https://wiki.math.wisc.edu/api.php?action=feedcontributions&user=Csimpson6&feedformat=atomUW-Math Wiki - User contributions [en]2024-03-29T07:46:48ZUser contributionsMediaWiki 1.39.5https://wiki.math.wisc.edu/index.php?title=Madison_Math_Circle&diff=21380Madison Math Circle2021-09-01T02:06:05Z<p>Csimpson6: </p>
<hr />
<div>[[Image:logo.png|right|600px]]<br />
<br />
For the site in Spanish, visit [[Math Circle de Madison]]<br />
=COVID-19 Update=<br />
We are back to in person talks during the Fall 2021 semester.<br />
<br />
As is the university's policy, all participants must wear masks. We will make every effort to maintain social distancing where possible.<br />
<br />
=What is a Math Circle?=<br />
The Madison Math Circle is a weekly series of mathematically based activities aimed at interested middle school and high school students. It is an outreach program organized by the UW Math Department. Our goal is to provide a taste of exciting ideas in math and science. In the past we've had talks about plasma and weather in outer space, video game graphics, and encryption. In the sessions, students (and parents) are often asked to explore problems on their own, with the presenter facilitating a discussion. The talks are independent of one another, so new students are welcome at any point.<br />
<br />
The level of the audience varies quite widely, including a mix of middle school and high school students, and the speakers generally address this by considering subjects that will be interesting for a wide range of students.<br />
<br />
<br />
[[Image: MathCircle_2.jpg|550px]] [[Image: MathCircle_4.jpg|550px]] <br />
<br />
<br />
After each talk we'll have pizza provided by the Mathematics Department, and students will have an opportunity to mingle and chat with the speaker and with other participants, to ask questions about some of the topics that have been discussed, and also about college, careers in science, etc.<br />
<br />
'''The Madison Math Circle was featured in Wisconsin State Journal:''' [http://host.madison.com/wsj/news/local/education/local_schools/school-spotlight-madison-math-circle-gives-young-students-a-taste/article_77f5c042-0b3d-11e1-ba5f-001cc4c03286.html check it out]!<br />
<br />
=All right, I want to come!=<br />
<br />
We usually have a weekly meeting, <b>Monday at 6pm in 3255 Helen C White Library</b>, during the school year. New students are welcome at any point! There is no fee and the talks are independent of one another, so you can just show up any week, but we ask all participants to take a moment to register by following the link below:<br />
<br />
[https://docs.google.com/forms/d/e/1FAIpQLSe_cKMfdjMQlmJc9uZg5bZ-sjKZ2q5SV9wLb1gSddrvB1Tk1A/viewform '''Math Circle Registration Form''']<br />
<br />
All of your information is kept private, and is only used by the Madison Math Circle organizer to help run the Circle. <br />
<br />
If you are a student, we hope you will tell other interested students about these talks, and speak with your parents or with your teacher about organizing a car pool to the UW campus. If you are a parent or a teacher, we hope you'll tell your students about these talks and organize a car pool to the UW (all talks take place in 3255 Helen C White Library, on the UW-Madison campus, right next to the Memorial Union).<br />
<br />
<br />
==Meetings for Fall 2021==<br />
<br />
<br />
<center><br />
<br />
{| style="color:black; font-size:120%" border="1" cellpadding="14" cellspacing="0"<br />
|-<br />
! colspan="3" style="background: #e8b2b2;" align="center" | Fall 2021<br />
|-<br />
! Date !! Speaker !! Topic<br />
|-<br />
| September 20th || TBA || TBA<br />
|-<br />
| September 27th || TBA || TBA<br />
|-<br />
| October 4th || TBA || TBA<br />
|-<br />
| October 11th || TBA || TBA<br />
|-<br />
| October 18th || TBA || TBA<br />
|-<br />
| October 25th || TBA || TBA<br />
|-<br />
| November 1st || TBA || TBA<br />
|-<br />
| November 8th || TBA || TBA<br />
|-<br />
| November 15th || TBA || TBA<br />
|-<br />
| November 22nd || TBA || TBA<br />
|}<br />
<br />
</center><br />
<br />
==Directions and parking==<br />
<br />
Our meetings are held on the 3rd floor of Helen C. White Hall in room 3255.<br />
<br />
<div class="center" style="width:auto; margin-left:auto; margin-right:auto;"><br />
[[File: Helencwhitemap.png|400px]]</div><br />
<br />
'''Parking.''' Parking on campus is rather limited. Here is as list of some options:<br />
<br />
*There is a parking garage in the basement of Helen C. White, with an hourly rate. Enter from Park Street.<br />
*A 0.5 mile walk to Helen C. White Hall via [http://goo.gl/cxTzJY these directions], many spots ('''free starting 4:30pm''') [http://goo.gl/maps/Gkx1C in Lot 26 along Observatory Drive].<br />
*A 0.3 mile walk to Helen C. White Hall via [http://goo.gl/yMJIRd these directions], many spots ('''free starting 4:30pm''') [http://goo.gl/maps/vs17X in Lot 34]. <br />
*A 0.3 mile walk to Helen C. White Hall via [http://goo.gl/yMJIRd these directions], 2 metered spots (25 minute max) [http://goo.gl/maps/ukTcu in front of Lathrop Hall].<br />
*A 0.2 mile walk to Helen C. White Hall via [http://goo.gl/b8pdk2 these directions] 6 metered spots (25 minute max) around [http://goo.gl/maps/6EAnc the loop in front of Chadbourne Hall] .<br />
*For more information, see the [http://transportation.wisc.edu/parking/parking.aspx UW-Madison Parking Info website].<br />
<br />
==Email list==<br />
The best way to keep up to date with the what is going is by signing up for our email list. Please add your email in the form:<br />
[https://docs.google.com/forms/d/e/1FAIpQLSe_cKMfdjMQlmJc9uZg5bZ-sjKZ2q5SV9wLb1gSddrvB1Tk1A/viewform '''Join Email List''']<br />
<br />
==Contact the organizers==<br />
The Madison Math Circle is organized by a group of professors and graduate students from the [http://www.math.wisc.edu Department of Mathematics] at the UW-Madison. If you have any questions, suggestions for topics, or so on, just email the '''organizers''' [mailto:mathcircleorganizers@g-groups.wisc.edu here]. We are always interested in feedback!<br />
<center><br />
<gallery widths=500px heights=300px mode="packed"><br />
<!--File:de.jpg|[https://www.math.wisc.edu/~derman/ Prof. Daniel Erman]--><br />
<!--File:Betsy.jpg|[http://www.math.wisc.edu/~stovall/ Prof. Betsy Stovall]--><br />
File:Uri.jpg|[https://www.math.wisc.edu/~andrews/ Prof. Uri Andrews]<br />
File: Omer.jpg|[https://www.math.wisc.edu/~omer/ Dr. Omer Mermelstein]<br />
</gallery><br />
<br />
<br />
<br />
<gallery widths=500px heights=250px mode="packed"><br />
<!--File:juliettebruce.jpg|[http://www.math.wisc.edu/~juliettebruce/ Juliette Bruce]--><br />
File:caitlynbooms.jpg|[https://sites.google.com/wisc.edu/cbooms Caitlyn Booms]<br />
File:colincrowley.jpg|[https://sites.google.com/view/colincrowley/home Colin Crowley]<br />
<!--File:hyunjongkim.jpg|Hyun Jong Kim --><br />
File:Xshen.jpg|[https://www.math.wisc.edu/~xshen// Xiao Shen]<br />
</gallery><br />
</center><br />
and [http://www.math.wisc.edu/~csimpson6/ Connor Simpson].<br />
<br />
==Donations==<br />
Please consider donating to the Madison Math Circle. Our main costs consist of pizza and occasional supplies for the speakers. So far our costs have been covered by donations from the UW Mathematics Department as well as a generous gifts from private donors. The easiest way to donate is to go to the link:<br />
<br />
[http://www.math.wisc.edu/donate Online Donation Link]<br />
<br />
There are instructions on that page for donating to the Math Department. <b> Be sure and add a Gift Note saying that the donation is intended for the "Madison Math Circle"!</b> The money goes into the Mathematics Department Annual Fund and is routed through the University of Wisconsin Foundation, which is convenient for record-keeping, etc.<br />
<br />
Alternately, you can bring a check to one of the Math Circle Meetings. If you write a check, be sure to make it payable to the "WFAA" and add the note "Math Circle Donation" on the check. <br />
<br />
Or you can make donations in cash, and we'll give you a receipt.<br />
<br />
==Help us grow!==<br />
If you like Math Circle, please help us continue to grow! Students, parents, and teachers can help by:<br />
* Like our [https://facebook.com/madisonmathcircle '''Facebook Page'''] and share our events with others! <br />
* Posting our [https://www.math.wisc.edu/wiki/images/Math_Circle_Flyer_2021.pdf '''flyer'''] at schools or anywhere that might have interested students.<br />
* Discussing the Math Circle with students, parents, teachers, administrators, and others.<br />
* Making an announcement about Math Circle at PTO meetings.<br />
* Donating to Math Circle.<br />
Contact the organizers if you have questions or your own ideas about how to help out.<br />
<br />
=Useful Resources=<br />
<!--==Annual Reports==<br />
[https://www.math.wisc.edu/wiki/images/Math_Circle_Newsletter.pdf 2013-2014 Annual Report]--><br />
<br />
== Archived Abstracts ==<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts_2020-2021 2020 - 2021 Abstracts]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts_2019-2020 2019 - 2020 Abstracts]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_2016-2017 2016 - 2017 Math Circle Page]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts_2016-2017 2016 - 2017 Abstracts]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_2015-2016 2015 - 2016 Math Circle Page]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Math_Circle_de_Madison_2015-2016 2015 - 2016 Math Circle Page (Spanish)]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts_2015-2016 2015 - 2015 Abstracts]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Archived_Math_Circle_Material The way-back archives]<br />
<br />
==Link for presenters (in progress)==<br />
[https://www.math.wisc.edu/wiki/index.php/Math_Circle_Presentations Advice For Math Circle Presenters]<br />
<br />
[http://www.geometer.org/mathcircles/ Sample Talk Ideas/Problems from Tom Davis]<br />
<br />
[https://www.mathcircles.org/activities Sample Talks from the National Association of Math Circles]<br />
<br />
[https://epdf.pub/circle-in-a-box715623b97664e247f2118ddf7bec4bfa35437.html "Circle in a Box"]</div>Csimpson6https://wiki.math.wisc.edu/index.php?title=New_GAGS&diff=19377New GAGS2020-04-22T01:30:19Z<p>Csimpson6: </p>
<hr />
<div><center><br />
{| style="color:black; font-size:120%; text-align:left;background-color:#eeeeee"<br />
|- style="background-color:#dddddd"<br />
! width="130" | Date<br />
! width="550" | Speaker<br />
|- style="vertical-align:top"<br />
|rowspan="2" style="background-color:#dddddd"| January 29<br />
| Colin Crowley<br />
|- sytle="bottom-margin:5px"<br />
| <div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:550px; overflow:auto;"><i><br />
A good talk<br />
</i><div class="mw-collapsible-content"><br />
owing year he won a decisive victory over the French at the Battle of the Nile and remained in the Mediterranean to support the Kingdom of Naples against a French invasion. In 1801 he was dispatched to the Baltic and won another victory, this time over the Danes at the Battle of Copenhagen. He commanded the blockade of the French and Spanish fleets at Toulon and, after their escape, chased them to the West Indies and back but failed to bring them to battle. After a brief return to England he took over the Cádiz blockade in 1805. On 21 October 1805, the Franco-Spanish fleet came out of port, and Nelson's fleet engaged them at the Battle of Trafalgar. The battle became one of Britain's greatest naval victories, but Nelson, aboard HMS Victory, was fatally wounded by a French sharpshooter. His body was brought back to England where he was <br />
</div></div><br />
|-<br />
|- style="vertical-align:top"<br />
|rowspan="2" style="background-color:#dddddd"| January 29<br />
| Colin Crowley<br />
|- style="border-width:0px 0px 0px 3px; border-style:solid"<br />
| <div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:550px; overflow:auto;"><i><br />
A good talk<br />
</i><div class="mw-collapsible-content"><br />
owing year he won a decisive victory over the French at the Battle of the Nile and remained in the Mediterranean to support the Kingdom of Naples against a French invasion. In 1801 he was dispatched to the Baltic and won another victory, this time over the Danes at the Battle of Copenhagen. He commanded the blockade of the French and Spanish fleets at Toulon and, after their escape, chased them to the West Indies and back but failed to bring them to battle. After a brief return to England he took over the Cádiz blockade in 1805. On 21 October 1805, the Franco-Spanish fleet came out of port, and Nelson's fleet engaged them at the Battle of Trafalgar. The battle became one of Britain's greatest naval victories, but Nelson, aboard HMS Victory, was fatally wounded by a French sharpshooter. His body was brought back to England where he was <br />
</div></div><br />
|-<br />
</center></div>Csimpson6https://wiki.math.wisc.edu/index.php?title=New_GAGS&diff=19376New GAGS2020-04-22T00:36:14Z<p>Csimpson6: </p>
<hr />
<div>== Spring 2020 ==<br />
<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="120" align="center"|'''Date'''<br />
| bgcolor="#A6B658" width="350" align="center"|'''Speaker'''<br />
|-<br />
|| January 29<br />
|| Colin Crowley<br />
|-<br />
| Can it work?<br />
|-<br />
| bgcolor="#E0E0E0"| February 5<br />
| bgcolor="#C6D46E"| Asvin Gothandaraman<br />
|-<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: <br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <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></div>Csimpson6https://wiki.math.wisc.edu/index.php?title=New_GAGS&diff=19375New GAGS2020-04-22T00:35:52Z<p>Csimpson6: </p>
<hr />
<div>== Spring 2020 ==<br />
<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="20%" align="center"|'''Date'''<br />
| bgcolor="#A6B658" width="80%" align="center"|'''Speaker'''<br />
|-<br />
|| January 29<br />
|| Colin Crowley<br />
|-<br />
| Can it work?<br />
|-<br />
| bgcolor="#E0E0E0"| February 5<br />
| bgcolor="#C6D46E"| Asvin Gothandaraman<br />
|-<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: <br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <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></div>Csimpson6https://wiki.math.wisc.edu/index.php?title=New_GAGS&diff=19374New GAGS2020-04-22T00:35:26Z<p>Csimpson6: </p>
<hr />
<div>== Spring 2020 ==<br />
<br />
<center><br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="100" align="center"|'''Date'''<br />
| bgcolor="#A6B658" width="300" align="center"|'''Speaker'''<br />
|-<br />
|| January 29<br />
|| Colin Crowley<br />
|-<br />
| Can it work?<br />
|-<br />
| bgcolor="#E0E0E0"| February 5<br />
| bgcolor="#C6D46E"| Asvin Gothandaraman<br />
|-<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: <br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <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></div>Csimpson6https://wiki.math.wisc.edu/index.php?title=New_GAGS&diff=19373New GAGS2020-04-22T00:35:09Z<p>Csimpson6: </p>
<hr />
<div>== 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 />
|-<br />
|| January 29<br />
|| Colin Crowley<br />
|-<br />
| Can it work?<br />
|-<br />
| bgcolor="#E0E0E0"| February 5<br />
| bgcolor="#C6D46E"| Asvin Gothandaraman<br />
|-<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: <br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <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></div>Csimpson6https://wiki.math.wisc.edu/index.php?title=New_GAGS&diff=19372New GAGS2020-04-22T00:30:04Z<p>Csimpson6: </p>
<hr />
<div>== 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 />
|-<br />
| bgcolor="#E0E0E0"| January 29<br />
| bgcolor="#C6D46E"|<details><br />
<summary>Colin Crowley, A talk about Lefschetz</summary><br />
Some details like an abstrct lorem ipsum <br />
</details><br />
|-<br />
| Can it work?<br />
|-<br />
| bgcolor="#E0E0E0"| February 5<br />
| bgcolor="#C6D46E"| Asvin Gothandaraman<br />
|-<br />
| bgcolor="#E0E0E0"| February 12<br />
| bgcolor="#C6D46E"| Qiao He<br />
|-<br />
| bgcolor="#E0E0E0"| February 19<br />
| bgcolor="#C6D46E"| Dima Arinkin<br />
|-<br />
| bgcolor="#E0E0E0"| February 26<br />
| bgcolor="#C6D46E"| Connor Simpson<br />
|-<br />
| bgcolor="#E0E0E0"| March 4<br />
| bgcolor="#C6D46E"| Peter<br />
|-<br />
| bgcolor="#E0E0E0"| March 11<br />
| bgcolor="#C6D46E"| Caitlyn Booms<br />
|-<br />
| bgcolor="#E0E0E0"| March 25<br />
| bgcolor="#C6D46E"| Steven He<br />
|-<br />
| bgcolor="#E0E0E0"| April 1<br />
| bgcolor="#C6D46E"| Vlad Sotirov<br />
|-<br />
| bgcolor="#E0E0E0"| April 8<br />
