />
== February 8 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Dima Arinkin'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Motivated introduction to geometric Langlands<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: The Langlands program originated from bold conjectures formulated by Robert Langlands in the late 1960's. The conjectures <br />
combine number theory and representation theory in a highly unexpected way. The geometric Langlands program adds algebro-<br />
geometric methods (and, sometimes, physics) to the mix.<br />
<br />
This interplay of ideas creates a beautiful picture... and a very challenging subject. In my talk, I will suggest one possible <br />
way to approach the area. I plan to focus on questions rather than answers: the goal is to explain how (some of) the questions fit together,<br />
and to tell you the keywords that go into the answers. <br />
|} <br />
</center><br />
<br />
== February 15 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''n/a'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: No Talk<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: n/a<br />
|} <br />
</center><br />
<br />
== February 22 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''n/a'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: No Talk<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: n/a<br />
|} <br />
</center><br />
<br />
== March 1 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Brandon Boggess'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: An Introduction to Mori's Program<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: In studying the birational classification of varieties, one plan of attack is to construct a "simplest" variety in each birational equivalence class. We will see how this approach gives a full structure theory for surfaces, and investigate what new challenges arise in the case of threefolds.<br />
<br />
|} <br />
</center><br />
<br />
== March 8 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''David Wagner'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Picard groups of moduli problems<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: In a pastoral traipse, I will discuss some lower bounds on the time it takes an average adult to drink a medium Frosty from Wendy's, including some results of my own about making these bounds sharp. Time permitting, I will also explain how this theory can be extended to study the ingestion of M&M's, a connection previously unkown.<br />
|} <br />
</center><br />
<br />
== March 15 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''n/'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: No Talk<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: n/a<br />
|} <br />
</center><br />
<br />
== March 22 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Spring Break'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: No Seminar.<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: n/a<br />
|} <br />
</center><br />
<br />
== March 29 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBA'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
== April 5 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''John Wiltshire-Gordon'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
== April 12 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBA'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center> <br />
<br />
== April 19 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBA'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center> <br />
<br />
== April 26 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBA'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center> <br />
<br />
== Organizers' Contact Info ==<br />
[http://www.math.wisc.edu/~djbruce DJ Bruce]<br />
<br />
[http://www.math.wisc.edu/~clement Nathan Clement]<br />
<br />
[https://www.math.wisc.edu/~moises Moisés Herradón Cueto]<br />
<br />
== Past Semesters ==<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2016 Fall 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2016 Spring 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_(Fall_2015) Fall 2015]</div>Cchenghttps://wiki.math.wisc.edu/index.php?title=Graduate_Algebraic_Geometry_Seminar_Fall_2017&diff=11893Graduate Algebraic Geometry Seminar Fall 20172016-05-02T03:14:39Z<p>Ccheng: </p>
<hr />
<div>'''<br />
'''When:''' Wednesdays 4:00pm<br />
<br />
'''Where:'''Van Vleck B139<br />
[[Image:cat.jpg|thumb|220px| | Lizzie the OFFICIAL mascot of GAGS!!]]<br />
<br />
'''Who:''' YOU!!<br />
<br />
'''Why:''' The purpose of this seminar is to learn algebraic geometry by giving and listening to talks in a informal setting. Talks are typically accessible to beginning graduate students and take many different forms. Sometimes people present an interesting paper they find. Other times people give a prep talk for the Friday Algebraic Geometry Seminar. Other times people give a series of talks on a topic they have been studying in-depth.<br />
<br />
'''How:'''If you want to get emails regarding time, place, and talk topics ('''which are often assigned quite last minute''') add yourself to the gags mailing list: gags@lists.wisc.edu. The list registration page is [https://admin.lists.wisc.edu/index.php?p=11&l=gags here].<br />
'''<br />
<br />
<br />
<br />
<br />
<br />
== Give a talk! ==<br />
We need volunteers to give talks this semester. If you're interested contact [mailto:djbruce@math.wisc.edu DJ], or just add yourself to the list (though in that case we might move your talk later without your permission). Beginning graduate students are particularly encouraged to give a talk, since it's a great way to get your feet wet with the material.<br />
<br />
<br />
== Wish List ==<br />
If there is a subject or a paper which you'd like to see someone give a talk on, add it to this list. If you want to give a talk and can't find a topic, try one from this list.<br />
<br />
* Sheaf operations on D-modules (the point is that then you can get a Fourier-Mukai transform between certain O-modules and certain D-modules, which is more or less how geometric Langlands is supposed to work)<br />
<br />
* A careful explanation of the correspondence between graded modules and sheaves on projective varieties.<br />
<br />
* Braverman and Bezrukavnikov: geometric Langlands correspondence for D-modules in prime characteristic: the GL(n) case (Note: this title sounds tough but prime characteristic makes things ''easier'')<br />
<br />
* Homological projective duality<br />
<br />
* The orbit method (for classifying representations of a Lie group)<br />
<br />
* Kaledin: geometry and topology of symplectic resolutions<br />
<br />
* Kashiwara: D-modules and representation theory of Lie groups (Note: Check out that diagram on page 2!)<br />
<br />
* Geometric complexity theory, maybe something like arXiv:1508.05788.<br />
<br />
__NOTOC__<br />
<br />
== Spring 2016 ==<br />
<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#A6B658" width="300" align="center"|'''Speaker'''<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title (click to see abstract)'''<br />
|-<br />
| bgcolor="#E0E0E0"| January 20<br />
| bgcolor="#C6D46E"| Jay Yang<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#January 20| Tropical Geometry II]]<br />
|-<br />
| bgcolor="#E0E0E0"| January 27<br />
| bgcolor="#C6D46E"| Jay Yang<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#January 27| Tropical Geometry III ]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 3<br />
| bgcolor="#C6D46E"| Ed Dewey<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 3| Derived Category of Projective Space ]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 10 <br />
| bgcolor="#C6D46E"| Ed Dewey<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 10| More Derived Category of Projective Space ]] <br />
|-<br />
| bgcolor="#E0E0E0"| February 17<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 17| TBD ]] <br />
|-<br />
| bgcolor="#E0E0E0"| February 24<br />
| bgcolor="#C6D46E"| DJ Bruce<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 24| Divisors and Stuff I]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 2<br />
| bgcolor="#C6D46E"| DJ Bruce<br />
| bgcolor="#BCE2FE"| [[Graduate Algebraic Geometry Seminar#March 2| Divisors and Stuff II]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 9<br />
| bgcolor="#C6D46E"| DJ Bruce<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 9| Divisors and Stuff III]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 16<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 16| TBD]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 23<br />
| bgcolor="#C6D46E"| N/A<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 23| No GAGS This Week ]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 30<br />
| bgcolor="#C6D46E"| Daniel Hast<br />
| bgcolor="#BCE2FE"| [[Graduate Algebraic Geometry Seminar#March 30| Jacobians, path integrals, and fundamental groups of curves I]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 6<br />
| bgcolor="#C6D46E"| Daniel Hast<br />
| bgcolor="#BCE2FE"| [[Graduate Algebraic Geometry Seminar#April 6| Jacobians, path integrals, and fundamental groups of curves II]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 13<br />
| bgcolor="#C6D46E"| Jason Steinberg<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 13|Something Something Shimura Varieties ]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 20<br />
| bgcolor="#C6D46E"| Quinton Westrich<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 20| Projective Duality ]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 27<br />
| bgcolor="#C6D46E"| Zachary Charles<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 27| Polynomial systems, toric geometry, and Newton polytopes]] <br />
|-<br />
| bgcolor="#E0E0E0"| May 4<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#May 4| TBD ]] <br />
|-<br />
| bgcolor="#E0E0E0"| May 11<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#May 11| TBD ]] <br />
|}<br />
</center><br />
<br />
== January 20 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Jay Yang'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Tropical Geometry II<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: Previously we discussed the basic definitions of tropical geometry, and<br />
the connection to algebraic geometry. Now we use this to count curves<br />
through points on P^2. This is a well known result initially proven<br />
without the use of tropical tools. But using tropical tools we can give<br />
a proof that relies on the combinatorics of lattice paths. I will begin<br />
with a review of some facts from tropical geometry that we need for this<br />
proof. <br />
|} <br />
</center><br />
<br />
== January 27 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
== February 3 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Ed Dewey'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Derived Category of Projective Space<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: I will talk about the derived category of projective space, covering mostly the same material that Andrei did at the end of his homological algebra course, but at a more leisurely pace. My main reference is the ''Skimming.'' <br />
|}<br />
</center><br />
<br />
== February 10 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Ed Dewey'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: More Derived Category of Projective Space<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: I will explain in what sense we now "know" the derived category of projective space from Beilinson's result. There is a very nice answer in terms of quivers but I got distracted by another, much less efficient but maybe more flexible approach using dg categories, so that is what we will do. If my understanding permits, we will also talk about the derived category of a projective space bundle.<br />
|} <br />
</center><br />
<br />
== February 17 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD <br />
|} <br />
</center><br />
== February 24 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''DJ Bruce'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Divisors and Stuff I<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
<br />
|} <br />
</center><br />
<br />
== March 2 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''DJ Bruce'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Divisors and Stuff II<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
== March 9 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''DJ Bruce'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Divisors and Stuff III<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
== March 16 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
<br />
|} <br />
</center><br />
<br />
== March 23 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''No Seminar This Week'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: N/A<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: Enjoy your break!<br />
|} <br />
</center><br />
<br />
== March 30 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Daniel Hast'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Jacobians, path integrals, and fundamental groups of curves I<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
== April 6 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Daniel Hast'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Jacobians, path integrals, and fundamental groups of curves II<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
== April 13 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Jason Steinberg '''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Something Something Shimura Varieties<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
|} <br />
</center><br />
<br />
== April 20 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Quinton Westrich'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Projective Duality<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: Intro to discriminants and duals of projective varieties. My field will be C.<br />
|} <br />
</center><br />
<br />
== April 27 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Zachary Charles'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Polynomial systems, toric geometry, and Newton polytopes<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: While the Bezout bound generically gives us the number of roots of a polynomial system in projective space, often much more can be said about specific systems in affine space. Kushnirenko's Theorem (and later Bernstein's theorem) gives better bounds for "sparse" systems of polynomials. These bounds are based on the volume of Newton polytopes. I will prove Kushnirenko's theorem using ideas from toric geometry, commutative algebra, and the geometry of polytopes. If time permits we will give applications of this theorem to power systems.<br />
|} <br />
</center><br />
<br />
== May 4 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
== May 11 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
== Organizers' Contact Info ==<br />
[http://www.math.wisc.edu/~djbruce DJ Bruce]<br />
<br />
[http://www.math.wisc.edu/~clement Nathan Clement]<br />
<br />
[http://www.math.wisc.edu/~dewey/ Ed Dewey]<br />
<br />
== Past Semesters ==<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_(Fall_2015) Fall 2015]</div>Cchenghttps://wiki.math.wisc.edu/index.php?title=Graduate_Algebraic_Geometry_Seminar_Fall_2017&diff=11892Graduate Algebraic Geometry Seminar Fall 20172016-04-30T21:22:04Z<p>Ccheng: </p>
<hr />
<div>'''<br />
'''When:''' Wednesdays 4:00pm<br />
<br />
'''Where:'''Van Vleck B139<br />
[[Image:cat.jpg|thumb|220px| | Lizzie the OFFICIAL mascot of GAGS!!]]<br />
<br />
'''Who:''' YOU!!<br />
<br />
'''Why:''' The purpose of this seminar is to learn algebraic geometry by giving and listening to talks in a informal setting. Talks are typically accessible to beginning graduate students and take many different forms. Sometimes people present an interesting paper they find. Other times people give a prep talk for the Friday Algebraic Geometry Seminar. Other times people give a series of talks on a topic they have been studying in-depth.<br />
<br />
'''How:'''If you want to get emails regarding time, place, and talk topics ('''which are often assigned quite last minute''') add yourself to the gags mailing list: gags@lists.wisc.edu. The list registration page is [https://admin.lists.wisc.edu/index.php?p=11&l=gags here].<br />
'''<br />
<br />
<br />
<br />
<br />
<br />
== Give a talk! ==<br />
We need volunteers to give talks this semester. If you're interested contact [mailto:djbruce@math.wisc.edu DJ], or just add yourself to the list (though in that case we might move your talk later without your permission). Beginning graduate students are particularly encouraged to give a talk, since it's a great way to get your feet wet with the material.<br />
<br />
<br />
== Wish List ==<br />
If there is a subject or a paper which you'd like to see someone give a talk on, add it to this list. If you want to give a talk and can't find a topic, try one from this list.<br />
<br />
* Sheaf operations on D-modules (the point is that then you can get a Fourier-Mukai transform between certain O-modules and certain D-modules, which is more or less how geometric Langlands is supposed to work)<br />
<br />
* A careful explanation of the correspondence between graded modules and sheaves on projective varieties.<br />
<br />
* Braverman and Bezrukavnikov: geometric Langlands correspondence for D-modules in prime characteristic: the GL(n) case (Note: this title sounds tough but prime characteristic makes things ''easier'')<br />
<br />
* Homological projective duality<br />
<br />
* The orbit method (for classifying representations of a Lie group)<br />
<br />
* Kaledin: geometry and topology of symplectic resolutions<br />
<br />
* Kashiwara: D-modules and representation theory of Lie groups (Note: Check out that diagram on page 2!)<br />
<br />
* Geometric complexity theory, maybe something like arXiv:1508.05788.<br />
<br />
__NOTOC__<br />
<br />
== Spring 2016 ==<br />
<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#A6B658" width="300" align="center"|'''Speaker'''<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title (click to see abstract)'''<br />
|-<br />
| bgcolor="#E0E0E0"| January 20<br />
| bgcolor="#C6D46E"| Jay Yang<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#January 20| Tropical Geometry II]]<br />
|-<br />
| bgcolor="#E0E0E0"| January 27<br />
| bgcolor="#C6D46E"| Jay Yang<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#January 27| Tropical Geometry III ]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 3<br />
| bgcolor="#C6D46E"| Ed Dewey<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 3| Derived Category of Projective Space ]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 10 <br />
| bgcolor="#C6D46E"| Ed Dewey<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 10| More Derived Category of Projective Space ]] <br />
|-<br />
| bgcolor="#E0E0E0"| February 17<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 17| TBD ]] <br />
|-<br />
| bgcolor="#E0E0E0"| February 24<br />
| bgcolor="#C6D46E"| DJ Bruce<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 24| Divisors and Stuff I]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 2<br />
| bgcolor="#C6D46E"| DJ Bruce<br />
| bgcolor="#BCE2FE"| [[Graduate Algebraic Geometry Seminar#March 2| Divisors and Stuff II]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 9<br />
| bgcolor="#C6D46E"| DJ Bruce<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 9| Divisors and Stuff III]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 16<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 16| TBD]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 23<br />
| bgcolor="#C6D46E"| N/A<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 23| No GAGS This Week ]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 30<br />
| bgcolor="#C6D46E"| Daniel Hast<br />
| bgcolor="#BCE2FE"| [[Graduate Algebraic Geometry Seminar#March 30| Jacobians, path integrals, and fundamental groups of curves I]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 6<br />
| bgcolor="#C6D46E"| Daniel Hast<br />
| bgcolor="#BCE2FE"| [[Graduate Algebraic Geometry Seminar#April 6| Jacobians, path integrals, and fundamental groups of curves II]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 13<br />
| bgcolor="#C6D46E"| Jason Steinberg<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 13|Something Something Shimura Varieties ]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 20<br />
| bgcolor="#C6D46E"| Quinton Westrich<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 20| Projective Duality ]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 27<br />
| bgcolor="#C6D46E"| Zachary Charles<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 27| Polynomial systems, toric geometry, and Newton polytopes]] <br />
|-<br />
| bgcolor="#E0E0E0"| May 4<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#May 4| TBD ]] <br />
|-<br />
| bgcolor="#E0E0E0"| May 11<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#May 11| TBD ]] <br />
|}<br />
</center><br />
<br />
== January 20 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Jay Yang'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Tropical Geometry II<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: Previously we discussed the basic definitions of tropical geometry, and<br />
the connection to algebraic geometry. Now we use this to count curves<br />
through points on P^2. This is a well known result initially proven<br />
without the use of tropical tools. But using tropical tools we can give<br />
a proof that relies on the combinatorics of lattice paths. I will begin<br />
with a review of some facts from tropical geometry that we need for this<br />
proof. <br />
|} <br />
</center><br />
<br />
== January 27 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
== February 3 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Ed Dewey'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Derived Category of Projective Space<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: I will talk about the derived category of projective space, covering mostly the same material that Andrei did at the end of his homological algebra course, but at a more leisurely pace. My main reference is the ''Skimming.'' <br />
|}<br />
</center><br />
<br />
== February 10 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Ed Dewey'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: More Derived Category of Projective Space<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: I will explain in what sense we now "know" the derived category of projective space from Beilinson's result. There is a very nice answer in terms of quivers but I got distracted by another, much less efficient but maybe more flexible approach using dg categories, so that is what we will do. If my understanding permits, we will also talk about the derived category of a projective space bundle.<br />