| bgcolor="#C6D46E"| Maya Banks<br />
|-<br />
| bgcolor="#E0E0E0"| April 15<br />
| bgcolor="#C6D46E"| Alex Hof<br />
|-<br />
| bgcolor="#E0E0E0"| April 22<br />
| bgcolor="#C6D46E"| Ruofan<br />
|-<br />
| bgcolor="#E0E0E0"| April 29<br />
| bgcolor="#C6D46E"| John Cobb<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: <br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <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></div>Csimpson6https://wiki.math.wisc.edu/index.php?title=New_GAGS&diff=19371New GAGS2020-04-22T00:28:09Z<p>Csimpson6: </p>
<hr />
<div>== 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 />
|-<br />
| bgcolor="#E0E0E0"| January 29<br />
| bgcolor="#C6D46E"|<details><br />
<summary>Colin Crowley, A talk about Lefschetz</summary><br />
Some details like an abstrct lorem ipsum <br />
</details><br />
|-<br />
| bgcolor="#E0E0E0"| February 5<br />
| bgcolor="#C6D46E"| Asvin Gothandaraman<br />
|-<br />
| bgcolor="#E0E0E0"| February 12<br />
| bgcolor="#C6D46E"| Qiao He<br />
|-<br />
| bgcolor="#E0E0E0"| February 19<br />
| bgcolor="#C6D46E"| Dima Arinkin<br />
|-<br />
| bgcolor="#E0E0E0"| February 26<br />
| bgcolor="#C6D46E"| Connor Simpson<br />
|-<br />
| bgcolor="#E0E0E0"| March 4<br />
| bgcolor="#C6D46E"| Peter<br />
|-<br />
| bgcolor="#E0E0E0"| March 11<br />
| bgcolor="#C6D46E"| Caitlyn Booms<br />
|-<br />
| bgcolor="#E0E0E0"| March 25<br />
| bgcolor="#C6D46E"| Steven He<br />
|-<br />
| bgcolor="#E0E0E0"| April 1<br />
| bgcolor="#C6D46E"| Vlad Sotirov<br />
|-<br />
| bgcolor="#E0E0E0"| April 8<br />
| bgcolor="#C6D46E"| Maya Banks<br />
|-<br />
| bgcolor="#E0E0E0"| April 15<br />
| bgcolor="#C6D46E"| Alex Hof<br />
|-<br />
| bgcolor="#E0E0E0"| April 22<br />
| bgcolor="#C6D46E"| Ruofan<br />
|-<br />
| bgcolor="#E0E0E0"| April 29<br />
| bgcolor="#C6D46E"| John Cobb<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: <br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <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></div>Csimpson6https://wiki.math.wisc.edu/index.php?title=New_GAGS&diff=19370New GAGS2020-04-22T00:20:09Z<p>Csimpson6: temporary page for improving the GAGS page</p>
<hr />
<div><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| Title]]<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: <br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <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></div>Csimpson6https://wiki.math.wisc.edu/index.php?title=Graduate_Algebraic_Geometry_Seminar&diff=19127Graduate Algebraic Geometry Seminar2020-02-25T04:22:18Z<p>Csimpson6: </p>
<hr />
<div>'''<br />
'''When:''' Wednesdays 4:25pm<br />
<br />
'''Where:''' Van Vleck B317<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 />
==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 />
== 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| Title]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 11<br />
| bgcolor="#C6D46E"| Caitlyn Booms<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 11| Title]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 25<br />
| bgcolor="#C6D46E"| Steven He<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 25| Title]]<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 Mine<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 15| Title]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 22<br />
| bgcolor="#C6D46E"| Ruofan<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 22| Title]]<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'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: <br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <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: <br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <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: <br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <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 Mine'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: <br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <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: <br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <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 />
== 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>Csimpson6https://wiki.math.wisc.edu/index.php?title=Madison_Math_Circle&diff=18966Madison Math Circle2020-02-10T05:53:14Z<p>Csimpson6: </p>
<hr />
<div>[[Image:logo.png|right|440px]]<br />
<br />
For the site in Spanish, visit [[Math Circle de Madison]]<br />
=What is a Math Circle?=<br />
The Madison Math Circle is a weekly series of mathematically based activities aimed at interested middle school and high school students. It is an outreach program organized by the UW Math Department. Our goal is to provide a taste of exciting ideas in math and science. In the past we've had talks about plasma and weather in outer space, video game graphics, and encryption. In the sessions, students (and parents) are often asked to explore problems on their own, with the presenter facilitating a discussion. The talks are independent of one another, so new students are welcome at any point.<br />
<br />
The level of the audience varies quite widely, including a mix of middle school and high school students, and the speakers generally address this by considering subjects that will be interesting for a wide range of students.<br />
<br />
<br />
[[Image: MathCircle_2.jpg|500px]] [[Image: MathCircle_4.jpg|500px]] <br />
<br />
<br />
After each talk we'll have pizza provided by the Mathematics Department, and students will have an opportunity to mingle and chat with the speaker and with other participants, to ask questions about some of the topics that have been discussed, and also about college, careers in science, etc.<br />
<br />
'''The Madison Math circle was featured in Wisconsin State Journal:''' [http://host.madison.com/wsj/news/local/education/local_schools/school-spotlight-madison-math-circle-gives-young-students-a-taste/article_77f5c042-0b3d-11e1-ba5f-001cc4c03286.html check it out]!<br />
<br />
=All right, I want to come!=<br />
<br />
We have a weekly meeting, <b>Monday at 6pm in 3255 Helen C White Library</b>, during the school year. <b>New students are welcome at any point! </b> There is no fee and the talks are independent of one another, so you can just show up any week, but we ask all participants to take a moment to register by following the link below:<br />
<br />
[https://uwmadison.co1.qualtrics.com/jfe/form/SV_e9WdAs2SXNurWFD '''Math Circle Registration Form''']<br />
<br />
All of your information is kept private, and is only used by the Madison Math Circle organizer to help run the Circle. <br />
<br />
If you are a student, we hope you will tell other interested students about these talks, and speak with your parents or with your teacher about organizing a car pool to the UW campus. If you are a parent or a teacher, we hope you'll tell your students about these talks and organize a car pool to the UW (all talks take place in 3255 Helen C White Library, on the UW-Madison campus, right next to the Memorial Union).<br />
<br />
<br />
==Directions and parking==<br />
Our meetings are held on the 3rd floor of Helen C. White Hall in room 3255.<br />
<br />
<div class="center" style="width:auto; margin-left:auto; margin-right:auto;"><br />
[[File: Helencwhitemap.png|400px]]</div><br />
<br />
'''Parking.''' Parking on campus is rather limited. Here is as list of some options:<br />
<br />
*There is a parking garage in the basement of Helen C. White, with an hourly rate. Enter from Park Street.<br />
*A 0.5 mile walk to Helen C. White Hall via [http://goo.gl/cxTzJY these directions], many spots ('''free starting 4:30pm''') [http://goo.gl/maps/Gkx1C in Lot 26 along Observatory Drive].<br />
*A 0.3 mile walk to Helen C. White Hall via [http://goo.gl/yMJIRd these directions], many spots ('''free starting 4:30pm''') [http://goo.gl/maps/vs17X in Lot 34]. <br />
*A 0.3 mile walk to Helen C. White Hall via [http://goo.gl/yMJIRd these directions], 2 metered spots (25 minute max) [http://goo.gl/maps/ukTcu in front of Lathrop Hall].<br />
*A 0.2 mile walk to Helen C. White Hall via [http://goo.gl/b8pdk2 these directions] 6 metered spots (25 minute max) around [http://goo.gl/maps/6EAnc the loop in front of Chadbourne Hall] .<br />
*For more information, see the [http://transportation.wisc.edu/parking/parking.aspx UW-Madison Parking Info website].<br />
<br />
==Email list==<br />
The best way to keep up to date with the what is going is by signing up for our email list. Send an empty email to join-mathcircle@lists.wisc.edu<br />
<br />
==Contact the organizers==<br />
The Madison Math Circle is organized by a group of professors and graduate students from the [http://www.math.wisc.edu Department of Mathematics] at the UW-Madison. If you have any questions, suggestions for topics, or so on, just email the '''organizers''' [mailto:cbooms@wisc.edu here]. We are always interested in feedback!<br />
<center><br />
<gallery widths=500px heights=250px mode="packed"><br />
File:de.jpg|[https://www.math.wisc.edu/~derman/ Prof. Daniel Erman]<br />
<!--File:Betsy.jpg|[http://www.math.wisc.edu/~stovall/ Prof. Betsy Stovall]--><br />
</gallery><br />
<br />
<gallery widths=500px heights=250px mode="packed"><br />
<!--File:juliettebruce.jpg|[http://www.math.wisc.edu/~juliettebruce/ Juliette Bruce] File:Ee.jpg|[http://www.math.wisc.edu/~evaelduque/ Eva Elduque] File:mrjulian.jpg|[http://www.math.wisc.edu/~mrjulian/ Ryan Julian] File:soumyasankar.jpg|[http://www.math.wisc.edu/~soumyasankar Soumya Sankar]--><br />
File:caitlynbooms.jpg|[https://sites.google.com/wisc.edu/cbooms Caitlyn Booms]<br />
File:colincrowley.jpg|[https://sites.google.com/view/colincrowley/home Colin Crowley]<br />
File:hyunjongkim.jpg|Hyun Jong Kim<br />
File:Xshen.jpg|[https://www.math.wisc.edu/~xshen// Xiao Shen]<br />
File:connorsimpson.jpg|[http://www.math.wisc.edu/~csimpson6/ Connor Simpson]<br />
</gallery><br />
</center><br />
<br />
==Donations==<br />
Please consider donating to the Madison Math Circle. As noted in our [https://www.math.wisc.edu/wiki/images/Math_Circle_Newsletter.pdf annual report], our main costs consist of pizza and occasional supplies for the speakers. So far our costs have been covered by donations from the UW Mathematics Department as well as a generous gifts from a private donor. But our costs are rising, primarily because this year we expect to hold more meetings than in any previous year. In fact, this year, we expect to spend at least $2500 on pizza and supplies alone.<br />
<br />
So please consider donating to support your math circle! The easiest way to donate is to go to the link:<br />
<br />
[http://www.math.wisc.edu/donate Online Donation Link]<br />
<br />
There are instructions on that page for donating to the Math Department. <b> Be sure and add a Gift Note saying that the donation is intended for the "Madison Math Circle"!</b> The money goes into the Mathematics Department Annual Fund and is routed through the University of Wisconsin Foundation, which is convenient for record-keeping, etc.<br />
<br />
Alternately, you can bring a check to one of the Math Circle Meetings. If you write a check, be sure to make it payable to the "WFAA" and add the note "Math Circle Donation" on the check. <br />
<br />
Or you can just pay in cash, and we'll give you a receipt.<br />
<br />
==Help us grow!==<br />
If you like Math Circle, please help us continue to grow! Students, parents, and teachers can help by:<br />
* Like our [https://facebook.com/madisonmathcircle '''Facebook Page'''] and share our events with others! <br />
* Posting our [https://www.math.wisc.edu/wiki/images/MMC_Flyer_2016.pdf '''flyer'''] at schools or anywhere that might have interested students.<br />
* Discussing the Math Circle with students, parents, teachers, administrators, and others.<br />
* Making an announcement about Math Circle at PTO meetings.<br />
* Donating to Math Circle.<br />
Contact the organizers if you have questions or your own ideas about how to help out.<br />
<br />
=Meetings for Fall 2019=<br />
<br />
<center><br />
<br />
Talks start at '''6pm in room 3255 of Helen C. White Library''', unless otherwise noted.<br />
<br />
</center><br />
<br />
<center><br />
<br />
{| style="color:black; font-size:120%" border="1" cellpadding="14" cellspacing="0"<br />
|-<br />
! colspan="3" style="background: #e8b2b2;" align="center" | Fall 2019<br />
|-<br />
! Date !! Speaker !! Topic<br />
|-<br />
| September 23, 2019 || Soumya Sankar || Why don't map makers like high heels?<br />
|-<br />
| September 30, 2019 || Erika Pirnes || Why do ice hockey players fall in love with mathematicians?<br />
|-<br />
| October 7, 2019 || Uri Andrews || Self-reference, proofs, and computer programming<br />
|-<br />
| October 14, 2019 || James Hanson || When is a puzzle impossible?<br />
|-<br />
| October 21, 2019 || Owen Goff || Symbolic Logic and How It's Really Just Arithmetic<br />
|-<br />
| October 28, 2019 || Ian Seong || Counting, but Not Like Kindergarteners<br />
|-<br />
| November 4, 2019 || Omer Mermelstein || Ciphers: To Gibberish and Back Again<br />
|-<br />
| November 11, 2019 || Colin Crowley || Many Pennies<br />
|-<br />
| November 18, 2019 || Daniel Corey || The K<span>&#246;</span>nigsberg Bridge Problem<br />
|-<br />
|}<br />
<br />
</center><br />
<br />
=Meetings for Spring 2020=<br />
<br />
<center><br />
<br />
Talks start at '''6pm in room 3255 of Helen C. White Library''', unless otherwise noted.<br />
<br />
</center><br />
<br />
<center><br />
<br />
{| style="color:black; font-size:120%" border="1" cellpadding="14" cellspacing="0"<br />
|-<br />
! colspan="3" style="background: #e8b2b2;" align="center" | Spring 2020<br />
|-<br />
! Date !! Speaker !! Topic<br />
|-<br />
| January 27, 2020 || Caitlyn Booms || Magic or Math?<br />
|-<br />
| February 3, 2020 || Erika Pirnes || Finding Your Roots<br />
|-<br />
| February 10, 2020 || Xiao Shen || Constructing the 17-gon<br />
|-<br />
| February 17, 2020 || Ben Bruce || 1+1=2 and Other Integer Partitions<br />
|-<br />
| February 24, 2020 || TBD || TBD<br />
|-<br />
| March 2, 2020 || TBD || TBD<br />
|-<br />
| March 9, 2020 || Connor Simpson || Counting ways to color graphs<br />
|-<br />
| March 23, 2020 || TBD || TBD<br />
|-<br />
| March 30, 2020 || TBD || TBD<br />
|-<br />
| April 6, 2020 || TBD || TBD<br />
|-<br />
| April 13, 2020 || TBD || TBD<br />
|-<br />
| April 20, 2020 || TBD || TBD<br />
|-<br />
|}<br />
<br />
</center><br />
<br />
=Off-Site Meetings=<br />
<br />
We will hold some Math Circle meetings at local high schools on early release days. If you are interesting in having us come to your high school, please contact us!<br />
<br />
<center><br />
<br />
{| style="color:black; font-size:120%" border="1" cellpadding="14" cellspacing="0"<br />
|-<br />
! colspan="5" style="background: #e8b2b2;" align="center" | Fall 2019<br />
|-<br />
|-<br />
! Date !! Location !! Speaker !! Title !! Abstract<br />
|-<br />
| October 7, 2019 || 2:45pm East High || Solly Parenti || Tangled Up in Two || Every tangled cord you have ever encountered is secretly a number. Once you learn how to count these cords, cleaning your room will be as easy as 1-2-3.<br />
|-<br />
| November 4, 2019 || 2:45pm James Madison Memorial || Caitlyn Booms || Sneaky Segments || We call a line segment drawn between two lattice points in the coordinate plane sneaky if it does not pass through any other lattice points. During this presentation, we will try to understand exactly when this happens, and we'll discuss how to calculate the probability that two randomly chosen lattice points are connected by a sneaky segment.<br />
|-<br />
| November 11, 2019 || 2:45pm East High || Maya Banks || Tic-Tac-Topology || Tic-Tac-Toe is a game usually played on a flat piece of paper. In this standard setting, there is winning strategy--that is, if the player who goes first chooses their moves correctly, they will never lose. But we can also play Tic-Tac-Toe on a surface that isn't lying flat in a plane! In this talk, we will explore the game of Tic-Tac-Toe on cylinders, donuts, and even some wilder surfaces. We'll look for optimal strategies, and learn some topology in the process.<br />
|-<br />
| December 16, 2019 || 2:45pm James Madison Memorial || Daniel Erman || Really Big Numbers || We will discuss the role that really really, really big numbers play in modern mathematics and in science. This will be a discussion of estimation and an introduction to some of the ways that mathematicians express unfathomably big numbers.<br />
|}<br />
<br />
<br />
<br />