|} <br />
</center><br />
<br />
== February 17 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD <br />
|} <br />
</center><br />
== February 24 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''DJ Bruce'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Divisors and Stuff I<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
<br />
|} <br />
</center><br />
<br />
== March 2 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''DJ Bruce'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Divisors and Stuff II<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
== March 9 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''DJ Bruce'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Divisors and Stuff III<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
== March 16 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
<br />
|} <br />
</center><br />
<br />
== March 23 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''No Seminar This Week'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: N/A<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: Enjoy your break!<br />
|} <br />
</center><br />
<br />
== March 30 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Daniel Hast'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Jacobians, path integrals, and fundamental groups of curves I<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
== April 6 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Daniel Hast'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Jacobians, path integrals, and fundamental groups of curves II<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
== April 13 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Jason Steinberg '''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Something Something Shimura Varieties<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
|} <br />
</center><br />
<br />
== April 20 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Quinton Westrich'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Projective Duality<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: Intro to discriminants and duals of projective varieties. My field will be C.<br />
|} <br />
</center><br />
<br />
== April 27 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Zachary Charles'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Polynomial systems, toric geometry, and Newton polytopes<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: While the Bezout bound generically gives us the number of roots of a polynomial system in projective space, often much more can be said about specific systems in affine space. Kushnirenko's Theorem (and later Bernstein's theorem) gives better bounds for "sparse" systems of polynomials. These bounds are based on the volume of Newton polytopes. I will prove Kushnirenko's theorem using ideas from toric geometry, commutative algebra, and the geometry of polytopes. If time permits we will give applications of this theorem to power systems.<br />
|} <br />
</center><br />
<br />
== May 4 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Wendy Cheng'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
== May 11 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
== Organizers' Contact Info ==<br />
[http://www.math.wisc.edu/~djbruce DJ Bruce]<br />
<br />
[http://www.math.wisc.edu/~clement Nathan Clement]<br />
<br />
[http://www.math.wisc.edu/~dewey/ Ed Dewey]<br />
<br />
== Past Semesters ==<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_(Fall_2015) Fall 2015]</div>Cchenghttps://wiki.math.wisc.edu/index.php?title=Graduate_Algebraic_Geometry_Seminar_Fall_2017&diff=11867Graduate Algebraic Geometry Seminar Fall 20172016-04-23T21:34:32Z<p>Ccheng: </p>
<hr />
<div>'''<br />
'''When:''' Wednesdays 4:00pm<br />
<br />
'''Where:'''Van Vleck B139<br />
[[Image:cat.jpg|thumb|220px| | Lizzie the OFFICIAL mascot of GAGS!!]]<br />
<br />
'''Who:''' YOU!!<br />
<br />
'''Why:''' The purpose of this seminar is to learn algebraic geometry by giving and listening to talks in a informal setting. Talks are typically accessible to beginning graduate students and take many different forms. Sometimes people present an interesting paper they find. Other times people give a prep talk for the Friday Algebraic Geometry Seminar. Other times people give a series of talks on a topic they have been studying in-depth.<br />
<br />
'''How:'''If you want to get emails regarding time, place, and talk topics ('''which are often assigned quite last minute''') add yourself to the gags mailing list: gags@lists.wisc.edu. The list registration page is [https://admin.lists.wisc.edu/index.php?p=11&l=gags here].<br />
'''<br />
<br />
<br />
<br />
<br />
<br />
== Give a talk! ==<br />
We need volunteers to give talks this semester. If you're interested contact [mailto:djbruce@math.wisc.edu DJ], or just add yourself to the list (though in that case we might move your talk later without your permission). Beginning graduate students are particularly encouraged to give a talk, since it's a great way to get your feet wet with the material.<br />
<br />
<br />
== Wish List ==<br />
If there is a subject or a paper which you'd like to see someone give a talk on, add it to this list. If you want to give a talk and can't find a topic, try one from this list.<br />
<br />
* Sheaf operations on D-modules (the point is that then you can get a Fourier-Mukai transform between certain O-modules and certain D-modules, which is more or less how geometric Langlands is supposed to work)<br />
<br />
* A careful explanation of the correspondence between graded modules and sheaves on projective varieties.<br />
<br />
* Braverman and Bezrukavnikov: geometric Langlands correspondence for D-modules in prime characteristic: the GL(n) case (Note: this title sounds tough but prime characteristic makes things ''easier'')<br />
<br />
* Homological projective duality<br />
<br />
* The orbit method (for classifying representations of a Lie group)<br />
<br />
* Kaledin: geometry and topology of symplectic resolutions<br />
<br />
* Kashiwara: D-modules and representation theory of Lie groups (Note: Check out that diagram on page 2!)<br />
<br />
* Geometric complexity theory, maybe something like arXiv:1508.05788.<br />
<br />
__NOTOC__<br />
<br />
== Spring 2016 ==<br />
<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#A6B658" width="300" align="center"|'''Speaker'''<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title (click to see abstract)'''<br />
|-<br />
| bgcolor="#E0E0E0"| January 20<br />
| bgcolor="#C6D46E"| Jay Yang<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#January 20| Tropical Geometry II]]<br />
|-<br />
| bgcolor="#E0E0E0"| January 27<br />
| bgcolor="#C6D46E"| Jay Yang<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#January 27| Tropical Geometry III ]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 3<br />
| bgcolor="#C6D46E"| Ed Dewey<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 3| Derived Category of Projective Space ]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 10 <br />
| bgcolor="#C6D46E"| Ed Dewey<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 10| More Derived Category of Projective Space ]] <br />
|-<br />
| bgcolor="#E0E0E0"| February 17<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 17| TBD ]] <br />
|-<br />
| bgcolor="#E0E0E0"| February 24<br />
| bgcolor="#C6D46E"| DJ Bruce<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 24| Divisors and Stuff I]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 2<br />
| bgcolor="#C6D46E"| DJ Bruce<br />
| bgcolor="#BCE2FE"| [[Graduate Algebraic Geometry Seminar#March 2| Divisors and Stuff II]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 9<br />
| bgcolor="#C6D46E"| DJ Bruce<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 9| Divisors and Stuff III]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 16<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 16| TBD]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 23<br />
| bgcolor="#C6D46E"| N/A<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 23| No GAGS This Week ]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 30<br />
| bgcolor="#C6D46E"| Daniel Hast<br />
| bgcolor="#BCE2FE"| [[Graduate Algebraic Geometry Seminar#March 30| Jacobians, path integrals, and fundamental groups of curves I]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 6<br />
| bgcolor="#C6D46E"| Daniel Hast<br />
| bgcolor="#BCE2FE"| [[Graduate Algebraic Geometry Seminar#April 6| Jacobians, path integrals, and fundamental groups of curves II]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 13<br />
| bgcolor="#C6D46E"| Jason Steinberg<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 13|Something Something Shimura Varieties ]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 20<br />
| bgcolor="#C6D46E"| Quinton Westrich<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 20| Projective Duality ]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 27<br />
| bgcolor="#C6D46E"| Zachary Charles<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 27| Polynomial systems, toric geometry, and Newton polytopes]] <br />
|-<br />
| bgcolor="#E0E0E0"| May 4<br />
| bgcolor="#C6D46E"| Wendy Cheng<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#May 4| Cohomology of Sheaves, Affine Scheme and Projective Space (Cancelled due to time conflict with Peter Sarnak's talk)]] <br />
|-<br />
| bgcolor="#E0E0E0"| May 11<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#May 11| TBD ]] <br />
|}<br />
</center><br />
<br />
== January 20 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Jay Yang'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Tropical Geometry II<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: Previously we discussed the basic definitions of tropical geometry, and<br />
the connection to algebraic geometry. Now we use this to count curves<br />
through points on P^2. This is a well known result initially proven<br />
without the use of tropical tools. But using tropical tools we can give<br />
a proof that relies on the combinatorics of lattice paths. I will begin<br />
with a review of some facts from tropical geometry that we need for this<br />
proof. <br />
|} <br />
</center><br />
<br />
== January 27 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
== February 3 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Ed Dewey'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Derived Category of Projective Space<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: I will talk about the derived category of projective space, covering mostly the same material that Andrei did at the end of his homological algebra course, but at a more leisurely pace. My main reference is the ''Skimming.'' <br />
|}<br />
</center><br />
<br />
== February 10 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Ed Dewey'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: More Derived Category of Projective Space<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: I will explain in what sense we now "know" the derived category of projective space from Beilinson's result. There is a very nice answer in terms of quivers but I got distracted by another, much less efficient but maybe more flexible approach using dg categories, so that is what we will do. If my understanding permits, we will also talk about the derived category of a projective space bundle.<br />