{| style="color:black; font-size:120%" border="1" cellpadding="14" cellspacing="0"<br />
|-<br />
! colspan="5" style="background: #e8b2b2;" align="center" | Spring 2020<br />
|-<br />
|-<br />
! Date !! Location !! Speaker !! Title !! Abstract<br />
|-<br />
| February 17, 2020 || 2:45pm James Madison Memorial || Maya Banks || Tic-Tac-Topology || Tic-Tac-Toe is a game usually played on a flat piece of paper. In this standard setting, there is winning strategy--that is, if the player who goes first chooses their moves correctly, they will never lose. But we can also play Tic-Tac-Toe on a surface that isn't lying flat in a plane! In this talk, we will explore the game of Tic-Tac-Toe on cylinders, donuts, and even some wilder surfaces. We'll look for optimal strategies, and learn some topology in the process.<br />
|-<br />
| March 9, 2020 || 2:45pm East High || Michel Alexis || TBD || TBD<br />
|-<br />
| April 13, 2020 || 2:45pm James Madison Memorial || Juliette Bruce || TBD || TBD<br />
|-<br />
| April 20, 2020 || 2:45pm East High || TBD || TBD || TBD<br />
|}<br />
</center><br />
<br />
=Useful Resources=<br />
==Annual Reports==<br />
[https://www.math.wisc.edu/wiki/images/Math_Circle_Newsletter.pdf 2013-2014 Annual Report]<br />
<br />
== Archived Abstracts ==<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_2016-2017 2016 - 2017 Math Circle Page]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts_2016-2017 2016 - 2017 Abstracts]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_2015-2016 2015 - 2016 Math Circle Page]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Math_Circle_de_Madison_2015-2016 2015 - 2016 Math Circle Page (Spanish)]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts_2015-2016 2015 - 2015 Abstracts]<br />
<br />
[[Archived Math Circle Material]]<br />
<br />
==Link for presenters (in progress)==<br />
[https://www.math.wisc.edu/wiki/index.php/Math_Circle_Presentations Advice For Math Circle Presenters]<br />
<br />
[http://www.geometer.org/mathcircles/ Sample Talk Ideas/Problems from Tom Davis]<br />
<br />
[https://www.mathcircles.org/activities Sample Talks from the National Association of Math Circles]<br />
<br />
[https://epdf.pub/circle-in-a-box715623b97664e247f2118ddf7bec4bfa35437.html "Circle in a Box"]</div>Csimpson6https://wiki.math.wisc.edu/index.php?title=Graduate_Algebraic_Geometry_Seminar&diff=18864Graduate Algebraic Geometry Seminar2020-02-02T04:48:00Z<p>Csimpson6: </p>
<hr />
<div>'''<br />
'''When:''' Wednesdays 4:25pm<br />
<br />
'''Where:''' Van Vleck B317<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 />
==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 />
== 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"| Speaker<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#January 29| Title]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 5<br />
| bgcolor="#C6D46E"| Speaker<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 5| Title]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 12<br />
| bgcolor="#C6D46E"| Speaker<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 12| Title]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 19<br />
| bgcolor="#C6D46E"| Speaker<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 19| Title]]<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"| Speaker<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 4| Title]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 11<br />
| bgcolor="#C6D46E"| Caitlyn Booms<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 11| Title]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 25<br />
| bgcolor="#C6D46E"| Speaker<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 25| Title]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 1<br />
| bgcolor="#C6D46E"| Speaker<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 1| Title]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 8<br />
| bgcolor="#C6D46E"| Speaker<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 8| Title]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 15<br />
| bgcolor="#C6D46E"| Speaker<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 15| Title]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 22<br />
| bgcolor="#C6D46E"| Speaker<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 22| Title]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 29<br />
| bgcolor="#C6D46E"| Speaker<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%" | '''Speaker'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: <br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
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</center><br />
<br />
== February 5 ==<br />
<center><br />
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|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Speaker'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: <br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
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</center><br />
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== 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%" | '''Speaker'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: <br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
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</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%" | '''Speaker'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: <br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
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</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%" | '''Speaker'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: <br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <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%" | '''Speaker'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: <br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
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</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: <br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <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%" | '''Speaker'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: <br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
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</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%" | '''Speaker'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: <br />
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| bgcolor="#BCD2EE" | Abstract: <br />
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</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%" | '''Speaker'''<br />
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| bgcolor="#BCD2EE" | Abstract: <br />
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</center><br />
<br />
== April 15 ==<br />
<center><br />
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|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Speaker'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: <br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
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</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%" | '''Speaker'''<br />
|-<br />
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|-<br />
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</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%" | '''Speaker'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: <br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
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<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 />
== 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>Csimpson6https://wiki.math.wisc.edu/index.php?title=Madison_Math_Circle&diff=18806Madison Math Circle2020-01-27T20:37:01Z<p>Csimpson6: /* Meetings for Spring 2020 */</p>
<hr />
<div>[[Image:logo.png|right|440px]]<br />
<br />
For the site in Spanish, visit [[Math Circle de Madison]]<br />
=What is a Math Circle?=<br />
The Madison Math Circle is a weekly series of mathematically based activities aimed at interested middle school and high school students. It is an outreach program organized by the UW Math Department. Our goal is to provide a taste of exciting ideas in math and science. In the past we've had talks about plasma and weather in outer space, video game graphics, and encryption. In the sessions, students (and parents) are often asked to explore problems on their own, with the presenter facilitating a discussion. The talks are independent of one another, so new students are welcome at any point.<br />
<br />
The level of the audience varies quite widely, including a mix of middle school and high school students, and the speakers generally address this by considering subjects that will be interesting for a wide range of students.<br />
<br />
<br />
[[Image: MathCircle_2.jpg|500px]] [[Image: MathCircle_4.jpg|500px]] <br />
<br />
<br />
After each talk we'll have pizza provided by the Mathematics Department, and students will have an opportunity to mingle and chat with the speaker and with other participants, to ask questions about some of the topics that have been discussed, and also about college, careers in science, etc.<br />
<br />
'''The Madison Math circle was featured in Wisconsin State Journal:''' [http://host.madison.com/wsj/news/local/education/local_schools/school-spotlight-madison-math-circle-gives-young-students-a-taste/article_77f5c042-0b3d-11e1-ba5f-001cc4c03286.html check it out]!<br />
<br />
=All right, I want to come!=<br />
<br />
We have a weekly meeting, <b>Monday at 6pm in 3255 Helen C White Library</b>, during the school year. <b>New students are welcome at any point! </b> There is no fee and the talks are independent of one another, so you can just show up any week, but we ask all participants to take a moment to register by following the link below:<br />
<br />
[https://uwmadison.co1.qualtrics.com/jfe/form/SV_e9WdAs2SXNurWFD '''Math Circle Registration Form''']<br />
<br />
All of your information is kept private, and is only used by the Madison Math Circle organizer to help run the Circle. <br />
<br />
If you are a student, we hope you will tell other interested students about these talks, and speak with your parents or with your teacher about organizing a car pool to the UW campus. If you are a parent or a teacher, we hope you'll tell your students about these talks and organize a car pool to the UW (all talks take place in 3255 Helen C White Library, on the UW-Madison campus, right next to the Memorial Union).<br />
<br />
<br />
==Directions and parking==<br />
Our meetings are held on the 3rd floor of Helen C. White Hall in room 3255.<br />
<br />
<div class="center" style="width:auto; margin-left:auto; margin-right:auto;"><br />
[[File: Helencwhitemap.png|400px]]</div><br />
<br />
'''Parking.''' Parking on campus is rather limited. Here is as list of some options:<br />
<br />
*There is a parking garage in the basement of Helen C. White, with an hourly rate. Enter from Park Street.<br />
*A 0.5 mile walk to Helen C. White Hall via [http://goo.gl/cxTzJY these directions], many spots ('''free starting 4:30pm''') [http://goo.gl/maps/Gkx1C in Lot 26 along Observatory Drive].<br />
*A 0.3 mile walk to Helen C. White Hall via [http://goo.gl/yMJIRd these directions], many spots ('''free starting 4:30pm''') [http://goo.gl/maps/vs17X in Lot 34]. <br />
*A 0.3 mile walk to Helen C. White Hall via [http://goo.gl/yMJIRd these directions], 2 metered spots (25 minute max) [http://goo.gl/maps/ukTcu in front of Lathrop Hall].<br />
*A 0.2 mile walk to Helen C. White Hall via [http://goo.gl/b8pdk2 these directions] 6 metered spots (25 minute max) around [http://goo.gl/maps/6EAnc the loop in front of Chadbourne Hall] .<br />
*For more information, see the [http://transportation.wisc.edu/parking/parking.aspx UW-Madison Parking Info website].<br />
<br />
==Email list==<br />
The best way to keep up to date with the what is going is by signing up for our email list. Send an empty email to join-mathcircle@lists.wisc.edu<br />
<br />
==Contact the organizers==<br />
The Madison Math Circle is organized by a group of professors and graduate students from the [http://www.math.wisc.edu Department of Mathematics] at the UW-Madison. If you have any questions, suggestions for topics, or so on, just email the '''organizers''' [mailto:cbooms@wisc.edu here]. We are always interested in feedback!<br />
<center><br />
<gallery widths=480px heights=240px mode="packed"><br />
File:de.jpg|[https://www.math.wisc.edu/~derman/ Prof. Daniel Erman]<br />
<!--File:Betsy.jpg|[http://www.math.wisc.edu/~stovall/ Prof. Betsy Stovall]--><br />
</gallery><br />
<br />
<gallery widths=500px heights=250px mode="packed"><br />
<!--File:juliettebruce.jpg|[http://www.math.wisc.edu/~juliettebruce/ Juliette Bruce] File:Ee.jpg|[http://www.math.wisc.edu/~evaelduque/ Eva Elduque] File:mrjulian.jpg|[http://www.math.wisc.edu/~mrjulian/ Ryan Julian] File:soumyasankar.jpg|[http://www.math.wisc.edu/~soumyasankar Soumya Sankar]--><br />
File:caitlynbooms.jpg|[https://sites.google.com/wisc.edu/cbooms Caitlyn Booms]<br />
File:colincrowley.jpg|[https://sites.google.com/view/colincrowley/home Colin Crowley]<br />
File:hyunjongkim.jpg|Hyun Jong Kim<br />
File:connorsimpson.jpg|[http://www.math.wisc.edu/~csimpson6/ Connor Simpson]<br />
</gallery><br />
</center><br />
<br />
==Donations==<br />
Please consider donating to the Madison Math Circle. As noted in our [https://www.math.wisc.edu/wiki/images/Math_Circle_Newsletter.pdf annual report], our main costs consist of pizza and occasional supplies for the speakers. So far our costs have been covered by donations from the UW Mathematics Department as well as a generous gifts from a private donor. But our costs are rising, primarily because this year we expect to hold more meetings than in any previous year. In fact, this year, we expect to spend at least $2500 on pizza and supplies alone.<br />
<br />
So please consider donating to support your math circle! The easiest way to donate is to go to the link:<br />
<br />
[http://www.math.wisc.edu/donate Online Donation Link]<br />
<br />
There are instructions on that page for donating to the Math Department. <b> Be sure and add a Gift Note saying that the donation is intended for the "Madison Math Circle"!</b> The money goes into the Mathematics Department Annual Fund and is routed through the University of Wisconsin Foundation, which is convenient for record-keeping, etc.<br />
<br />
Alternately, you can bring a check to one of the Math Circle Meetings. If you write a check, be sure to make it payable to the "WFAA" and add the note "Math Circle Donation" on the check. <br />
<br />
Or you can just pay in cash, and we'll give you a receipt.<br />
<br />
==Help us grow!==<br />
If you like Math Circle, please help us continue to grow! Students, parents, and teachers can help by:<br />
* Like our [https://facebook.com/madisonmathcircle '''Facebook Page'''] and share our events with others! <br />
* Posting our [https://www.math.wisc.edu/wiki/images/MMC_Flyer_2016.pdf '''flyer'''] at schools or anywhere that might have interested students.<br />
* Discussing the Math Circle with students, parents, teachers, administrators, and others.<br />
* Making an announcement about Math Circle at PTO meetings.<br />
* Donating to Math Circle.<br />
Contact the organizers if you have questions or your own ideas about how to help out.<br />
<br />
=Meetings for Fall 2019=<br />
<br />
<center><br />
<br />
Talks start at '''6pm in room 3255 of Helen C. White Library''', unless otherwise noted.<br />
<br />
</center><br />
<br />
<center><br />
<br />
{| style="color:black; font-size:120%" border="1" cellpadding="14" cellspacing="0"<br />
|-<br />
! colspan="3" style="background: #e8b2b2;" align="center" | Fall 2019<br />
|-<br />
! Date !! Speaker !! Topic<br />
|-<br />
| September 23, 2019 || Soumya Sankar || Why don't map makers like high heels?<br />
|-<br />
| September 30, 2019 || Erika Pirnes || Why do ice hockey players fall in love with mathematicians?<br />
|-<br />
| October 7, 2019 || Uri Andrews || Self-reference, proofs, and computer programming<br />
|-<br />
| October 14, 2019 || James Hanson || When is a puzzle impossible?<br />
|-<br />
| October 21, 2019 || Owen Goff || Symbolic Logic and How It's Really Just Arithmetic<br />
|-<br />
| October 28, 2019 || Ian Seong || Counting, but Not Like Kindergarteners<br />
|-<br />
| November 4, 2019 || Omer Mermelstein || Ciphers: To Gibberish and Back Again<br />
|-<br />
| November 11, 2019 || Colin Crowley || Many Pennies<br />
|-<br />
| November 18, 2019 || Daniel Corey || The K<span>&#246;</span>nigsberg Bridge Problem<br />
|-<br />
|}<br />
<br />
</center><br />
<br />
=Meetings for Spring 2020=<br />
<br />
<center><br />
<br />
Talks start at '''6pm in room 3255 of Helen C. White Library''', unless otherwise noted.<br />
<br />
</center><br />
<br />
<center><br />
<br />
{| style="color:black; font-size:120%" border="1" cellpadding="14" cellspacing="0"<br />
|-<br />
! colspan="3" style="background: #e8b2b2;" align="center" | Spring 2020<br />
|-<br />
! Date !! Speaker !! Topic<br />
|-<br />
| January 27, 2020 || Caitlyn Booms || Magic or Math?<br />
|-<br />
| February 3, 2020 || Erika Pirnes || Finding Your Roots<br />
|-<br />
| February 10, 2020 || Xiao Shen || Constructing the 7-gon<br />
|-<br />
| February 17, 2020 || Ben Bruce || TBD<br />
|-<br />
| February 24, 2020 || TBD || TBD<br />
|-<br />
| March 2, 2020 || TBD || TBD<br />
|-<br />
| March 9, 2020 || TBD || TBD<br />
|-<br />
| March 23, 2020 || TBD || TBD<br />
|-<br />
| March 30, 2020 || TBD || TBD<br />
|-<br />
| April 6, 2020 || TBD || TBD<br />
|-<br />
| April 13, 2020 || TBD || TBD<br />
|-<br />
| April 20, 2020 || TBD || TBD<br />
|-<br />
|}<br />
<br />
</center><br />
<br />
=Off-Site Meetings=<br />
<br />
We will hold some Math Circle meetings at local high schools on early release days. If you are interesting in having us come to your high school, please contact us!<br />
<br />
<center><br />
<br />
{| style="color:black; font-size:120%" border="1" cellpadding="14" cellspacing="0"<br />
|-<br />
! colspan="5" style="background: #e8b2b2;" align="center" | Fall 2019<br />
|-<br />
|-<br />
! Date !! Location !! Speaker !! Title !! Abstract<br />
|-<br />
| October 7, 2019 || 2:45pm East High || Solly Parenti || Tangled Up in Two || Every tangled cord you have ever encountered is secretly a number. Once you learn how to count these cords, cleaning your room will be as easy as 1-2-3.<br />
|-<br />
| November 4, 2019 || 2:45pm James Madison Memorial || Caitlyn Booms || Sneaky Segments || We call a line segment drawn between two lattice points in the coordinate plane sneaky if it does not pass through any other lattice points. During this presentation, we will try to understand exactly when this happens, and we'll discuss how to calculate the probability that two randomly chosen lattice points are connected by a sneaky segment.<br />
|-<br />
| November 11, 2019 || 2:45pm East High || Maya Banks || Tic-Tac-Topology || Tic-Tac-Toe is a game usually played on a flat piece of paper. In this standard setting, there is winning strategy--that is, if the player who goes first chooses their moves correctly, they will never lose. But we can also play Tic-Tac-Toe on a surface that isn't lying flat in a plane! In this talk, we will explore the game of Tic-Tac-Toe on cylinders, donuts, and even some wilder surfaces. We'll look for optimal strategies, and learn some topology in the process.<br />
|-<br />
| December 16, 2019 || 2:45pm James Madison Memorial || Daniel Erman || Really Big Numbers || We will discuss the role that really really, really big numbers play in modern mathematics and in science. This will be a discussion of estimation and an introduction to some of the ways that mathematicians express unfathomably big numbers.<br />
|}<br />
<br />
<br />
<br />
{| style="color:black; font-size:120%" border="1" cellpadding="14" cellspacing="0"<br />
|-<br />
! colspan="5" style="background: #e8b2b2;" align="center" | Spring 2020<br />
|-<br />
|-<br />
! Date !! Location !! Speaker !! Title !! Abstract<br />
|-<br />
| February 17, 2020 || 2:45pm James Madison Memorial || TBD || TBD || TBD<br />
|-<br />
| March 9, 2020 || 2:45pm East High || TBD || TBD || TBD<br />
|-<br />
| April 13, 2020 || 2:45pm James Madison Memorial || TBD || TBD || TBD<br />
|-<br />
| April 20, 2020 || 2:45pm East High || TBD || TBD || TBD<br />
|}<br />
</center><br />
<br />
=Useful Resources=<br />
==Annual Reports==<br />
[https://www.math.wisc.edu/wiki/images/Math_Circle_Newsletter.pdf 2013-2014 Annual Report]<br />
<br />
== Archived Abstracts ==<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_2016-2017 2016 - 2017 Math Circle Page]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts_2016-2017 2016 - 2017 Abstracts]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_2015-2016 2015 - 2016 Math Circle Page]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Math_Circle_de_Madison_2015-2016 2015 - 2016 Math Circle Page (Spanish)]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts_2015-2016 2015 - 2015 Abstracts]<br />
<br />
[[Archived Math Circle Material]]<br />
<br />
==Link for presenters (in progress)==<br />
[https://www.math.wisc.edu/wiki/index.php/Math_Circle_Presentations Advice For Math Circle Presenters]<br />
<br />
[http://www.mathcircles.org/math-problems-2/ Sample Talk Ideas/Problems]<br />
<br />
[https://www.mathcircles.org/wp-content/uploads/2017/07/circleinabox.pdf "Circle in a Box"]</div>Csimpson6https://wiki.math.wisc.edu/index.php?title=Graduate_Algebraic_Geometry_Seminar&diff=18009Graduate Algebraic Geometry Seminar2019-09-25T14:38:19Z<p>Csimpson6: </p>
<hr />
<div>'''<br />
'''When:''' Wednesdays 4:25pm<br />
<br />
'''Where:''' Van Vleck B317<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 />
<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 />
== Fall 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"| September 18<br />
| bgcolor="#C6D46E"| David Wagner<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#September 18| M_g Potpourri]]<br />
|-<br />
| bgcolor="#E0E0E0"| September 25<br />
| bgcolor="#C6D46E"| Shengyuan Huang<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#September 25| Derived Groups and Groupoids]]<br />
|-<br />
| bgcolor="#E0E0E0"| October 2<br />
| bgcolor="#C6D46E"| Niundun Wang<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#October 2| Title TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| October 9<br />
| bgcolor="#C6D46E"| Brandon Boggess<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#October 9| Title TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| October 16<br />
| bgcolor="#C6D46E"| Soumya Sankar<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#October 16| Title TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| October 23<br />
| bgcolor="#C6D46E"| Alex Mine<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#October 23| Title TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| October 30<br />
| bgcolor="#C6D46E"| Vlad Sotirov<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#October 30| Title TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| November 6<br />
| bgcolor="#C6D46E"| Connor Simpson<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#November 6| Lorentzian Polynomials]]<br />
|-<br />
| bgcolor="#E0E0E0"| November 13<br />
| bgcolor="#C6D46E"| Alex Hof<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#November 13| Title TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| November 20<br />
| bgcolor="#C6D46E"| Caitlyn Booms<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#November 20| Title TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| November 27<br />
| bgcolor="#C6D46E"| Thanksgiving Break<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#November 27| ]]<br />
|-<br />
| bgcolor="#E0E0E0"| December 4<br />
| bgcolor="#C6D46E"| Colin Crowley<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#December 4| Title TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| December 11<br />
| bgcolor="#C6D46E"| Erika Pirnes<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#December 11| Title TBD]]<br />
|}<br />
</center><br />
<br />
== September 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%" | '''David Wagner'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: M_g Potpourri<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: In 1983, David Mumford proposed that the rational cohomology ring of Mg should be a polynomial algebra. I will discuss some of the history of Mumford's conjecture, possibly indicating a few ideas from the 2007 proof as the Madsen-Weiss theorem. If all goes well, the talk will take us through such diverse places as homotopy theory, representation stability, combinatorics of ribbon graph complexes, and deformations of algebras.<br />
<br />
|} <br />
</center><br />
<br />
== September 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%" | '''Shengyuan Huang'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Derived Groups and Groupoids<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: In this talk, we will discuss groups and groupoids in the derived category of dg schemes. I will focus on examples instead of the abstract theory. If X is a smooth subscheme of a smooth scheme S over the field of complex numbers, then the derived self-intersection of X in S is a groupoid. We will investigate the corresponding Lie algebroid of the groupoid I mentioned above, and exponential map between them.<br />
<br />
|} <br />
</center><br />
<br />
== October 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%" | '''Niundun Wang'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title:<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
|} <br />
</center><br />
<br />
== October 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%" | '''Brandon Boggess'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title:<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
|} <br />
</center><br />
<br />
== October 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%" | '''Soumya Sankar'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title:<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
|} <br />
</center><br />
<br />
== October 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%" | '''Alex Mine'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title:<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
|} <br />
</center><br />
<br />
== October 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%" | '''Vlad Sotirov'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title:<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
|} <br />
</center><br />
<br />
== November 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" align="center" | Title:<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract:<br />
<br />
|} <br />
</center><br />
<br />
== November 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%" | '''Alex Hof'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title:<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
|} <br />
</center><br />
<br />
== November 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" align="center" | Title:<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
|} <br />
</center><br />
<br />
== November 28 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Thanksgiving Break'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title:<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
|} <br />
</center><br />
<br />
== December 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%" | '''Colin Crowley'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title:<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract:<br />
<br />
|} <br />
</center><br />
<br />
== December 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%" | '''Erika Pirnes'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title:<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract:<br />
<br />
|} <br />
</center><br />
<br />
== Organizers' Contact Info ==<br />
<br />
<br />
[https://sites.google.com/wisc.edu/cbooms/ Caitlyn Booms]<br />
<br />
[http://www.math.wisc.edu/~drwagner/ David Wagner]<br />
<br />
<br />
== Past Semesters ==<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>Csimpson6https://wiki.math.wisc.edu/index.php?title=Matroids_seminar&diff=17420Matroids seminar2019-05-03T22:15:08Z<p>Csimpson6: </p>
<hr />
<div>The matroids seminar & reading group meets '''10:00--10:45 on Fridays in Van Vleck 901''' in order to discuss matroids from a variety of viewpoints.<br />
In particular, we aim to<br />
* survey open conjectures and recent work in the area<br />
* compute many interesting examples<br />
* discover concrete applications<br />
For updates, join our mailing list, matroids [at] lists.wisc.edu<br />
<br />
We are happy to have new leaders of the discussion, and the wide range of topics to which matroids are related mean that each week is a great chance for a new participant to drop in! If you would like to talk but need ideas, see the [[Matroids seminar/ideas]] page.<br />
<br />
To help develop an inclusive environment, a subset of the organizers will be available before the talk in the ninth floor lounge to informally discuss background material e.g., "What is a variety?", "What is a circuit?", "What is a greedy algorithm?" (this is especially for those coming from an outside area).<br />
<br />
'''Organizers''': Colin Crowley, Connor Simpson; Daniel Corey, Jose Israel Rodriguez<br />
{|cellpadding="8px" style="vertical-align:top; text-align:left; cellpadding:10px;"<br />
|-<br />
|5/03/2019<br />
|<br />
<div style="font-weight:bold;">[http://www.math.wisc.edu/~csimpson6/ Connor Simpson]</div><br />
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"><br />
<div><i>A flip-free proof of the Heron-Rota-Welsh conjecture</i></div><br />
<div class="mw-collapsible-content"><br />
The simplicial presentation of a matroid yields a flip-free proof of the Kahler package in degree 1 for the Chow ring of a matroid, which is enough to give a new proof of the Heron-Rota-Welsh conjecture.<br />
This talk is more or less a continuation of the one that Chris Eur gave earlier in the semester in the algebra seminar, and is based on the same joint work with Spencer Backman and Chris Eur.<br />
</div></div><br />
|-<br />
|4/12/2019 & 4/19/2019<br />
|<br />
<div style="font-weight:bold;">No seminar</div><br />
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"><br />
<div><i>Many organizers are traveling.</i></div><br />
<div class="mw-collapsible-content"><br />
None. <br />
</div></div><br />
|-<br />
|4/05/2019<br />
|<br />
<div style="font-weight:bold;">Jose Israel Rodriguez</div><br />
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"><br />
<div><i>Planar pentads, polynomial systems, and polymatroids</i></div><br />
<div class="mw-collapsible-content"><br />
Computing exceptional sets using fiber products naturally yields multihomogeneous systems of polynomial equations. <br />
In this talk, I will utilize a variety of tools from the forthcoming paper "A numerical toolkit for multiprojective varieties" to work out an example from kinematics: exceptional planar pentads.<br />
In particular, we will derive a multihomogeneous polynomial system whose solutions have meaning in kinematics and discuss how polymatroids play a role in describing the solutions. <br />
</div></div><br />
|-<br />
|3/29/2019<br />
|<br />
<div style="font-weight:bold;">Colin Crowley</div><br />
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"><br />
<div><i>Binary matroids and Seymour's decomposition in coding theory</i></div><br />
<div class="mw-collapsible-content"><br />
We will begin by discussing the equivalence between a binary matroid and a binary linear code. And then following [https://ac.els-cdn.com/009589568990052X/1-s2.0-009589568990052X-main.pdf?_tid=a1d8598e-c5f2-4c07-8d7b-0843e88c416f&acdnat=1552505468_33915774714b2e407e4fd7001ba33100 this paper] and [https://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=4544972 this one], we will describe the Maximum Likelihood decoding problem and then outline how Seymour's decomposition theorem for regular matroids led to a polynomial time algorithm on a subclass of binary linear codes.<br />
</div></div><br />
|-<br />
|3/15/2019<br />
|<br />
<div style="font-weight:bold;">[https://sites.google.com/site/dcorey2814/home Daniel Corey]</div><br />
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"><br />
<div><i>The geometry of thin Schubert cells</i></div><br />
<div class="mw-collapsible-content"><br />
We will cover the distinction between the thin Schubert cell of a matroid and the realization space of a matroid, how to compute examples, Mnev universality, and time permitting, maps between thin Schubert cells. <br />
</div></div><br />
|-<br />
|3/8/2019<br />
|<br />
<div style="font-weight:bold;">Vladmir Sotirov</div><br />
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"><br />
<div><i>is sick</i></div><br />
<div class="mw-collapsible-content"><br />
Plague and pestilence!<br />
</div></div><br />
|-<br />
|3/1/2019<br />