|} <br />
</center><br />
<br />
== February 17 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD <br />
|} <br />
</center><br />
== February 24 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''DJ Bruce'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Divisors and Stuff I<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
<br />
|} <br />
</center><br />
<br />
== March 2 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''DJ Bruce'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Divisors and Stuff II<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
== March 9 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''DJ Bruce'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Divisors and Stuff III<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
== March 16 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
<br />
|} <br />
</center><br />
<br />
== March 23 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''No Seminar This Week'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: N/A<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: Enjoy your break!<br />
|} <br />
</center><br />
<br />
== March 30 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Daniel Hast'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Jacobians, path integrals, and fundamental groups of curves I<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
== April 6 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Daniel Hast'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Jacobians, path integrals, and fundamental groups of curves II<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
== April 13 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Jason Steinberg '''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Something Something Shimura Varieties<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
|} <br />
</center><br />
<br />
== April 20 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Quinton Westrich'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Projective Duality<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: Intro to discriminants and duals of projective varieties. My field will be C.<br />
|} <br />
</center><br />
<br />
== April 27 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Zachary Charles'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Polynomial systems, toric geometry, and Newton polytopes<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
== May 4 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Wendy Cheng'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Cohomology of Sheaves, Affine Scheme and Projective Space<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
== May 11 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
== Organizers' Contact Info ==<br />
[http://www.math.wisc.edu/~djbruce DJ Bruce]<br />
<br />
[http://www.math.wisc.edu/~clement Nathan Clement]<br />
<br />
[http://www.math.wisc.edu/~dewey/ Ed Dewey]<br />
<br />
== Past Semesters ==<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_(Fall_2015) Fall 2015]</div>Cchenghttps://wiki.math.wisc.edu/index.php?title=Graduate_Algebraic_Geometry_Seminar_Fall_2017&diff=11866Graduate Algebraic Geometry Seminar Fall 20172016-04-22T14:22:10Z<p>Ccheng: </p>
<hr />
<div>'''<br />
'''When:''' Wednesdays 4:00pm<br />
<br />
'''Where:'''Van Vleck B139<br />
[[Image:cat.jpg|thumb|220px| | Lizzie the OFFICIAL mascot of GAGS!!]]<br />
<br />
'''Who:''' YOU!!<br />
<br />
'''Why:''' The purpose of this seminar is to learn algebraic geometry by giving and listening to talks in a informal setting. Talks are typically accessible to beginning graduate students and take many different forms. Sometimes people present an interesting paper they find. Other times people give a prep talk for the Friday Algebraic Geometry Seminar. Other times people give a series of talks on a topic they have been studying in-depth.<br />
<br />
'''How:'''If you want to get emails regarding time, place, and talk topics ('''which are often assigned quite last minute''') add yourself to the gags mailing list: gags@lists.wisc.edu. The list registration page is [https://admin.lists.wisc.edu/index.php?p=11&l=gags here].<br />
'''<br />
<br />
<br />
<br />
<br />
<br />
== Give a talk! ==<br />
We need volunteers to give talks this semester. If you're interested contact [mailto:djbruce@math.wisc.edu DJ], or just add yourself to the list (though in that case we might move your talk later without your permission). Beginning graduate students are particularly encouraged to give a talk, since it's a great way to get your feet wet with the material.<br />
<br />
<br />
== Wish List ==<br />
If there is a subject or a paper which you'd like to see someone give a talk on, add it to this list. If you want to give a talk and can't find a topic, try one from this list.<br />
<br />
* Sheaf operations on D-modules (the point is that then you can get a Fourier-Mukai transform between certain O-modules and certain D-modules, which is more or less how geometric Langlands is supposed to work)<br />
<br />
* A careful explanation of the correspondence between graded modules and sheaves on projective varieties.<br />
<br />
* Braverman and Bezrukavnikov: geometric Langlands correspondence for D-modules in prime characteristic: the GL(n) case (Note: this title sounds tough but prime characteristic makes things ''easier'')<br />
<br />
* Homological projective duality<br />
<br />
* The orbit method (for classifying representations of a Lie group)<br />
<br />
* Kaledin: geometry and topology of symplectic resolutions<br />
<br />
* Kashiwara: D-modules and representation theory of Lie groups (Note: Check out that diagram on page 2!)<br />
<br />
* Geometric complexity theory, maybe something like arXiv:1508.05788.<br />
<br />
__NOTOC__<br />
<br />
== Spring 2016 ==<br />
<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#A6B658" width="300" align="center"|'''Speaker'''<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title (click to see abstract)'''<br />
|-<br />
| bgcolor="#E0E0E0"| January 20<br />
| bgcolor="#C6D46E"| Jay Yang<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#January 20| Tropical Geometry II]]<br />
|-<br />
| bgcolor="#E0E0E0"| January 27<br />
| bgcolor="#C6D46E"| Jay Yang<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#January 27| Tropical Geometry III ]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 3<br />
| bgcolor="#C6D46E"| Ed Dewey<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 3| Derived Category of Projective Space ]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 10 <br />
| bgcolor="#C6D46E"| Ed Dewey<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 10| More Derived Category of Projective Space ]] <br />
|-<br />
| bgcolor="#E0E0E0"| February 17<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 17| TBD ]] <br />
|-<br />
| bgcolor="#E0E0E0"| February 24<br />
| bgcolor="#C6D46E"| DJ Bruce<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 24| Divisors and Stuff I]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 2<br />
| bgcolor="#C6D46E"| DJ Bruce<br />
| bgcolor="#BCE2FE"| [[Graduate Algebraic Geometry Seminar#March 2| Divisors and Stuff II]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 9<br />
| bgcolor="#C6D46E"| DJ Bruce<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 9| Divisors and Stuff III]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 16<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 16| TBD]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 23<br />
| bgcolor="#C6D46E"| N/A<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 23| No GAGS This Week ]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 30<br />
| bgcolor="#C6D46E"| Daniel Hast<br />
| bgcolor="#BCE2FE"| [[Graduate Algebraic Geometry Seminar#March 30| Jacobians, path integrals, and fundamental groups of curves I]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 6<br />
| bgcolor="#C6D46E"| Daniel Hast<br />
| bgcolor="#BCE2FE"| [[Graduate Algebraic Geometry Seminar#April 6| Jacobians, path integrals, and fundamental groups of curves II]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 13<br />
| bgcolor="#C6D46E"| Jason Steinberg<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 13|Something Something Shimura Varieties ]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 20<br />
| bgcolor="#C6D46E"| Quinton Westrich<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 20| Projective Duality ]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 27<br />
| bgcolor="#C6D46E"| Zachary Charles<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 27| Polynomial systems, toric geometry, and Newton polytopes]] <br />
|-<br />
| bgcolor="#E0E0E0"| May 4<br />
| bgcolor="#C6D46E"| Wendy Cheng<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#May 4| Cohomology of Sheaves, Affine Scheme and Projective Space (Cancelled due to time conflict with Peter Sarnak's talk]] <br />
|-<br />
| bgcolor="#E0E0E0"| May 11<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#May 11| TBD ]] <br />
|}<br />
</center><br />
<br />
== January 20 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Jay Yang'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Tropical Geometry II<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: Previously we discussed the basic definitions of tropical geometry, and<br />
the connection to algebraic geometry. Now we use this to count curves<br />
through points on P^2. This is a well known result initially proven<br />
without the use of tropical tools. But using tropical tools we can give<br />
a proof that relies on the combinatorics of lattice paths. I will begin<br />
with a review of some facts from tropical geometry that we need for this<br />
proof. <br />
|} <br />
</center><br />
<br />
== January 27 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
== February 3 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Ed Dewey'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Derived Category of Projective Space<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: I will talk about the derived category of projective space, covering mostly the same material that Andrei did at the end of his homological algebra course, but at a more leisurely pace. My main reference is the ''Skimming.'' <br />
|}<br />
</center><br />
<br />
== February 10 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Ed Dewey'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: More Derived Category of Projective Space<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: I will explain in what sense we now "know" the derived category of projective space from Beilinson's result. There is a very nice answer in terms of quivers but I got distracted by another, much less efficient but maybe more flexible approach using dg categories, so that is what we will do. If my understanding permits, we will also talk about the derived category of a projective space bundle.<br />
|} <br />
</center><br />
<br />
== February 17 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD <br />
|} <br />
</center><br />
== February 24 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''DJ Bruce'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Divisors and Stuff I<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
<br />
|} <br />
</center><br />
<br />