|<br />
<div style="font-weight:bold;">[https://math.berkeley.edu/~ceur/ Chris Eur]</div><br />
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"><br />
<div><i>The multivariate Tutte polynomial of a flag matroid</i></div><br />
<div class="mw-collapsible-content"><br />
Flag matroids are combinatorial objects whose relation to ordinary matroids are akin to that of flag varieties to Grassmannians. We define a multivariate Tutte polynomial of a flag matroid, and show that it is Lorentzian in the sense of [https://arxiv.org/abs/1902.03719 Branden-Huh '19]. As a consequence, we obtain a flag matroid generalization of Mason’s conjecture concerning the f-vector of independent subsets of a matroid. This is an on-going joint work with June Huh.<br />
</div></div><br />
|-<br />
|2/22/2019<br />
|<br />
<div style="font-weight:bold;">[https://www.math.wisc.edu/~wang/ Botong Wang]</div><br />
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"><br />
<div><i>The Kazhdan-Lusztig polynomial of a matroid</i></div><br />
<div class="mw-collapsible-content"><br />
Classically, Kazdhan-Lusztig polynomials are associated to intervals of the Bruhat poset of a Coxeter group. We will discuss an analogue of Kazdhan-Lusztig polynomials for matroids, including results and conjectures from [https://arxiv.org/pdf/1611.07474.pdf these] [https://arxiv.org/pdf/1412.7408.pdf two] papers. <br />
</div></div><br />
|-<br />
|2/15/2019<br />
|<br />
<div style="font-weight:bold;">Colin Crowley</div><br />
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"><br />
<div><i>Matroid polytopes</i></div><br />
<div class="mw-collapsible-content"><br />
We outline the original formulation of matroid polytopes as moment polytopes of subvarieties of the Grassmanian, following [http://www.math.ias.edu/~goresky/pdf/combinatorial.jour.pdf Combinatorial Geometries, Convex Polyhedra, and Schbert Cells].<br />
</div></div><br />
|-<br />
|2/8/2019<br />
|<br />
<div style="font-weight:bold;">[http://www.math.wisc.edu/~csimpson6/ Connor Simpson]</div><br />
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"><br />
<div><i>Proving the Heron-Rota-Welsh conjecture</i></div><br />
<div class="mw-collapsible-content"><br />
We outline the proof of the Heron-Rota-Welsh conjecture given by Adiprasito, Huh, and Katz in their paper [https://arxiv.org/abs/1511.02888 Hodge theory for combinatorial geometries]<br />
</div></div><br />
|-<br />
|1/25/2019 & 2/1/2019<br />
|<br />
<div style="font-weight:bold;">[https://www.math.wisc.edu/~jose/ Jose Israel Rodriguez]</div><br />
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"><br />
<div><i>Algebraic matroids in action</i></div><br />
<div class="mw-collapsible-content"><br />
We discuss algebraic matroids and their applications; see [https://arxiv.org/abs/1809.00865 Algebraic Matroids in Action].<br />
</div></div><br />
|-<br />
|1/18/2019<br />
|<br />
<div style="font-weight:bold;">[https://sites.google.com/site/dcorey2814/home Daniel Corey]</div><br />
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"><br />
<div><i>Introduction to matroids</i></div><br />
<div class="mw-collapsible-content"><br />
We'll cover the basic definitions and some examples, roughly following [http://web.ma.utexas.edu/users/sampayne/pdf/Math648Lecture3.pdf these notes].<br />
</div></div><br />
|-<br />
|}</div>Csimpson6https://wiki.math.wisc.edu/index.php?title=Main_Page&diff=17419Main Page2019-05-03T22:07:21Z<p>Csimpson6: </p>
<hr />
<div><br />
== Welcome to the University of Wisconsin Math Department Wiki ==<br />
<br />
This site is by and for the faculty, students and staff of the UW Mathematics Department. It contains useful information about the department, not always available from other sources. Pages can only be edited by members of the department but are viewable by everyone. <br />
<br />
*[[Getting Around Van Vleck]]<br />
<br />
*[[Computer Help]] <br />
<br />
*[[Connecting/Using our research servers]]<br />
<br />
*[[Graduate Student Guide]]<br />
<br />
*[[Teaching Resources]]<br />
<br />
== Research groups at UW-Madison ==<br />
<br />
*[[Algebra]]<br />
*[[Analysis]]<br />
*[[Applied|Applied Mathematics]]<br />
*[https://www.math.wisc.edu/wiki/index.php/Research_at_UW-Madison_in_DifferentialEquations Differential Equations]<br />
*[[Dynamics Special Lecture]]<br />
*[[Geometry and Topology]]<br />
* [http://www.math.wisc.edu/~lempp/logic.html Logic]<br />
*[[Probability]]<br />
<br />
== Math Seminars at UW-Madison ==<br />
<br />
*[[Colloquia|Colloquium]]<br />
*[[Algebra_and_Algebraic_Geometry_Seminar|Algebra and Algebraic Geometry Seminar]]<br />
*[[Analysis_Seminar|Analysis Seminar]]<br />
*[[Applied/ACMS|Applied and Computational Math Seminar]]<br />
*[http://www.math.wisc.edu/~zcharles/aas/index.html Applied Algebra Seminar]<br />
*[[Cookie_seminar|Cookie Seminar]]<br />
*[[Geometry_and_Topology_Seminar|Geometry and Topology Seminar]]<br />
*[[Group_Theory_Seminar|Group Theory Seminar]]<br />
*[[Matroids_seminar|Matroids seminar]]<br />
*[[Networks_Seminar|Networks Seminar]]<br />
*[[NTS|Number Theory Seminar]]<br />
*[[PDE_Geometric_Analysis_seminar| PDE and Geometric Analysis Seminar]]<br />
*[[Probability_Seminar|Probability Seminar]]<br />
* [http://www.math.wisc.edu/~lempp/conf/swlc.html Southern Wisconsin Logic Colloquium]<br />
*[[Research Recruitment Seminar]]<br />
<br />
=== Graduate Student Seminars ===<br />
<br />
*[[AMS_Student_Chapter_Seminar|AMS Student Chapter Seminar]]<br />
*[[Graduate_Algebraic_Geometry_Seminar|Graduate Algebraic Geometry Seminar]]<br />
*[[Graduate_Applied_Algebra_Seminar|Graduate Applied Algebra Seminar]]<br />
*[[Applied/GPS| GPS Applied Math Seminar]]<br />
*[[NTSGrad_Spring_2019|Graduate Number Theory/Representation Theory Seminar]]<br />
*[[Symplectic_Geometry_Seminar|Symplectic Geometry Seminar]]<br />
*[[Math843Seminar| Math 843 Homework Seminar]]<br />
*[[Graduate_student_reading_seminar|Graduate Probability Reading Seminar]]<br />
*[[Summer_stacks|Summer 2012 Stacks Reading Group]]<br />
*[[Graduate_Student_Singularity_Theory]]<br />
*[[Graduate/Postdoc Topology and Singularities Seminar]]<br />
*[[Shimura Varieties Reading Group]]<br />
*[[Summer graduate harmonic analysis seminar]]<br />
*[[Graduate Logic Seminar]]<br />
*[[SIAM Student Chapter Seminar]]<br />
*[[Summer 2019 Algebraic Geometry Reading Group]]<br />
<br />
=== Other ===<br />
*[[Madison Math Circle]]<br />
*[[High School Math Night]]<br />
*[http://www.siam-uw.org/ UW-Madison SIAM Student Chapter]<br />
*[http://www.math.wisc.edu/%7Emathclub/ UW-Madison Math Club]<br />
*[[Putnam Club]]<br />
*[[Undergraduate Math Competition]]<br />
*[[Basic Linux Seminar]]<br />
*[[Basic HTML Seminar]]<br />
<br />
== Graduate Program ==<br />
<br />
* [[Algebra Qualifying Exam]]<br />
* [[Analysis Qualifying Exam]]<br />
* [[Topology Qualifying Exam]]<br />
<br />
== Undergraduate Program ==<br />
<br />
* [[Overview of the undergraduate math program|Overview]]<br />
* [[Groups looking to hire students as tutors]]<br />
<br />
== Getting started with Wiki-stuff ==<br />
<br />
Consult the [http://meta.wikimedia.org/wiki/Help:Contents User's Guide] for information on using the wiki software.<br />
* [http://www.mediawiki.org/wiki/Manual:Configuration_settings Configuration settings list]<br />
* [http://www.mediawiki.org/wiki/Manual:FAQ MediaWiki FAQ]<br />
* [http://lists.wikimedia.org/mailman/listinfo/mediawiki-announce MediaWiki release mailing list]</div>Csimpson6https://wiki.math.wisc.edu/index.php?title=Summer_2019_Algebraic_Geometry_Reading_Group&diff=17348Summer 2019 Algebraic Geometry Reading Group2019-04-19T18:48:32Z<p>Csimpson6: </p>
<hr />
<div>This is the page for the Summer 2019 Algebraic Geometry Reading Group. <br />
<br />
== Resources ==<br />
<br />
We plan to primarily use the newest version of Ravi Vakil's The Rising Sea: Foundations of Algebraic Geometry, which can be found here: http://math.stanford.edu/~vakil/216blog/FOAGnov1817public.pdf.<br />
<br />
At times we may also use Hartshorne's Algebraic Geometry.<br />
<br />
== Schedule ==<br />
<br />
10 Total Weeks: May 13-31, June 24-August 9<br />
<br />
Roughly 3 meetings per week for 1-1.5 hours each.<br />
<br />
Exact days will be determined based on the schedules of the participants.<br />
<br />
<br />
'''Optimistic reading schedule (all chapters from Vakil):'''<br />
<br />
'''Week of May 13:''' Ch. 3, Ch. 4 (Affine schemes, structure sheaf)<br />
<br />
'''Week of May 20:''' Ch. 5, Start Ch. 6 (Properties of schemes, morphisms of schemes)<br />
<br />
'''Week of May 27:''' Finish Ch. 6, Ch. 7 (Classes of morphisms of schemes)<br />
<br />
'''Week of June 24:''' Ch. 8, Start Ch. 9 (Closed embeddings and Cartier divisors, fibered product of schemes)<br />
<br />
'''Week of July 1:''' Finish Ch. 9, Ch. 10 (Separated and proper morphisms, varieties)<br />
<br />
'''Week of July 8:''' Ch. 11, Start Ch. 12 (Dimension, regularity and smoothness)<br />
<br />
'''Week of July 15:''' Finish Ch. 12, Ch. 13 (Quasicoherent and coherent sheaves)<br />
<br />
'''Week of July 22:''' Ch. 14, Start Ch. 15 (Line bundles, projective schemes)<br />
<br />
'''Week of July 29:''' Finish Ch. 15, Ch. 16 (Pushforwards and pullbacks of quasicoherent sheaves)<br />
<br />
'''Week of August 5:''' Ch. 18, Ch. 19, Ch. 21 (Cech cohomology, curves, differentials)<br />
<br />
== General Meeting Structure ==<br />
<br />
This reading seminar will be structured as follows. Every meeting will have an assigned "leader," who will usually be one of the reading group participants, but could at times be an older grad student or professor. It will be expected that everyone attending will read the assigned chapters prior to the meeting. The "leader" is expected to additionally work out some examples prior and will be responsible for guiding the group discussion during the meeting. Meetings will primarily be spent discussing questions that everyone has about the reading and going through examples together. Depending on the interest of the group, we may also have problem solving sessions.<br />
<br />
'''If you are interested in joining this reading group, please contact Caitlyn Booms at cbooms@wisc.edu by May 8, 2019 and join the mailing list by emailing join-ag (at) lists.wisc.edu'''<br />
<br />
== Summer plans ==<br />
<br />
If you feel like telling us your general plans for the summer, so that we'll know when you are around Madison, please do so here:<br />
<br />
Caitlyn: out of town May 29-June 23 and Aug. 17-25</div>Csimpson6https://wiki.math.wisc.edu/index.php?title=Matroids_seminar&diff=17266Matroids seminar2019-04-01T20:46:52Z<p>Csimpson6: </p>
<hr />
<div>The matroids seminar & reading group meets '''10:00--10:45 on Fridays in Van Vleck 901''' in order to discuss matroids from a variety of viewpoints.<br />
In particular, we aim to<br />
* survey open conjectures and recent work in the area<br />
* compute many interesting examples<br />
* discover concrete applications<br />
For updates, join our mailing list, matroids [at] lists.wisc.edu<br />
<br />
We are happy to have new leaders of the discussion, and the wide range of topics to which matroids are related mean that each week is a great chance for a new participant to drop in! If you would like to talk but need ideas, see the [[Matroids seminar/ideas]] page.<br />
<br />
To help develop an inclusive environment, a subset of the organizers will be available before the talk in the ninth floor lounge to informally discuss background material e.g., "What is a variety?", "What is a circuit?", "What is a greedy algorithm?" (this is especially for those coming from an outside area).<br />
<br />
'''Organizers''': Colin Crowley, Connor Simpson; Daniel Corey, Jose Israel Rodriguez<br />
{| cellpadding="8px" style="vertical-align:top; text-align:left; cellpadding:10px;"<br />
|4/12/2019 & 4/19/2019<br />
|<br />
<div style="font-weight:bold;">No seminar</div><br />
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"><br />
<div><i>Many organizers are traveling.</i></div><br />
<div class="mw-collapsible-content"><br />
None. <br />
<br />
</div></div><br />
|-<br />
{| cellpadding="8px" style="vertical-align:top; text-align:left; cellpadding:10px;"<br />
|4/05/2019<br />
|<br />
<div style="font-weight:bold;">Jose Israel Rodriguez</div><br />
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"><br />
<div><i>Planar pentads, polynomial systems, and polymatroids</i></div><br />
<div class="mw-collapsible-content"><br />
Computing exceptional sets using fiber products naturally yields multihomogeneous systems of polynomial equations. <br />
In this talk, I will utilize a variety of tools from the forthcoming paper "A numerical toolkit for multiprojective varieties" to work out an example from kinematics: exceptional planar pentads.<br />
In particular, we will derive a multihomogeneous polynomial system whose solutions have meaning in kinematics and discuss how polymatroids play a role in describing the solutions. <br />
<br />
</div></div><br />
|-<br />
|3/29/2019<br />
|<br />
<div style="font-weight:bold;">Colin Crowley</div><br />
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"><br />
<div><i>Binary matroids and Seymour's decomposition in coding theory</i></div><br />
<div class="mw-collapsible-content"><br />
We will begin by discussing the equivalence between a binary matroid and a binary linear code. And then following [https://ac.els-cdn.com/009589568990052X/1-s2.0-009589568990052X-main.pdf?_tid=a1d8598e-c5f2-4c07-8d7b-0843e88c416f&acdnat=1552505468_33915774714b2e407e4fd7001ba33100 this paper] and [https://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=4544972 this one], we will describe the Maximum Likelihood decoding problem and then outline how Seymour's decomposition theorem for regular matroids led to a polynomial time algorithm on a subclass of binary linear codes.<br />
</div></div><br />
|-<br />
|3/15/2019<br />
|<br />
<div style="font-weight:bold;">[https://sites.google.com/site/dcorey2814/home Daniel Corey]</div><br />
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"><br />
<div><i>The geometry of thin Schubert cells</i></div><br />
<div class="mw-collapsible-content"><br />
We will cover the distinction between the thin Schubert cell of a matroid and the realization space of a matroid, how to compute examples, Mnev universality, and time permitting, maps between thin Schubert cells. <br />
</div></div><br />
|-<br />
|3/8/2019<br />
|<br />
<div style="font-weight:bold;">Vladmir Sotirov</div><br />
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"><br />
<div><i>is sick</i></div><br />
<div class="mw-collapsible-content"><br />
Plague and pestilence!<br />
</div></div><br />
|-<br />
|3/1/2019<br />
|<br />
<div style="font-weight:bold;">[https://math.berkeley.edu/~ceur/ Chris Eur]</div><br />
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"><br />
<div><i>The multivariate Tutte polynomial of a flag matroid</i></div><br />
<div class="mw-collapsible-content"><br />
Flag matroids are combinatorial objects whose relation to ordinary matroids are akin to that of flag varieties to Grassmannians. We define a multivariate Tutte polynomial of a flag matroid, and show that it is Lorentzian in the sense of [https://arxiv.org/abs/1902.03719 Branden-Huh '19]. As a consequence, we obtain a flag matroid generalization of Mason’s conjecture concerning the f-vector of independent subsets of a matroid. This is an on-going joint work with June Huh.<br />
</div></div><br />
|-<br />
|2/22/2019<br />
|<br />
<div style="font-weight:bold;">[https://www.math.wisc.edu/~wang/ Botong Wang]</div><br />
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"><br />
<div><i>The Kazhdan-Lusztig polynomial of a matroid</i></div><br />
<div class="mw-collapsible-content"><br />
Classically, Kazdhan-Lusztig polynomials are associated to intervals of the Bruhat poset of a Coxeter group. We will discuss an analogue of Kazdhan-Lusztig polynomials for matroids, including results and conjectures from [https://arxiv.org/pdf/1611.07474.pdf these] [https://arxiv.org/pdf/1412.7408.pdf two] papers. <br />
</div></div><br />
|-<br />
|2/15/2019<br />
|<br />
<div style="font-weight:bold;">Colin Crowley</div><br />
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"><br />
<div><i>Matroid polytopes</i></div><br />
<div class="mw-collapsible-content"><br />
We outline the original formulation of matroid polytopes as moment polytopes of subvarieties of the Grassmanian, following [http://www.math.ias.edu/~goresky/pdf/combinatorial.jour.pdf Combinatorial Geometries, Convex Polyhedra, and Schbert Cells].<br />
</div></div><br />
|-<br />
|2/8/2019<br />
|<br />
<div style="font-weight:bold;">[http://www.math.wisc.edu/~csimpson6/ Connor Simpson]</div><br />
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"><br />
<div><i>Proving the Heron-Rota-Welsh conjecture</i></div><br />
<div class="mw-collapsible-content"><br />
We outline the proof of the Heron-Rota-Welsh conjecture given by Adiprasito, Huh, and Katz in their paper [https://arxiv.org/abs/1511.02888 Hodge theory for combinatorial geometries]<br />
</div></div><br />
|-<br />
|1/25/2019 & 2/1/2019<br />
|<br />
<div style="font-weight:bold;">[https://www.math.wisc.edu/~jose/ Jose Israel Rodriguez]</div><br />
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"><br />
<div><i>Algebraic matroids in action</i></div><br />
<div class="mw-collapsible-content"><br />
We discuss algebraic matroids and their applications; see [https://arxiv.org/abs/1809.00865 Algebraic Matroids in Action].<br />
</div></div><br />
|-<br />
|1/18/2019<br />
|<br />
<div style="font-weight:bold;">[https://sites.google.com/site/dcorey2814/home Daniel Corey]</div><br />
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"><br />
<div><i>Introduction to matroids</i></div><br />
<div class="mw-collapsible-content"><br />
We'll cover the basic definitions and some examples, roughly following [http://web.ma.utexas.edu/users/sampayne/pdf/Math648Lecture3.pdf these notes].<br />
</div></div><br />
|-<br />
|}</div>Csimpson6https://wiki.math.wisc.edu/index.php?title=Matroids_seminar&diff=17156Matroids seminar2019-03-14T20:23:02Z<p>Csimpson6: </p>
<hr />
<div>The matroids seminar & reading group meets '''10:00--10:45 on Fridays in Van Vleck 901''' in order to discuss matroids from a variety of viewpoints.<br />
In particular, we aim to<br />
* survey open conjectures and recent work in the area<br />
* compute many interesting examples<br />
* discover concrete applications<br />
<br />
We are happy to have new leaders of the discussion, and the wide range of topics to which matroids are related mean that each week is a great chance for a new participant to drop in! If you would like to talk but need ideas, see the [[Matroids seminar/ideas]] page.<br />
<br />
To help develop an inclusive environment, a subset of the organizers will be available before the talk in the ninth floor lounge to informally discuss background material e.g., "What is a variety?", "What is a circuit?", "What is a greedy algorithm?" (this is especially for those coming from an outside area).<br />
<br />
'''Organizers''': Colin Crowley, Connor Simpson; Daniel Corey, Jose Israel Rodriguez<br />
<br />
{| cellpadding="8px" style="vertical-align:top; text-align:left; cellpadding:10px;"<br />
|3/29/2019<br />
|<br />
<div style="font-weight:bold;">Colin Crowley</div><br />
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"><br />
<div><i>Binary matroids and Seymour's decomposition in coding theory</i></div><br />
<div class="mw-collapsible-content"><br />
We will begin by discussing the equivalence between a binary matroid and a binary linear code. And then following [https://ac.els-cdn.com/009589568990052X/1-s2.0-009589568990052X-main.pdf?_tid=a1d8598e-c5f2-4c07-8d7b-0843e88c416f&acdnat=1552505468_33915774714b2e407e4fd7001ba33100 this paper] and [https://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=4544972 this one], we will describe the Maximum Likelihood decoding problem and then outline how Seymour's decomposition theorem for binary matroids led to a polynomial time algorithm on a subclass of binary linear codes.<br />
</div></div><br />
|-<br />
|3/15/2019<br />
|<br />
<div style="font-weight:bold;">[https://sites.google.com/site/dcorey2814/home Daniel Corey]</div><br />
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"><br />
<div><i>The geometry of thin Schubert cells</i></div><br />
<div class="mw-collapsible-content"><br />
We will cover the distinction between the thin Schubert cell of a matroid and the realization space of a matroid, how to compute examples, Mnev universality, and time permitting, maps between thin Schubert cells. <br />
</div></div><br />
|-<br />
|3/8/2019<br />
|<br />
<div style="font-weight:bold;">Vladmir Sotirov</div><br />
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"><br />
<div><i>is sick</i></div><br />
<div class="mw-collapsible-content"><br />
Plague and pestilence!<br />
</div></div><br />
|-<br />
|3/1/2019<br />
|<br />
<div style="font-weight:bold;">[https://math.berkeley.edu/~ceur/ Chris Eur]</div><br />
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"><br />
<div><i>The multivariate Tutte polynomial of a flag matroid</i></div><br />
<div class="mw-collapsible-content"><br />
Flag matroids are combinatorial objects whose relation to ordinary matroids are akin to that of flag varieties to Grassmannians. We define a multivariate Tutte polynomial of a flag matroid, and show that it is Lorentzian in the sense of [https://arxiv.org/abs/1902.03719 Branden-Huh '19]. As a consequence, we obtain a flag matroid generalization of Mason’s conjecture concerning the f-vector of independent subsets of a matroid. This is an on-going joint work with June Huh.<br />
</div></div><br />
|-<br />
|2/22/2019<br />
|<br />
<div style="font-weight:bold;">[https://www.math.wisc.edu/~wang/ Botong Wang]</div><br />
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"><br />
<div><i>The Kazhdan-Lusztig polynomial of a matroid</i></div><br />
<div class="mw-collapsible-content"><br />
Classically, Kazdhan-Lusztig polynomials are associated to intervals of the Bruhat poset of a Coxeter group. We will discuss an analogue of Kazdhan-Lusztig polynomials for matroids, including results and conjectures from [https://arxiv.org/pdf/1611.07474.pdf these] [https://arxiv.org/pdf/1412.7408.pdf two] papers. <br />
</div></div><br />
|-<br />
|2/15/2019<br />
|<br />
<div style="font-weight:bold;">Colin Crowley</div><br />
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"><br />
<div><i>Matroid polytopes</i></div><br />
<div class="mw-collapsible-content"><br />
We outline the original formulation of matroid polytopes as moment polytopes of subvarieties of the Grassmanian, following [http://www.math.ias.edu/~goresky/pdf/combinatorial.jour.pdf Combinatorial Geometries, Convex Polyhedra, and Schbert Cells].<br />
</div></div><br />
|-<br />
|2/8/2019<br />
|<br />
<div style="font-weight:bold;">[http://www.math.wisc.edu/~csimpson6/ Connor Simpson]</div><br />
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"><br />
<div><i>Proving the Heron-Rota-Welsh conjecture</i></div><br />
<div class="mw-collapsible-content"><br />
We outline the proof of the Heron-Rota-Welsh conjecture given by Adiprasito, Huh, and Katz in their paper [https://arxiv.org/abs/1511.02888 Hodge theory for combinatorial geometries]<br />
</div></div><br />
|-<br />
|1/25/2019 & 2/1/2019<br />
|<br />
<div style="font-weight:bold;">[https://www.math.wisc.edu/~jose/ Jose Israel Rodriguez]</div><br />
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"><br />
<div><i>Algebraic matroids in action</i></div><br />
<div class="mw-collapsible-content"><br />
We discuss algebraic matroids and their applications; see [https://arxiv.org/abs/1809.00865 Algebraic Matroids in Action].<br />
</div></div><br />
|-<br />
|1/18/2019<br />
|<br />
<div style="font-weight:bold;">[https://sites.google.com/site/dcorey2814/home Daniel Corey]</div><br />
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"><br />
<div><i>Introduction to matroids</i></div><br />
<div class="mw-collapsible-content"><br />
We'll cover the basic definitions and some examples, roughly following [http://web.ma.utexas.edu/users/sampayne/pdf/Math648Lecture3.pdf these notes].<br />
</div></div><br />
|-<br />
|}</div>Csimpson6https://wiki.math.wisc.edu/index.php?title=Matroids_seminar&diff=17155Matroids seminar2019-03-14T20:22:04Z<p>Csimpson6: </p>
<hr />
<div>The matroids seminar & reading group meets '''10:00--10:45 on Fridays in Van Vleck 901''' in order to discuss matroids from a variety of viewpoints.<br />
In particular, we aim to<br />
* survey open conjectures and recent work in the area<br />
* compute many interesting examples<br />
* discover concrete applications<br />
<br />
We are happy to have new leaders of the discussion, and the wide range of topics to which matroids are related mean that each week is a great chance for a new participant to drop in! If you would like to talk but need ideas, see the [[Matroids seminar/ideas]] page.<br />
<br />
To help develop an inclusive environment, a subset of the organizers will be available before the talk in the ninth floor lounge to informally discuss background material e.g., "What is a variety?", "What is a circuit?", "What is a greedy algorithm?" (this is especially for those coming from an outside area).<br />
<br />
'''Organizers''': Colin Crowley, Connor Simpson; Daniel Corey, Jose Israel Rodriguez<br />
<br />
{| cellpadding="8px" style="vertical-align:top; text-align:left; cellpadding:10px;"<br />
|3/29/2019<br />
|<br />
<div style="font-weight:bold;">Colin Crowley</div><br />
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"><br />
<div><i>Binary matroids and Seymour's decomposition in coding theory</i></div><br />
<div class="mw-collapsible-content"><br />
We will begin by discussing the equivalence between a binary matroid and a binary linear code. And then following [https://ac.els-cdn.com/009589568990052X/1-s2.0-009589568990052X-main.pdf?_tid=a1d8598e-c5f2-4c07-8d7b-0843e88c416f&acdnat=1552505468_33915774714b2e407e4fd7001ba33100 this paper] and [https://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=4544972 this one], we will describe the Maximum Likelihood decoding problem and then outline how Seymour's decomposition theorem for binary matroids led to a polynomial time algorithm on a subclass of binary linear codes.<br />
</div></div><br />
|-<br />
|3/15/2019<br />
|<br />
<div style="font-weight:bold;">Daniel Corey</div><br />
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"><br />
<div><i>The geometry of thin Schubert cells</i></div><br />
<div class="mw-collapsible-content"><br />
We will cover the distinction between the thin Schubert cell of a matroid and the realization space of a matroid, how to compute examples, Mnev universality, and time permitting, maps between thin Schubert cells. <br />
</div></div><br />
|-<br />
|3/8/2019<br />
|<br />
<div style="font-weight:bold;">Vladmir Sotirov</div><br />
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"><br />
<div><i>is sick</i></div><br />
<div class="mw-collapsible-content"><br />
Plague and pestilence!<br />
</div></div><br />
|-<br />
|3/1/2019<br />
|<br />
<div style="font-weight:bold;">[https://math.berkeley.edu/~ceur/ Chris Eur]</div><br />
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"><br />
<div><i>The multivariate Tutte polynomial of a flag matroid</i></div><br />
<div class="mw-collapsible-content"><br />
Flag matroids are combinatorial objects whose relation to ordinary matroids are akin to that of flag varieties to Grassmannians. We define a multivariate Tutte polynomial of a flag matroid, and show that it is Lorentzian in the sense of [https://arxiv.org/abs/1902.03719 Branden-Huh '19]. As a consequence, we obtain a flag matroid generalization of Mason’s conjecture concerning the f-vector of independent subsets of a matroid. This is an on-going joint work with June Huh.<br />
</div></div><br />
|-<br />
|2/22/2019<br />
|<br />
<div style="font-weight:bold;">[https://www.math.wisc.edu/~wang/ Botong Wang]</div><br />
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"><br />
<div><i>The Kazhdan-Lusztig polynomial of a matroid</i></div><br />
<div class="mw-collapsible-content"><br />
Classically, Kazdhan-Lusztig polynomials are associated to intervals of the Bruhat poset of a Coxeter group. We will discuss an analogue of Kazdhan-Lusztig polynomials for matroids, including results and conjectures from [https://arxiv.org/pdf/1611.07474.pdf these] [https://arxiv.org/pdf/1412.7408.pdf two] papers. <br />
</div></div><br />
|-<br />
|2/15/2019<br />
|<br />
<div style="font-weight:bold;">Colin Crowley</div><br />
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"><br />
<div><i>Matroid polytopes</i></div><br />
<div class="mw-collapsible-content"><br />
We outline the original formulation of matroid polytopes as moment polytopes of subvarieties of the Grassmanian, following [http://www.math.ias.edu/~goresky/pdf/combinatorial.jour.pdf Combinatorial Geometries, Convex Polyhedra, and Schbert Cells].<br />
</div></div><br />
|-<br />
|2/8/2019<br />
|<br />
<div style="font-weight:bold;">[http://www.math.wisc.edu/~csimpson6/ Connor Simpson]</div><br />
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"><br />
<div><i>Proving the Heron-Rota-Welsh conjecture</i></div><br />
<div class="mw-collapsible-content"><br />
We outline the proof of the Heron-Rota-Welsh conjecture given by Adiprasito, Huh, and Katz in their paper [https://arxiv.org/abs/1511.02888 Hodge theory for combinatorial geometries]<br />
</div></div><br />
|-<br />
|1/25/2019 & 2/1/2019<br />
|<br />
<div style="font-weight:bold;">[https://www.math.wisc.edu/~jose/ Jose Israel Rodriguez]</div><br />
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"><br />
<div><i>Algebraic matroids in action</i></div><br />
<div class="mw-collapsible-content"><br />
We discuss algebraic matroids and their applications; see [https://arxiv.org/abs/1809.00865 Algebraic Matroids in Action].<br />
</div></div><br />
|-<br />
|1/18/2019<br />
|<br />
<div style="font-weight:bold;">[https://sites.google.com/site/dcorey2814/home Daniel Corey]</div><br />
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"><br />
<div><i>Introduction to matroids</i></div><br />
<div class="mw-collapsible-content"><br />
We'll cover the basic definitions and some examples, roughly following [http://web.ma.utexas.edu/users/sampayne/pdf/Math648Lecture3.pdf these notes].<br />
</div></div><br />
|-<br />
|}</div>Csimpson6https://wiki.math.wisc.edu/index.php?title=Matroids_seminar&diff=17154Matroids seminar2019-03-14T20:21:41Z<p>Csimpson6: </p>
<hr />
<div>The matroids seminar & reading group meets '''10:00--10:45 on Fridays in Van Vleck 901''' in order to discuss matroids from a variety of viewpoints.<br />
In particular, we aim to<br />
* survey open conjectures and recent work in the area<br />
* compute many interesting examples<br />
* discover concrete applications<br />
<br />
We are happy to have new leaders of the discussion, and the wide range of topics to which matroids are related mean that each week is a great chance for a new participant to drop in! If you would like to talk but need ideas, see the [[Matroids seminar/ideas]] page.<br />
<br />
To help develop an inclusive environment, a subset of the organizers will be available before the talk in the ninth floor lounge to informally discuss background material e.g., "What is a variety?", "What is a circuit?", "What is a greedy algorithm?" (this is especially for those coming from an outside area).<br />
<br />
'''Organizers''': Colin Crowley, Connor Simpson; Daniel Corey, Jose Israel Rodriguez<br />
<br />
{| cellpadding="8px" style="vertical-align:top; text-align:left; cellpadding:10px;"<br />
|3/29/2019<br />
|<br />
<div style="font-weight:bold;">Colin Crowley</div><br />
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"><br />
<div><i>Binary matroids and Seymour's decomposition in coding theory</i></div><br />
<div class="mw-collapsible-content"><br />
We will begin by discussing the equivalence between a binary matroid and a binary linear code. And then following [https://ac.els-cdn.com/009589568990052X/1-s2.0-009589568990052X-main.pdf?_tid=a1d8598e-c5f2-4c07-8d7b-0843e88c416f&acdnat=1552505468_33915774714b2e407e4fd7001ba33100 this paper] and [https://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=4544972 this one], we will describe the Maximum Likelihood decoding problem and then outline how Seymour's decomposition theorem for binary matroids led to a polynomial time algorithm on a subclass of binary linear codes.<br />
</div></div><br />
|-<br />
|3/15/2019<br />
|<br />
<div style="font-weight:bold;">Daniel Corey</div><br />
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"><br />
<div><i>Thin Schubert cells</i></div><br />
<div class="mw-collapsible-content"><br />
We will cover the distinction between the thin Schubert cell of a matroid and the realization space of a matroid, how to compute examples, Mnev universality, and time permitting, maps between thin Schubert cells. <br />
</div></div><br />
|-<br />
|3/8/2019<br />
|<br />