== March 2 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''DJ Bruce'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Divisors and Stuff II<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
== March 9 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''DJ Bruce'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Divisors and Stuff III<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
== March 16 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
<br />
|} <br />
</center><br />
<br />
== March 23 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''No Seminar This Week'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: N/A<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: Enjoy your break!<br />
|} <br />
</center><br />
<br />
== March 30 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Daniel Hast'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Jacobians, path integrals, and fundamental groups of curves I<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
== April 6 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Daniel Hast'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Jacobians, path integrals, and fundamental groups of curves II<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
== April 13 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Jason Steinberg '''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Something Something Shimura Varieties<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
|} <br />
</center><br />
<br />
== April 20 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Quinton Westrich'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Projective Duality<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: Intro to discriminants and duals of projective varieties. My field will be C.<br />
|} <br />
</center><br />
<br />
== April 27 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Zachary Charles'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Polynomial systems, toric geometry, and Newton polytopes<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
== May 4 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Wendy Cheng'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Cohomology of Sheaves, Affine Scheme and Projective Space<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
== May 11 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
== Organizers' Contact Info ==<br />
[http://www.math.wisc.edu/~djbruce DJ Bruce]<br />
<br />
[http://www.math.wisc.edu/~clement Nathan Clement]<br />
<br />
[http://www.math.wisc.edu/~dewey/ Ed Dewey]<br />
<br />
== Past Semesters ==<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_(Fall_2015) Fall 2015]</div>Cchenghttps://wiki.math.wisc.edu/index.php?title=Graduate_Algebraic_Geometry_Seminar_Fall_2017&diff=11827Graduate Algebraic Geometry Seminar Fall 20172016-04-16T01:20:53Z<p>Ccheng: </p>
<hr />
<div>'''<br />
'''When:''' Wednesdays 4:00pm<br />
<br />
'''Where:'''Van Vleck B139<br />
[[Image:cat.jpg|thumb|220px| | Lizzie the OFFICIAL mascot of GAGS!!]]<br />
<br />
'''Who:''' YOU!!<br />
<br />
'''Why:''' The purpose of this seminar is to learn algebraic geometry by giving and listening to talks in a informal setting. Talks are typically accessible to beginning graduate students and take many different forms. Sometimes people present an interesting paper they find. Other times people give a prep talk for the Friday Algebraic Geometry Seminar. Other times people give a series of talks on a topic they have been studying in-depth.<br />
<br />
'''How:'''If you want to get emails regarding time, place, and talk topics ('''which are often assigned quite last minute''') add yourself to the gags mailing list: gags@lists.wisc.edu. The list registration page is [https://admin.lists.wisc.edu/index.php?p=11&l=gags here].<br />
'''<br />
<br />
<br />
<br />
<br />
<br />
== Give a talk! ==<br />
We need volunteers to give talks this semester. If you're interested contact [mailto:djbruce@math.wisc.edu DJ], or just add yourself to the list (though in that case we might move your talk later without your permission). Beginning graduate students are particularly encouraged to give a talk, since it's a great way to get your feet wet with the material.<br />
<br />
<br />
== Wish List ==<br />
If there is a subject or a paper which you'd like to see someone give a talk on, add it to this list. If you want to give a talk and can't find a topic, try one from this list.<br />
<br />
* Sheaf operations on D-modules (the point is that then you can get a Fourier-Mukai transform between certain O-modules and certain D-modules, which is more or less how geometric Langlands is supposed to work)<br />
<br />
* A careful explanation of the correspondence between graded modules and sheaves on projective varieties.<br />
<br />
* Braverman and Bezrukavnikov: geometric Langlands correspondence for D-modules in prime characteristic: the GL(n) case (Note: this title sounds tough but prime characteristic makes things ''easier'')<br />
<br />
* Homological projective duality<br />
<br />
* The orbit method (for classifying representations of a Lie group)<br />
<br />
* Kaledin: geometry and topology of symplectic resolutions<br />
<br />
* Kashiwara: D-modules and representation theory of Lie groups (Note: Check out that diagram on page 2!)<br />
<br />
* Geometric complexity theory, maybe something like arXiv:1508.05788.<br />
<br />
__NOTOC__<br />
<br />
== Spring 2016 ==<br />
<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#A6B658" width="300" align="center"|'''Speaker'''<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title (click to see abstract)'''<br />
|-<br />
| bgcolor="#E0E0E0"| January 20<br />
| bgcolor="#C6D46E"| Jay Yang<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#January 20| Tropical Geometry II]]<br />
|-<br />
| bgcolor="#E0E0E0"| January 27<br />
| bgcolor="#C6D46E"| Jay Yang<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#January 27| Tropical Geometry III ]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 3<br />
| bgcolor="#C6D46E"| Ed Dewey<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 3| Derived Category of Projective Space ]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 10 <br />
| bgcolor="#C6D46E"| Ed Dewey<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 10| More Derived Category of Projective Space ]] <br />
|-<br />
| bgcolor="#E0E0E0"| February 17<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 17| TBD ]] <br />
|-<br />
| bgcolor="#E0E0E0"| February 24<br />
| bgcolor="#C6D46E"| DJ Bruce<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 24| Divisors and Stuff I]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 2<br />
| bgcolor="#C6D46E"| DJ Bruce<br />
| bgcolor="#BCE2FE"| [[Graduate Algebraic Geometry Seminar#March 2| Divisors and Stuff II]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 9<br />
| bgcolor="#C6D46E"| DJ Bruce<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 9| Divisors and Stuff III]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 16<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 16| TBD]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 23<br />
| bgcolor="#C6D46E"| N/A<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 23| No GAGS This Week ]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 30<br />
| bgcolor="#C6D46E"| Daniel Hast<br />
| bgcolor="#BCE2FE"| [[Graduate Algebraic Geometry Seminar#March 30| Jacobians, path integrals, and fundamental groups of curves I]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 6<br />
| bgcolor="#C6D46E"| Daniel Hast<br />
| bgcolor="#BCE2FE"| [[Graduate Algebraic Geometry Seminar#April 6| Jacobians, path integrals, and fundamental groups of curves II]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 13<br />
| bgcolor="#C6D46E"| Jason Steinberg<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 13|Something Something Shimura Varieties ]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 20<br />
| bgcolor="#C6D46E"| Quinton Westrich<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 20| Projective Duality ]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 27<br />
| bgcolor="#C6D46E"| Zachary Charles<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 27| Polynomial systems, toric geometry, and Newton polytopes]] <br />
|-<br />
| bgcolor="#E0E0E0"| May 4<br />
| bgcolor="#C6D46E"| Wendy Cheng<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#May 4| Cohomology of Sheaves, Affine Scheme and Projective Space ]] <br />
|-<br />
| bgcolor="#E0E0E0"| May 11<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#May 11| TBD ]] <br />
|}<br />
</center><br />
<br />
== January 20 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Jay Yang'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Tropical Geometry II<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: Previously we discussed the basic definitions of tropical geometry, and<br />
the connection to algebraic geometry. Now we use this to count curves<br />
through points on P^2. This is a well known result initially proven<br />
without the use of tropical tools. But using tropical tools we can give<br />
a proof that relies on the combinatorics of lattice paths. I will begin<br />
with a review of some facts from tropical geometry that we need for this<br />
proof. <br />
|} <br />
</center><br />
<br />
== January 27 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
== February 3 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Ed Dewey'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Derived Category of Projective Space<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: I will talk about the derived category of projective space, covering mostly the same material that Andrei did at the end of his homological algebra course, but at a more leisurely pace. My main reference is the ''Skimming.'' <br />
|}<br />
</center><br />
<br />
== February 10 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Ed Dewey'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: More Derived Category of Projective Space<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: I will explain in what sense we now "know" the derived category of projective space from Beilinson's result. There is a very nice answer in terms of quivers but I got distracted by another, much less efficient but maybe more flexible approach using dg categories, so that is what we will do. If my understanding permits, we will also talk about the derived category of a projective space bundle.<br />
|} <br />
</center><br />
<br />
== February 17 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD <br />
|} <br />
</center><br />
== February 24 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''DJ Bruce'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Divisors and Stuff I<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
<br />
|} <br />
</center><br />
<br />
== March 2 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''DJ Bruce'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Divisors and Stuff II<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
== March 9 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''DJ Bruce'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Divisors and Stuff III<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
== March 16 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
<br />
|} <br />
</center><br />
<br />
== March 23 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''No Seminar This Week'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: N/A<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: Enjoy your break!<br />
|} <br />
</center><br />
<br />
== March 30 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Daniel Hast'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Jacobians, path integrals, and fundamental groups of curves I<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
== April 6 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Daniel Hast'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Jacobians, path integrals, and fundamental groups of curves II<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
== April 13 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Jason Steinberg '''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Something Something Shimura Varieties<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
|} <br />
</center><br />
<br />
== April 20 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Quinton Westrich'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Projective Duality<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: Intro to discriminants and duals of projective varieties. My field will be C.<br />
|} <br />
</center><br />
<br />
== April 27 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Zachary Charles'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Polynomial systems, toric geometry, and Newton polytopes<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
== May 4 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Wendy Cheng'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Cohomology of Sheaves, Affine Scheme and Projective Space<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
== May 11 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
== Organizers' Contact Info ==<br />
[http://www.math.wisc.edu/~djbruce DJ Bruce]<br />
<br />
[http://www.math.wisc.edu/~clement Nathan Clement]<br />
<br />
[http://www.math.wisc.edu/~dewey/ Ed Dewey]<br />
<br />
== Past Semesters ==<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_(Fall_2015) Fall 2015]</div>Cchenghttps://wiki.math.wisc.edu/index.php?title=Graduate_Algebraic_Geometry_Seminar_Fall_2017&diff=11826Graduate Algebraic Geometry Seminar Fall 20172016-04-16T01:19:03Z<p>Ccheng: </p>
<hr />
<div>'''<br />
'''When:''' Wednesdays 4:00pm<br />
<br />
'''Where:'''Van Vleck B139<br />
[[Image:cat.jpg|thumb|220px| | Lizzie the OFFICIAL mascot of GAGS!!]]<br />
<br />
'''Who:''' YOU!!<br />
<br />
'''Why:''' The purpose of this seminar is to learn algebraic geometry by giving and listening to talks in a informal setting. Talks are typically accessible to beginning graduate students and take many different forms. Sometimes people present an interesting paper they find. Other times people give a prep talk for the Friday Algebraic Geometry Seminar. Other times people give a series of talks on a topic they have been studying in-depth.<br />
<br />
'''How:'''If you want to get emails regarding time, place, and talk topics ('''which are often assigned quite last minute''') add yourself to the gags mailing list: gags@lists.wisc.edu. The list registration page is [https://admin.lists.wisc.edu/index.php?p=11&l=gags here].<br />
'''<br />
<br />
<br />
<br />
<br />
<br />
== Give a talk! ==<br />
We need volunteers to give talks this semester. If you're interested contact [mailto:djbruce@math.wisc.edu DJ], or just add yourself to the list (though in that case we might move your talk later without your permission). Beginning graduate students are particularly encouraged to give a talk, since it's a great way to get your feet wet with the material.<br />
<br />
<br />
== Wish List ==<br />
If there is a subject or a paper which you'd like to see someone give a talk on, add it to this list. If you want to give a talk and can't find a topic, try one from this list.<br />
<br />
* Sheaf operations on D-modules (the point is that then you can get a Fourier-Mukai transform between certain O-modules and certain D-modules, which is more or less how geometric Langlands is supposed to work)<br />
<br />
* A careful explanation of the correspondence between graded modules and sheaves on projective varieties.<br />
<br />
* Braverman and Bezrukavnikov: geometric Langlands correspondence for D-modules in prime characteristic: the GL(n) case (Note: this title sounds tough but prime characteristic makes things ''easier'')<br />
<br />
* Homological projective duality<br />
<br />
* The orbit method (for classifying representations of a Lie group)<br />
<br />
* Kaledin: geometry and topology of symplectic resolutions<br />
<br />
* Kashiwara: D-modules and representation theory of Lie groups (Note: Check out that diagram on page 2!)<br />
<br />
* Geometric complexity theory, maybe something like arXiv:1508.05788.<br />
<br />
__NOTOC__<br />
<br />
== Spring 2016 ==<br />
<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#A6B658" width="300" align="center"|'''Speaker'''<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title (click to see abstract)'''<br />
|-<br />
| bgcolor="#E0E0E0"| January 20<br />
| bgcolor="#C6D46E"| Jay Yang<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#January 20| Tropical Geometry II]]<br />
|-<br />
| bgcolor="#E0E0E0"| January 27<br />
| bgcolor="#C6D46E"| Jay Yang<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#January 27| Tropical Geometry III ]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 3<br />
| bgcolor="#C6D46E"| Ed Dewey<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 3| Derived Category of Projective Space ]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 10 <br />
| bgcolor="#C6D46E"| Ed Dewey<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 10| More Derived Category of Projective Space ]] <br />
|-<br />
| bgcolor="#E0E0E0"| February 17<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 17| TBD ]] <br />
|-<br />
| bgcolor="#E0E0E0"| February 24<br />
| bgcolor="#C6D46E"| DJ Bruce<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 24| Divisors and Stuff I]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 2<br />
| bgcolor="#C6D46E"| DJ Bruce<br />
| bgcolor="#BCE2FE"| [[Graduate Algebraic Geometry Seminar#March 2| Divisors and Stuff II]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 9<br />
| bgcolor="#C6D46E"| DJ Bruce<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 9| Divisors and Stuff III]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 16<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 16| TBD]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 23<br />
| bgcolor="#C6D46E"| N/A<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 23| No GAGS This Week ]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 30<br />
| bgcolor="#C6D46E"| Daniel Hast<br />
| bgcolor="#BCE2FE"| [[Graduate Algebraic Geometry Seminar#March 30| Jacobians, path integrals, and fundamental groups of curves I]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 6<br />
| bgcolor="#C6D46E"| Daniel Hast<br />
| bgcolor="#BCE2FE"| [[Graduate Algebraic Geometry Seminar#April 6| Jacobians, path integrals, and fundamental groups of curves II]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 13<br />
| bgcolor="#C6D46E"| Jason Steinberg<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 13|Something Something Shimura Varieties ]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 20<br />
| bgcolor="#C6D46E"| Quinton Westrich<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 20| Projective Duality ]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 27<br />
| bgcolor="#C6D46E"| Zachary Charles<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 27| Polynomial systems, toric geometry, and Newton polytopes]] <br />
|-<br />
| bgcolor="#E0E0E0"| May 4<br />
| bgcolor="#C6D46E"| Wendy Cheng<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#May 4| Cohomology of sheaves, affine schemes and projective spaces ]] <br />
|-<br />
| bgcolor="#E0E0E0"| May 11<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#May 11| TBD ]] <br />
|}<br />
</center><br />
<br />
== January 20 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Jay Yang'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Tropical Geometry II<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: Previously we discussed the basic definitions of tropical geometry, and<br />
the connection to algebraic geometry. Now we use this to count curves<br />
through points on P^2. This is a well known result initially proven<br />
without the use of tropical tools. But using tropical tools we can give<br />
a proof that relies on the combinatorics of lattice paths. I will begin<br />
with a review of some facts from tropical geometry that we need for this<br />
proof. <br />
|} <br />
</center><br />
<br />
== January 27 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
== February 3 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Ed Dewey'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Derived Category of Projective Space<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: I will talk about the derived category of projective space, covering mostly the same material that Andrei did at the end of his homological algebra course, but at a more leisurely pace. My main reference is the ''Skimming.'' <br />
|}<br />
</center><br />
<br />
== February 10 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Ed Dewey'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: More Derived Category of Projective Space<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: I will explain in what sense we now "know" the derived category of projective space from Beilinson's result. There is a very nice answer in terms of quivers but I got distracted by another, much less efficient but maybe more flexible approach using dg categories, so that is what we will do. If my understanding permits, we will also talk about the derived category of a projective space bundle.<br />
|} <br />
</center><br />
<br />
== February 17 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD <br />
|} <br />
</center><br />
== February 24 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''DJ Bruce'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Divisors and Stuff I<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
<br />
|} <br />
</center><br />
<br />
== March 2 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''DJ Bruce'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Divisors and Stuff II<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
== March 9 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''DJ Bruce'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Divisors and Stuff III<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
== March 16 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
<br />
|} <br />
</center><br />
<br />
== March 23 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''No Seminar This Week'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: N/A<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: Enjoy your break!<br />
|} <br />
</center><br />
<br />
== March 30 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Daniel Hast'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Jacobians, path integrals, and fundamental groups of curves I<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
== April 6 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Daniel Hast'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Jacobians, path integrals, and fundamental groups of curves II<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