<div style="font-weight:bold;">Vladmir Sotirov</div><br />
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"><br />
<div><i>is sick</i></div><br />
<div class="mw-collapsible-content"><br />
Plague and pestilence!<br />
</div></div><br />
|-<br />
|3/1/2019<br />
|<br />
<div style="font-weight:bold;">[https://math.berkeley.edu/~ceur/ Chris Eur]</div><br />
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"><br />
<div><i>The multivariate Tutte polynomial of a flag matroid</i></div><br />
<div class="mw-collapsible-content"><br />
Flag matroids are combinatorial objects whose relation to ordinary matroids are akin to that of flag varieties to Grassmannians. We define a multivariate Tutte polynomial of a flag matroid, and show that it is Lorentzian in the sense of [https://arxiv.org/abs/1902.03719 Branden-Huh '19]. As a consequence, we obtain a flag matroid generalization of Mason’s conjecture concerning the f-vector of independent subsets of a matroid. This is an on-going joint work with June Huh.<br />
</div></div><br />
|-<br />
|2/22/2019<br />
|<br />
<div style="font-weight:bold;">[https://www.math.wisc.edu/~wang/ Botong Wang]</div><br />
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"><br />
<div><i>The Kazhdan-Lusztig polynomial of a matroid</i></div><br />
<div class="mw-collapsible-content"><br />
Classically, Kazdhan-Lusztig polynomials are associated to intervals of the Bruhat poset of a Coxeter group. We will discuss an analogue of Kazdhan-Lusztig polynomials for matroids, including results and conjectures from [https://arxiv.org/pdf/1611.07474.pdf these] [https://arxiv.org/pdf/1412.7408.pdf two] papers. <br />
</div></div><br />
|-<br />
|2/15/2019<br />
|<br />
<div style="font-weight:bold;">Colin Crowley</div><br />
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"><br />
<div><i>Matroid polytopes</i></div><br />
<div class="mw-collapsible-content"><br />
We outline the original formulation of matroid polytopes as moment polytopes of subvarieties of the Grassmanian, following [http://www.math.ias.edu/~goresky/pdf/combinatorial.jour.pdf Combinatorial Geometries, Convex Polyhedra, and Schbert Cells].<br />
</div></div><br />
|-<br />
|2/8/2019<br />
|<br />
<div style="font-weight:bold;">[http://www.math.wisc.edu/~csimpson6/ Connor Simpson]</div><br />
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"><br />
<div><i>Proving the Heron-Rota-Welsh conjecture</i></div><br />
<div class="mw-collapsible-content"><br />
We outline the proof of the Heron-Rota-Welsh conjecture given by Adiprasito, Huh, and Katz in their paper [https://arxiv.org/abs/1511.02888 Hodge theory for combinatorial geometries]<br />
</div></div><br />
|-<br />
|1/25/2019 & 2/1/2019<br />
|<br />
<div style="font-weight:bold;">[https://www.math.wisc.edu/~jose/ Jose Israel Rodriguez]</div><br />
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"><br />
<div><i>Algebraic matroids in action</i></div><br />
<div class="mw-collapsible-content"><br />
We discuss algebraic matroids and their applications; see [https://arxiv.org/abs/1809.00865 Algebraic Matroids in Action].<br />
</div></div><br />
|-<br />
|1/18/2019<br />
|<br />
<div style="font-weight:bold;">[https://sites.google.com/site/dcorey2814/home Daniel Corey]</div><br />
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"><br />
<div><i>Introduction to matroids</i></div><br />
<div class="mw-collapsible-content"><br />
We'll cover the basic definitions and some examples, roughly following [http://web.ma.utexas.edu/users/sampayne/pdf/Math648Lecture3.pdf these notes].<br />
</div></div><br />
|-<br />
|}</div>Csimpson6https://wiki.math.wisc.edu/index.php?title=Matroids_seminar&diff=17146Matroids seminar2019-03-13T05:02:12Z<p>Csimpson6: </p>
<hr />
<div>The matroids seminar & reading group meets '''10:00--10:45 on Fridays in Van Vleck 901''' in order to discuss matroids from a variety of viewpoints.<br />
In particular, we aim to<br />
* survey open conjectures and recent work in the area<br />
* compute many interesting examples<br />
* discover concrete applications<br />
<br />
We are happy to have new leaders of the discussion, and the wide range of topics to which matroids are related mean that each week is a great chance for a new participant to drop in! If you would like to talk but need ideas, see the [[Matroids seminar/ideas]] page.<br />
<br />
To help develop an inclusive environment, a subset of the organizers will be available before the talk in the ninth floor lounge to informally discuss background material e.g., "What is a variety?", "What is a circuit?", "What is a greedy algorithm?" (this is especially for those coming from an outside area).<br />
<br />
'''Organizers''': Colin Crowley, Connor Simpson; Daniel Corey, Jose Israel Rodriguez<br />
<br />
{| cellpadding="8px" style="vertical-align:top; text-align:left; cellpadding:10px;"<br />
|3/15/2019<br />
|<br />
<div style="font-weight:bold;">Daniel Corey</div><br />
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"><br />
<div><i>Thin Schubert cells</i></div><br />
<div class="mw-collapsible-content"><br />
Tentatively, we will discuss thin schubert cells, their geometry, and maps between them in relation to faces of matroid polytopes. We will also give a statement of Mnev universality.<br />
</div></div><br />
|-<br />
|3/8/2019<br />
|<br />
<div style="font-weight:bold;">Vladmir Sotirov</div><br />
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"><br />
<div><i>is sick</i></div><br />
<div class="mw-collapsible-content"><br />
Plague and pestilence!<br />
</div></div><br />
|-<br />
|3/1/2019<br />
|<br />
<div style="font-weight:bold;">[https://math.berkeley.edu/~ceur/ Chris Eur]</div><br />
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"><br />
<div><i>The multivariate Tutte polynomial of a flag matroid</i></div><br />
<div class="mw-collapsible-content"><br />
Flag matroids are combinatorial objects whose relation to ordinary matroids are akin to that of flag varieties to Grassmannians. We define a multivariate Tutte polynomial of a flag matroid, and show that it is Lorentzian in the sense of [https://arxiv.org/abs/1902.03719 Branden-Huh '19]. As a consequence, we obtain a flag matroid generalization of Mason’s conjecture concerning the f-vector of independent subsets of a matroid. This is an on-going joint work with June Huh.<br />
</div></div><br />
|-<br />
|2/22/2019<br />
|<br />
<div style="font-weight:bold;">[https://www.math.wisc.edu/~wang/ Botong Wang]</div><br />
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"><br />
<div><i>The Kazhdan-Lusztig polynomial of a matroid</i></div><br />
<div class="mw-collapsible-content"><br />
Classically, Kazdhan-Lusztig polynomials are associated to intervals of the Bruhat poset of a Coxeter group. We will discuss an analogue of Kazdhan-Lusztig polynomials for matroids, including results and conjectures from [https://arxiv.org/pdf/1611.07474.pdf these] [https://arxiv.org/pdf/1412.7408.pdf two] papers. <br />
</div></div><br />
|-<br />
|2/15/2019<br />
|<br />
<div style="font-weight:bold;">Colin Crowley</div><br />
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"><br />
<div><i>Matroid polytopes</i></div><br />
<div class="mw-collapsible-content"><br />
We outline the original formulation of matroid polytopes as moment polytopes of subvarieties of the Grassmanian, following [http://www.math.ias.edu/~goresky/pdf/combinatorial.jour.pdf Combinatorial Geometries, Convex Polyhedra, and Schbert Cells].<br />
</div></div><br />
|-<br />
|2/8/2019<br />
|<br />
<div style="font-weight:bold;">[http://www.math.wisc.edu/~csimpson6/ Connor Simpson]</div><br />
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"><br />
<div><i>Proving the Heron-Rota-Welsh conjecture</i></div><br />
<div class="mw-collapsible-content"><br />
We outline the proof of the Heron-Rota-Welsh conjecture given by Adiprasito, Huh, and Katz in their paper [https://arxiv.org/abs/1511.02888 Hodge theory for combinatorial geometries]<br />
</div></div><br />
|-<br />
|1/25/2019 & 2/1/2019<br />
|<br />
<div style="font-weight:bold;">[https://www.math.wisc.edu/~jose/ Jose Israel Rodriguez]</div><br />
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"><br />
<div><i>Algebraic matroids in action</i></div><br />
<div class="mw-collapsible-content"><br />
We discuss algebraic matroids and their applications; see [https://arxiv.org/abs/1809.00865 Algebraic Matroids in Action].<br />
</div></div><br />
|-<br />
|1/18/2019<br />
|<br />
<div style="font-weight:bold;">[https://sites.google.com/site/dcorey2814/home Daniel Corey]</div><br />
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"><br />
<div><i>Introduction to matroids</i></div><br />
<div class="mw-collapsible-content"><br />
We'll cover the basic definitions and some examples, roughly following [http://web.ma.utexas.edu/users/sampayne/pdf/Math648Lecture3.pdf these notes].<br />
</div></div><br />
|-<br />
|}</div>Csimpson6https://wiki.math.wisc.edu/index.php?title=Matroids_seminar&diff=17105Matroids seminar2019-03-04T22:09:06Z<p>Csimpson6: </p>
<hr />
<div>The matroids seminar & reading group meets '''10:00--10:45 on Fridays in Van Vleck 901''' in order to discuss matroids from a variety of viewpoints.<br />
In particular, we aim to<br />
* survey open conjectures and recent work in the area<br />
* compute many interesting examples<br />
* discover concrete applications<br />
<br />
We are happy to have new leaders of the discussion, and the wide range of topics to which matroids are related mean that each week is a great chance for a new participant to drop in! If you would like to talk but need ideas, see the [[Matroids seminar/ideas]] page.<br />
<br />
To help develop an inclusive environment, a subset of the organizers will be available before the talk in the ninth floor lounge to informally discuss background material e.g., "What is a variety?", "What is a circuit?", "What is a greedy algorithm?" (this is especially for those coming from an outside area).<br />
<br />
'''Organizers''': Colin Crowley, Connor Simpson; Daniel Corey, Jose Israel Rodriguez<br />
<br />
{| cellpadding="8px" style="vertical-align:top; text-align:left; cellpadding:10px;"<br />
|3/8/2019<br />
|<br />
<div style="font-weight:bold;">Vladmir Sotirov</div><br />
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"><br />
<div><i>Infinite matroids</i></div><br />
<div class="mw-collapsible-content"><br />
TBA<br />
</div></div><br />
|-<br />
|3/1/2019<br />
|<br />
<div style="font-weight:bold;">[https://math.berkeley.edu/~ceur/ Chris Eur]</div><br />
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"><br />
<div><i>The multivariate Tutte polynomial of a flag matroid</i></div><br />
<div class="mw-collapsible-content"><br />
Flag matroids are combinatorial objects whose relation to ordinary matroids are akin to that of flag varieties to Grassmannians. We define a multivariate Tutte polynomial of a flag matroid, and show that it is Lorentzian in the sense of [https://arxiv.org/abs/1902.03719 Branden-Huh '19]. As a consequence, we obtain a flag matroid generalization of Mason’s conjecture concerning the f-vector of independent subsets of a matroid. This is an on-going joint work with June Huh.<br />
</div></div><br />
|-<br />
|2/22/2019<br />
|<br />
<div style="font-weight:bold;">[https://www.math.wisc.edu/~wang/ Botong Wang]</div><br />
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"><br />
<div><i>The Kazhdan-Lusztig polynomial of a matroid</i></div><br />
<div class="mw-collapsible-content"><br />
Classically, Kazdhan-Lusztig polynomials are associated to intervals of the Bruhat poset of a Coxeter group. We will discuss an analogue of Kazdhan-Lusztig polynomials for matroids, including results and conjectures from [https://arxiv.org/pdf/1611.07474.pdf these] [https://arxiv.org/pdf/1412.7408.pdf two] papers. <br />
</div></div><br />
|-<br />
|2/15/2019<br />
|<br />
<div style="font-weight:bold;">Colin Crowley</div><br />
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"><br />
<div><i>Matroid polytopes</i></div><br />
<div class="mw-collapsible-content"><br />
We outline the original formulation of matroid polytopes as moment polytopes of subvarieties of the Grassmanian, following [http://www.math.ias.edu/~goresky/pdf/combinatorial.jour.pdf Combinatorial Geometries, Convex Polyhedra, and Schbert Cells].<br />
</div></div><br />
|-<br />
|2/8/2019<br />
|<br />
<div style="font-weight:bold;">[http://www.math.wisc.edu/~csimpson6/ Connor Simpson]</div><br />
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"><br />
<div><i>Proving the Heron-Rota-Welsh conjecture</i></div><br />
<div class="mw-collapsible-content"><br />
We outline the proof of the Heron-Rota-Welsh conjecture given by Adiprasito, Huh, and Katz in their paper [https://arxiv.org/abs/1511.02888 Hodge theory for combinatorial geometries]<br />
</div></div><br />
|-<br />
|1/25/2019 & 2/1/2019<br />
|<br />
<div style="font-weight:bold;">[https://www.math.wisc.edu/~jose/ Jose Israel Rodriguez]</div><br />
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"><br />
<div><i>Algebraic matroids in action</i></div><br />
<div class="mw-collapsible-content"><br />
We discuss algebraic matroids and their applications; see [https://arxiv.org/abs/1809.00865 Algebraic Matroids in Action].<br />
</div></div><br />
|-<br />
|1/18/2019<br />
|<br />
<div style="font-weight:bold;">[https://sites.google.com/site/dcorey2814/home Daniel Corey]</div><br />
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"><br />
<div><i>Introduction to matroids</i></div><br />
<div class="mw-collapsible-content"><br />
We'll cover the basic definitions and some examples, roughly following [http://web.ma.utexas.edu/users/sampayne/pdf/Math648Lecture3.pdf these notes].<br />
</div></div><br />
|-<br />
|}</div>Csimpson6https://wiki.math.wisc.edu/index.php?title=Matroids_seminar&diff=17104Matroids seminar2019-03-04T22:02:06Z<p>Csimpson6: </p>
<hr />
<div>The matroids seminar & reading group meets '''10:00--10:45 on Fridays in Van Vleck 901''' in order to discuss matroids from a variety of viewpoints.<br />
In particular, we aim to<br />
* survey open conjectures and recent work in the area<br />
* compute many interesting examples<br />
* discover concrete applications<br />
<br />
We are happy to have new leaders of the discussion, and the wide range of topics to which matroids are related mean that each week is a great chance for a new participant to drop in! If you would like to talk but need ideas, see the [[Matroids seminar/ideas]] page.<br />
<br />
To help develop an inclusive environment, a subset of the organizers will be available before the talk in the ninth floor lounge to informally discuss background material e.g., "What is a variety?", "What is a circuit?", "What is a greedy algorithm?" (this is especially for those coming from an outside area).<br />
<br />
'''Organizers''': Colin Crowley, Connor Simpson; Daniel Corey, Jose Israel Rodriguez<br />
<br />
{| cellpadding="8px" style="vertical-align:top; text-align:left; cellpadding:10px;"<br />
|1/18/2019<br />
|<br />
<div style="font-weight:bold;">[https://sites.google.com/site/dcorey2814/home Daniel Corey]</div><br />
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"><br />
<div><i>Introduction to matroids</i></div><br />
<div class="mw-collapsible-content"><br />
We'll cover the basic definitions and some examples, roughly following [http://web.ma.utexas.edu/users/sampayne/pdf/Math648Lecture3.pdf these notes].<br />
</div></div><br />
|-<br />
|1/25/2019 & 2/1/2019<br />
|<br />
<div style="font-weight:bold;">[https://www.math.wisc.edu/~jose/ Jose Israel Rodriguez]</div><br />
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"><br />
<div><i>Algebraic matroids in action</i></div><br />
<div class="mw-collapsible-content"><br />
We discuss algebraic matroids and their applications; see [https://arxiv.org/abs/1809.00865 Algebraic Matroids in Action].<br />
</div></div><br />
|-<br />
|2/8/2019<br />
|<br />
<div style="font-weight:bold;">[http://www.math.wisc.edu/~csimpson6/ Connor Simpson]</div><br />
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"><br />
<div><i>Proving the Heron-Rota-Welsh conjecture</i></div><br />
<div class="mw-collapsible-content"><br />
We outline the proof of the Heron-Rota-Welsh conjecture given by Adiprasito, Huh, and Katz in their paper [https://arxiv.org/abs/1511.02888 Hodge theory for combinatorial geometries]<br />
</div></div><br />
|-<br />
|2/15/2019<br />
|<br />
<div style="font-weight:bold;">Colin Crowley</div><br />
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"><br />
<div><i>Matroid polytopes</i></div><br />