== April 13 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Jason Steinberg '''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Something Something Shimura Varieties<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
|} <br />
</center><br />
<br />
== April 20 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Quinton Westrich'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Projective Duality<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: Intro to discriminants and duals of projective varieties. My field will be C.<br />
|} <br />
</center><br />
<br />
== April 27 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Zachary Charles'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Polynomial systems, toric geometry, and Newton polytopes<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
== May 4 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Wendy Cheng'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Cohomology of sheaves, affine schemes and projective spaces<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
== May 11 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
== Organizers' Contact Info ==<br />
[http://www.math.wisc.edu/~djbruce DJ Bruce]<br />
<br />
[http://www.math.wisc.edu/~clement Nathan Clement]<br />
<br />
[http://www.math.wisc.edu/~dewey/ Ed Dewey]<br />
<br />
== Past Semesters ==<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_(Fall_2015) Fall 2015]</div>Cchenghttps://wiki.math.wisc.edu/index.php?title=Graduate_Algebraic_Geometry_Seminar_Fall_2017&diff=11825Graduate Algebraic Geometry Seminar Fall 20172016-04-16T01:17:32Z<p>Ccheng: </p>
<hr />
<div>'''<br />
'''When:''' Wednesdays 4:00pm<br />
<br />
'''Where:'''Van Vleck B139<br />
[[Image:cat.jpg|thumb|220px| | Lizzie the OFFICIAL mascot of GAGS!!]]<br />
<br />
'''Who:''' YOU!!<br />
<br />
'''Why:''' The purpose of this seminar is to learn algebraic geometry by giving and listening to talks in a informal setting. Talks are typically accessible to beginning graduate students and take many different forms. Sometimes people present an interesting paper they find. Other times people give a prep talk for the Friday Algebraic Geometry Seminar. Other times people give a series of talks on a topic they have been studying in-depth.<br />
<br />
'''How:'''If you want to get emails regarding time, place, and talk topics ('''which are often assigned quite last minute''') add yourself to the gags mailing list: gags@lists.wisc.edu. The list registration page is [https://admin.lists.wisc.edu/index.php?p=11&l=gags here].<br />
'''<br />
<br />
<br />
<br />
<br />
<br />
== Give a talk! ==<br />
We need volunteers to give talks this semester. If you're interested contact [mailto:djbruce@math.wisc.edu DJ], or just add yourself to the list (though in that case we might move your talk later without your permission). Beginning graduate students are particularly encouraged to give a talk, since it's a great way to get your feet wet with the material.<br />
<br />
<br />
== Wish List ==<br />
If there is a subject or a paper which you'd like to see someone give a talk on, add it to this list. If you want to give a talk and can't find a topic, try one from this list.<br />
<br />
* Sheaf operations on D-modules (the point is that then you can get a Fourier-Mukai transform between certain O-modules and certain D-modules, which is more or less how geometric Langlands is supposed to work)<br />
<br />
* A careful explanation of the correspondence between graded modules and sheaves on projective varieties.<br />
<br />
* Braverman and Bezrukavnikov: geometric Langlands correspondence for D-modules in prime characteristic: the GL(n) case (Note: this title sounds tough but prime characteristic makes things ''easier'')<br />
<br />
* Homological projective duality<br />
<br />
* The orbit method (for classifying representations of a Lie group)<br />
<br />
* Kaledin: geometry and topology of symplectic resolutions<br />
<br />
* Kashiwara: D-modules and representation theory of Lie groups (Note: Check out that diagram on page 2!)<br />
<br />
* Geometric complexity theory, maybe something like arXiv:1508.05788.<br />
<br />
__NOTOC__<br />
<br />
== Spring 2016 ==<br />
<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#A6B658" width="300" align="center"|'''Speaker'''<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title (click to see abstract)'''<br />
|-<br />
| bgcolor="#E0E0E0"| January 20<br />
| bgcolor="#C6D46E"| Jay Yang<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#January 20| Tropical Geometry II]]<br />
|-<br />
| bgcolor="#E0E0E0"| January 27<br />
| bgcolor="#C6D46E"| Jay Yang<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#January 27| Tropical Geometry III ]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 3<br />
| bgcolor="#C6D46E"| Ed Dewey<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 3| Derived Category of Projective Space ]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 10 <br />
| bgcolor="#C6D46E"| Ed Dewey<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 10| More Derived Category of Projective Space ]] <br />
|-<br />
| bgcolor="#E0E0E0"| February 17<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 17| TBD ]] <br />
|-<br />
| bgcolor="#E0E0E0"| February 24<br />
| bgcolor="#C6D46E"| DJ Bruce<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 24| Divisors and Stuff I]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 2<br />
| bgcolor="#C6D46E"| DJ Bruce<br />
| bgcolor="#BCE2FE"| [[Graduate Algebraic Geometry Seminar#March 2| Divisors and Stuff II]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 9<br />
| bgcolor="#C6D46E"| DJ Bruce<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 9| Divisors and Stuff III]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 16<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 16| TBD]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 23<br />
| bgcolor="#C6D46E"| N/A<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 23| No GAGS This Week ]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 30<br />
| bgcolor="#C6D46E"| Daniel Hast<br />
| bgcolor="#BCE2FE"| [[Graduate Algebraic Geometry Seminar#March 30| Jacobians, path integrals, and fundamental groups of curves I]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 6<br />
| bgcolor="#C6D46E"| Daniel Hast<br />
| bgcolor="#BCE2FE"| [[Graduate Algebraic Geometry Seminar#April 6| Jacobians, path integrals, and fundamental groups of curves II]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 13<br />
| bgcolor="#C6D46E"| Jason Steinberg<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 13|Something Something Shimura Varieties ]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 20<br />
| bgcolor="#C6D46E"| Quinton Westrich<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 20| Projective Duality ]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 27<br />
| bgcolor="#C6D46E"| Zachary Charles<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 27| Polynomial systems, toric geometry, and Newton polytopes]] <br />
|-<br />
| bgcolor="#E0E0E0"| May 4<br />
| bgcolor="#C6D46E"| Wendy Cheng<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#May 4| Cohomology of sheaves, affine schemes and projective spaces ]] <br />
|-<br />
| bgcolor="#E0E0E0"| May 11<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#May 11| TBD ]] <br />
|}<br />
</center><br />
<br />
== January 20 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Jay Yang'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Tropical Geometry II<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: Previously we discussed the basic definitions of tropical geometry, and<br />
the connection to algebraic geometry. Now we use this to count curves<br />
through points on P^2. This is a well known result initially proven<br />
without the use of tropical tools. But using tropical tools we can give<br />
a proof that relies on the combinatorics of lattice paths. I will begin<br />
with a review of some facts from tropical geometry that we need for this<br />
proof. <br />
|} <br />
</center><br />
<br />
== January 27 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
== February 3 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Ed Dewey'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Derived Category of Projective Space<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: I will talk about the derived category of projective space, covering mostly the same material that Andrei did at the end of his homological algebra course, but at a more leisurely pace. My main reference is the ''Skimming.'' <br />
|}<br />
</center><br />
<br />
== February 10 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Ed Dewey'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: More Derived Category of Projective Space<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: I will explain in what sense we now "know" the derived category of projective space from Beilinson's result. There is a very nice answer in terms of quivers but I got distracted by another, much less efficient but maybe more flexible approach using dg categories, so that is what we will do. If my understanding permits, we will also talk about the derived category of a projective space bundle.<br />
|} <br />
</center><br />
<br />
== February 17 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD <br />
|} <br />
</center><br />
== February 24 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''DJ Bruce'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Divisors and Stuff I<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
<br />
|} <br />
</center><br />
<br />
== March 2 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''DJ Bruce'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Divisors and Stuff II<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
== March 9 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''DJ Bruce'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Divisors and Stuff III<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
== March 16 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
<br />
|} <br />
</center><br />
<br />
== March 23 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''No Seminar This Week'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: N/A<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: Enjoy your break!<br />
|} <br />
</center><br />
<br />
== March 30 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Daniel Hast'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Jacobians, path integrals, and fundamental groups of curves I<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
== April 6 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Daniel Hast'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Jacobians, path integrals, and fundamental groups of curves II<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
== April 13 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Jason Steinberg '''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Something Something Shimura Varieties<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
|} <br />
</center><br />
<br />
== April 20 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Quinton Westrich'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Projective Duality<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: Intro to discriminants and duals of projective varieties. My field will be C.<br />
|} <br />
</center><br />
<br />
== April 27 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Zachary Charles'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Polynomial systems, toric geometry, and Newton polytopes<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
== May 4 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
== May 11 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
== Organizers' Contact Info ==<br />
[http://www.math.wisc.edu/~djbruce DJ Bruce]<br />
<br />
[http://www.math.wisc.edu/~clement Nathan Clement]<br />
<br />
[http://www.math.wisc.edu/~dewey/ Ed Dewey]<br />
<br />
== Past Semesters ==<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_(Fall_2015) Fall 2015]</div>Cchenghttps://wiki.math.wisc.edu/index.php?title=Graduate_Algebraic_Geometry_Seminar_Fall_2017&diff=11824Graduate Algebraic Geometry Seminar Fall 20172016-04-16T01:12:59Z<p>Ccheng: </p>
<hr />
<div>'''<br />
'''When:''' Wednesdays 4:00pm<br />
<br />
'''Where:'''Van Vleck B139<br />
[[Image:cat.jpg|thumb|220px| | Lizzie the OFFICIAL mascot of GAGS!!]]<br />
<br />
'''Who:''' YOU!!<br />
<br />
'''Why:''' The purpose of this seminar is to learn algebraic geometry by giving and listening to talks in a informal setting. Talks are typically accessible to beginning graduate students and take many different forms. Sometimes people present an interesting paper they find. Other times people give a prep talk for the Friday Algebraic Geometry Seminar. Other times people give a series of talks on a topic they have been studying in-depth.<br />
<br />
'''How:'''If you want to get emails regarding time, place, and talk topics ('''which are often assigned quite last minute''') add yourself to the gags mailing list: gags@lists.wisc.edu. The list registration page is [https://admin.lists.wisc.edu/index.php?p=11&l=gags here].<br />
'''<br />
<br />
<br />
<br />
<br />
<br />
== Give a talk! ==<br />
We need volunteers to give talks this semester. If you're interested contact [mailto:djbruce@math.wisc.edu DJ], or just add yourself to the list (though in that case we might move your talk later without your permission). Beginning graduate students are particularly encouraged to give a talk, since it's a great way to get your feet wet with the material.<br />
<br />
<br />
== Wish List ==<br />
If there is a subject or a paper which you'd like to see someone give a talk on, add it to this list. If you want to give a talk and can't find a topic, try one from this list.<br />
<br />
* Sheaf operations on D-modules (the point is that then you can get a Fourier-Mukai transform between certain O-modules and certain D-modules, which is more or less how geometric Langlands is supposed to work)<br />
<br />
* A careful explanation of the correspondence between graded modules and sheaves on projective varieties.<br />
<br />
* Braverman and Bezrukavnikov: geometric Langlands correspondence for D-modules in prime characteristic: the GL(n) case (Note: this title sounds tough but prime characteristic makes things ''easier'')<br />
<br />
* Homological projective duality<br />
<br />
* The orbit method (for classifying representations of a Lie group)<br />
<br />
* Kaledin: geometry and topology of symplectic resolutions<br />
<br />
* Kashiwara: D-modules and representation theory of Lie groups (Note: Check out that diagram on page 2!)<br />
<br />
* Geometric complexity theory, maybe something like arXiv:1508.05788.<br />
<br />
__NOTOC__<br />
<br />
== Spring 2016 ==<br />
<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#A6B658" width="300" align="center"|'''Speaker'''<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title (click to see abstract)'''<br />
|-<br />
| bgcolor="#E0E0E0"| January 20<br />
| bgcolor="#C6D46E"| Jay Yang<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#January 20| Tropical Geometry II]]<br />
|-<br />
| bgcolor="#E0E0E0"| January 27<br />
| bgcolor="#C6D46E"| Jay Yang<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#January 27| Tropical Geometry III ]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 3<br />
| bgcolor="#C6D46E"| Ed Dewey<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 3| Derived Category of Projective Space ]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 10 <br />
| bgcolor="#C6D46E"| Ed Dewey<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 10| More Derived Category of Projective Space ]] <br />
|-<br />
| bgcolor="#E0E0E0"| February 17<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 17| TBD ]] <br />
|-<br />
| bgcolor="#E0E0E0"| February 24<br />
| bgcolor="#C6D46E"| DJ Bruce<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 24| Divisors and Stuff I]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 2<br />
| bgcolor="#C6D46E"| DJ Bruce<br />
| bgcolor="#BCE2FE"| [[Graduate Algebraic Geometry Seminar#March 2| Divisors and Stuff II]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 9<br />
| bgcolor="#C6D46E"| DJ Bruce<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 9| Divisors and Stuff III]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 16<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 16| TBD]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 23<br />
| bgcolor="#C6D46E"| N/A<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 23| No GAGS This Week ]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 30<br />
| bgcolor="#C6D46E"| Daniel Hast<br />
| bgcolor="#BCE2FE"| [[Graduate Algebraic Geometry Seminar#March 30| Jacobians, path integrals, and fundamental groups of curves I]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 6<br />
| bgcolor="#C6D46E"| Daniel Hast<br />
| bgcolor="#BCE2FE"| [[Graduate Algebraic Geometry Seminar#April 6| Jacobians, path integrals, and fundamental groups of curves II]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 13<br />
| bgcolor="#C6D46E"| Jason Steinberg<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 13|Something Something Shimura Varieties ]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 20<br />
| bgcolor="#C6D46E"| Quinton Westrich<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 20| Projective Duality ]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 27<br />
| bgcolor="#C6D46E"| Zachary Charles<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 27| Polynomial systems, toric geometry, and Newton polytopes]] <br />
|-<br />
| bgcolor="#E0E0E0"| May 4<br />
| bgcolor="#C6D46E"| Wendy Cheng<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#May 4| TBD ]] <br />
|-<br />
| bgcolor="#E0E0E0"| May 11<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#May 11| TBD ]] <br />
|}<br />
</center><br />
<br />
== January 20 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Jay Yang'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Tropical Geometry II<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: Previously we discussed the basic definitions of tropical geometry, and<br />
the connection to algebraic geometry. Now we use this to count curves<br />
through points on P^2. This is a well known result initially proven<br />
without the use of tropical tools. But using tropical tools we can give<br />
a proof that relies on the combinatorics of lattice paths. I will begin<br />
with a review of some facts from tropical geometry that we need for this<br />
proof. <br />
|} <br />
</center><br />
<br />
== January 27 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
== February 3 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Ed Dewey'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Derived Category of Projective Space<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: I will talk about the derived category of projective space, covering mostly the same material that Andrei did at the end of his homological algebra course, but at a more leisurely pace. My main reference is the ''Skimming.'' <br />
|}<br />
</center><br />
<br />
== February 10 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Ed Dewey'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: More Derived Category of Projective Space<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: I will explain in what sense we now "know" the derived category of projective space from Beilinson's result. There is a very nice answer in terms of quivers but I got distracted by another, much less efficient but maybe more flexible approach using dg categories, so that is what we will do. If my understanding permits, we will also talk about the derived category of a projective space bundle.<br />
|} <br />
</center><br />
<br />
== February 17 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD <br />
|} <br />
</center><br />
== February 24 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''DJ Bruce'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Divisors and Stuff I<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
<br />
|} <br />
</center><br />
<br />
== March 2 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''DJ Bruce'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Divisors and Stuff II<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
== March 9 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''DJ Bruce'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Divisors and Stuff III<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
== March 16 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
<br />
|} <br />
</center><br />
<br />
== March 23 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''No Seminar This Week'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: N/A<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: Enjoy your break!<br />
|} <br />
</center><br />
<br />
== March 30 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Daniel Hast'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Jacobians, path integrals, and fundamental groups of curves I<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
== April 6 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Daniel Hast'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Jacobians, path integrals, and fundamental groups of curves II<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
== April 13 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Jason Steinberg '''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Something Something Shimura Varieties<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
|} <br />
</center><br />
<br />
== April 20 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Quinton Westrich'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Projective Duality<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: Intro to discriminants and duals of projective varieties. My field will be C.<br />
|} <br />
</center><br />
<br />
== April 27 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Zachary Charles'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Polynomial systems, toric geometry, and Newton polytopes<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
== May 4 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
== May 11 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
== Organizers' Contact Info ==<br />
[http://www.math.wisc.edu/~djbruce DJ Bruce]<br />
<br />
[http://www.math.wisc.edu/~clement Nathan Clement]<br />
<br />
[http://www.math.wisc.edu/~dewey/ Ed Dewey]<br />
<br />
== Past Semesters ==<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_(Fall_2015) Fall 2015]</div>Ccheng