<div class="mw-collapsible-content"><br />
We outline the original formulation of matroid polytopes as moment polytopes of subvarieties of the Grassmanian, following [http://www.math.ias.edu/~goresky/pdf/combinatorial.jour.pdf Combinatorial Geometries, Convex Polyhedra, and Schbert Cells].<br />
</div></div><br />
|-<br />
|2/22/2019<br />
|<br />
<div style="font-weight:bold;">[https://www.math.wisc.edu/~wang/ Botong Wang]</div><br />
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"><br />
<div><i>The Kazhdan-Lusztig polynomial of a matroid</i></div><br />
<div class="mw-collapsible-content"><br />
Classically, Kazdhan-Lusztig polynomials are associated to intervals of the Bruhat poset of a Coxeter group. We will discuss an analogue of Kazdhan-Lusztig polynomials for matroids, including results and conjectures from [https://arxiv.org/pdf/1611.07474.pdf these] [https://arxiv.org/pdf/1412.7408.pdf two] papers. <br />
</div></div><br />
|-<br />
|3/1/2019<br />
|<br />
<div style="font-weight:bold;">[https://math.berkeley.edu/~ceur/ Chris Eur]</div><br />
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"><br />
<div><i>The multivariate Tutte polynomial of a flag matroid</i></div><br />
<div class="mw-collapsible-content"><br />
Flag matroids are combinatorial objects whose relation to ordinary matroids are akin to that of flag varieties to Grassmannians. We define a multivariate Tutte polynomial of a flag matroid, and show that it is Lorentzian in the sense of [https://arxiv.org/abs/1902.03719 Branden-Huh '19]. As a consequence, we obtain a flag matroid generalization of Mason’s conjecture concerning the f-vector of independent subsets of a matroid. This is an on-going joint work with June Huh.<br />
</div></div><br />
|-<br />
|3/8/2019<br />
|<br />
<div style="font-weight:bold;">Vladmir Sotirov</div><br />
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"><br />
<div><i>Infinite matroids</i></div><br />
<div class="mw-collapsible-content"><br />
TBA<br />
</div></div><br />
|-<br />
|}</div>Csimpson6https://wiki.math.wisc.edu/index.php?title=Matroids_seminar&diff=17037Matroids seminar2019-02-25T04:59:44Z<p>Csimpson6: </p>
<hr />
<div>The matroids seminar & reading group meets '''10:00--10:45 on Fridays in Van Vleck 901''' in order to discuss matroids from a variety of viewpoints.<br />
In particular, we aim to<br />
* survey open conjectures and recent work in the area<br />
* compute many interesting examples<br />
* discover concrete applications<br />
<br />
We are happy to have new leaders of the discussion, and the wide range of topics to which matroids are related mean that each week is a great chance for a new participant to drop in! If you would like to talk but need ideas, see the [[Matroids seminar/ideas]] page.<br />
<br />
To help develop an inclusive environment, a subset of the organizers will be available before the talk in the ninth floor lounge to informally discuss background material e.g., "What is a variety?", "What is a circuit?", "What is a greedy algorithm?" (this is especially for those coming from an outside area).<br />
<br />
'''Organizers''': Colin Crowley, Connor Simpson; Daniel Corey, Jose Israel Rodriguez<br />
<br />
{| cellpadding="8px" style="vertical-align:top; text-align:left; cellpadding:10px;"<br />
|1/18/2019<br />
|<br />
<div style="font-weight:bold;">[https://sites.google.com/site/dcorey2814/home Daniel Corey]</div><br />
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"><br />
<div><i>Introduction to matroids</i></div><br />
<div class="mw-collapsible-content"><br />
We'll cover the basic definitions and some examples, roughly following [http://web.ma.utexas.edu/users/sampayne/pdf/Math648Lecture3.pdf these notes].<br />
</div></div><br />
|-<br />
|1/25/2019 & 2/1/2019<br />
|<br />
<div style="font-weight:bold;">[https://www.math.wisc.edu/~jose/ Jose Israel Rodriguez]</div><br />
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"><br />
<div><i>Algebraic matroids in action</i></div><br />
<div class="mw-collapsible-content"><br />
We discuss algebraic matroids and their applications; see [https://arxiv.org/abs/1809.00865 Algebraic Matroids in Action].<br />
</div></div><br />
|-<br />
|2/8/2019<br />
|<br />
<div style="font-weight:bold;">[http://www.math.wisc.edu/~csimpson6/ Connor Simpson]</div><br />
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"><br />
<div><i>Proving the Heron-Rota-Welsh conjecture</i></div><br />
<div class="mw-collapsible-content"><br />
We outline the proof of the Heron-Rota-Welsh conjecture given by Adiprasito, Huh, and Katz in their paper [https://arxiv.org/abs/1511.02888 Hodge theory for combinatorial geometries]<br />
</div></div><br />
|-<br />
|2/15/2019<br />
|<br />
<div style="font-weight:bold;">Colin Crowley</div><br />
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"><br />
<div><i>Matroid polytopes</i></div><br />
<div class="mw-collapsible-content"><br />
We outline the original formulation of matroid polytopes as moment polytopes of subvarieties of the Grassmanian, following [http://www.math.ias.edu/~goresky/pdf/combinatorial.jour.pdf Combinatorial Geometries, Convex Polyhedra, and Schbert Cells].<br />
</div></div><br />
|-<br />
|2/22/2019<br />
|<br />
<div style="font-weight:bold;">[https://www.math.wisc.edu/~wang/ Botong Wang]</div><br />
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"><br />
<div><i>The Kazhdan-Lusztig polynomial of a matroid</i></div><br />
<div class="mw-collapsible-content"><br />
Classically, Kazdhan-Lusztig polynomials are associated to intervals of the Bruhat poset of a Coxeter group. We will discuss an analogue of Kazdhan-Lusztig polynomials for matroids, including results and conjectures from [https://arxiv.org/pdf/1611.07474.pdf these] [https://arxiv.org/pdf/1412.7408.pdf two] papers. <br />
</div></div><br />
|-<br />
|3/1/2019<br />
|<br />
<div style="font-weight:bold;">[https://math.berkeley.edu/~ceur/ Chris Eur]</div><br />
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"><br />
<div><i>The multivariate Tutte polynomial of a flag matroid</i></div><br />
<div class="mw-collapsible-content"><br />
Flag matroids are combinatorial objects whose relation to ordinary matroids are akin to that of flag varieties to Grassmannians. We define a multivariate Tutte polynomial of a flag matroid, and show that it is Lorentzian in the sense of [https://arxiv.org/abs/1902.03719 Branden-Huh '19]. As a consequence, we obtain a flag matroid generalization of Mason’s conjecture concerning the f-vector of independent subsets of a matroid. This is an on-going joint work with June Huh.<br />
</div></div><br />
|-<br />
|}</div>Csimpson6https://wiki.math.wisc.edu/index.php?title=Matroids_seminar&diff=17036Matroids seminar2019-02-25T04:58:24Z<p>Csimpson6: </p>
<hr />
<div>The matroids seminar & reading group meets '''10:00--10:45 on Fridays in Van Vleck 901''' in order to discuss matroids from a variety of viewpoints.<br />
In particular, we aim to<br />
* survey open conjectures and recent work in the area<br />
* compute many interesting examples<br />
* discover concrete applications<br />
<br />
We are happy to have new leaders of the discussion, and the wide range of topics to which matroids are related mean that each week is a great chance for a new participant to drop in! If you would like to talk but need ideas, see the [[Matroids seminar/ideas]] page.<br />
<br />
To help develop an inclusive environment, a subset of the organizers will be available before the talk in the ninth floor lounge to informally discuss background material e.g., "What is a variety?", "What is a circuit?", "What is a greedy algorithm?" (this is especially for those coming from an outside area).<br />
<br />
'''Organizers''': Colin Crowley, Connor Simpson; Daniel Corey, Jose Israel Rodriguez<br />
<br />
{| cellpadding="8px" style="vertical-align:top; text-align:left; cellpadding:10px;"<br />
|1/18/2019<br />
|<br />
<div style="font-weight:bold;">[https://sites.google.com/site/dcorey2814/home Daniel Corey]</div><br />
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"><br />
<div><i>Introduction to matroids</i></div><br />
<div class="mw-collapsible-content"><br />
We'll cover the basic definitions and some examples, roughly following [http://web.ma.utexas.edu/users/sampayne/pdf/Math648Lecture3.pdf these notes].<br />
</div></div><br />
|-<br />
|1/25/2019 & 2/1/2019<br />
|<br />
<div style="font-weight:bold;">[https://www.math.wisc.edu/~jose/ Jose Israel Rodriguez]</div><br />
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"><br />
<div><i>Algebraic matroids in action</i></div><br />
<div class="mw-collapsible-content"><br />
We discuss algebraic matroids and their applications; see [https://arxiv.org/abs/1809.00865 Algebraic Matroids in Action].<br />
</div></div><br />
|-<br />
|2/8/2019<br />
|<br />
<div style="font-weight:bold;">[http://www.math.wisc.edu/~csimpson6/ Connor Simpson]</div><br />
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"><br />
<div><i>Proving the Heron-Rota-Welsh conjecture</i></div><br />
<div class="mw-collapsible-content"><br />
We outline the proof of the Heron-Rota-Welsh conjecture given by Adiprasito, Huh, and Katz in their paper [https://arxiv.org/abs/1511.02888 Hodge theory for combinatorial geometries]<br />
</div></div><br />
|-<br />
|2/15/2019<br />
|<br />
<div style="font-weight:bold;">Colin Crowley</div><br />
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"><br />
<div><i>Matroid polytopes</i></div><br />
<div class="mw-collapsible-content"><br />
We outline the original formulation of matroid polytopes as moment polytopes of subvarieties of the Grassmanian, following [http://www.math.ias.edu/~goresky/pdf/combinatorial.jour.pdf Combinatorial Geometries, Convex Polyhedra, and Schbert Cells].<br />
</div></div><br />
|-<br />
|2/22/2019<br />
|<br />
<div style="font-weight:bold;">[https://www.math.wisc.edu/~wang/ Botong Wang]</div><br />
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"><br />
<div><i>The Kazhdan-Lusztig polynomial of a matroid</i></div><br />
<div class="mw-collapsible-content"><br />
Classically, Kazdhan-Lusztig polynomials are associated to intervals of the Bruhat poset of a Coxeter group. We will discuss an analogue of Kazdhan-Lusztig polynomials for matroids, including results and conjectures from [https://arxiv.org/pdf/1611.07474.pdf these] [https://arxiv.org/pdf/1412.7408.pdf two] papers. <br />
</div></div><br />
|-<br />
|3/1/2019<br />
|<br />
<div style="font-weight:bold;">[https://math.berkeley.edu/~ceur/ Chris Eur]</div><br />
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"><br />
<div><i>The multivariate Tutte polynomial of a flag matroid</i></div><br />
<div class="mw-collapsible-content"><br />
Flag matroids are combinatorial objects whose relation to ordinary matroids are akin to that of flag varieties to Grassmannians. We define a multivariate Tutte polynomial of a flag matroid, and show that it is Lorentzian in the sense of [Branden-Huh '19]. As a consequence, we obtain a flag matroid generalization of Mason’s conjecture concerning the f-vector of independent subsets of a matroid. This is an on-going joint work with June Huh.<br />
</div></div><br />
|-<br />
|}</div>Csimpson6https://wiki.math.wisc.edu/index.php?title=AMS_Student_Chapter_Seminar&diff=16998AMS Student Chapter Seminar2019-02-19T20:43:20Z<p>Csimpson6: /* March 13, TBD */</p>
<hr />
<div>The AMS Student Chapter Seminar is an informal, graduate student seminar on a wide range of mathematical topics. Pastries (usually donuts) will be provided.<br />
<br />
* '''When:''' Wednesdays, 3:20 PM – 3:50 PM<br />
* '''Where:''' Van Vleck, 9th floor lounge (unless otherwise announced)<br />
* '''Organizers:''' [https://www.math.wisc.edu/~malexis/ Michel Alexis], [https://www.math.wisc.edu/~drwagner/ David Wagner], [http://www.math.wisc.edu/~nicodemus/ Patrick Nicodemus], [http://www.math.wisc.edu/~thaison/ Son Tu]<br />
<br />
Everyone is welcome to give a talk. To sign up, please contact one of the organizers with a title and abstract. Talks are 30 minutes long and should avoid assuming significant mathematical background beyond first-year graduate courses.<br />
<br />
The schedule of talks from past semesters can be found [[AMS Student Chapter Seminar, previous semesters|here]].<br />
<br />
== Spring 2019 ==<br />
<br />
=== February 6, Xiao Shen (in VV B139)===<br />
<br />
Title: Limit Shape in last passage percolation<br />
<br />
Abstract: Imagine the following situation, attached to each point on the integer lattice Z^2 there is an arbitrary amount of donuts. Fix x and y in Z^2, if you get to eat all the donuts along an up-right path between these two points, what would be the maximum amount of donuts you can get? This model is often called last passage percolation, and I will discuss a classical result about its scaling limit: what happens if we zoom out and let the distance between x and y tend to infinity.<br />
<br />
=== February 13, Michel Alexis (in VV B139)===<br />
<br />
Title: An instructive yet useless theorem about random Fourier Series<br />
<br />
Abstract: Consider a Fourier series with random, symmetric, independent coefficients. With what probability is this the Fourier series of a continuous function? An <math>L^{p}</math> function? A surprising result is the Billard theorem, which says such a series results almost surely from an <math>L^{\infty}</math> function if and only if it results almost surely from a continuous function. Although the theorem in of itself is kind of useless in of itself, its proof is instructive in that we will see how, via the principle of reduction, one can usually just pretend all symmetric random variables are just coin flips (Bernoulli trials with outcomes <math>\pm 1</math>).<br />
<br />
=== February 20, Geoff Bentsen ===<br />
<br />
Title: An Analyst Wanders into a Topology Conference<br />
<br />
Abstract: Fourier Restriction is a big open problem in Harmonic Analysis; given a "small" subset <math>E</math> of <math>R^d</math>, can we restrict the Fourier transform of an <math>L^p</math> function to <math>E</math> and retain any information about our original function? This problem has a nice (somewhat) complete solution for smooth manifolds of co-dimension one. I will explore how to start generalizing this result to smooth manifolds of higher co-dimension, and how a topology paper from the 60s about the hairy ball problem came in handy along the way.<br />
<br />
=== February 27, James Hanson ===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
=== March 6, Working Group to establish an Association of Mathematics Graduate Students ===<br />
<br />
Title: Math and Government<br />
<br />
Abstract: TBD<br />
<br />
=== March 13, Connor Simpson ===<br />
<br />
Title: Counting faces of polytopes with algebra<br />
<br />
Abstract: A natural question is: with a fixed dimension and number of vertices, what is the largest number of d-dimensional faces that a polytope can have? We will outline a proof of the answer to this question.<br />
<br />
=== March 26 (Prospective Student Visit Day), Multiple Speakers ===<br />
<br />
====Eva Elduque====<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
====Rajula Srivastava====<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
====Soumya Sankar====<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
====Ivan Ongay Valverde, 3pm====<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
====[Insert Speaker]====<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
====[Insert Speaker]====<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
====[Insert Speaker]====<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
====[Insert Speaker]====<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
====[Insert Speaker]====<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
=== April 3, TBD ===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
=== April 10, TBD ===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
=== April 17, Hyun-Jong ===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD<br />
<br />
=== April 24, TBD ===<br />
<br />
Title: TBD<br />
<br />
Abstract: TBD</div>Csimpson6https://wiki.math.wisc.edu/index.php?title=Matroids_seminar&diff=16952Matroids seminar2019-02-16T22:26:44Z<p>Csimpson6: </p>
<hr />
<div>The matroids seminar & reading group meets '''10:00--10:45 on Fridays in Van Vleck 901''' in order to discuss matroids from a variety of viewpoints.<br />
In particular, we aim to<br />
* survey open conjectures and recent work in the area<br />
* compute many interesting examples<br />
* discover concrete applications<br />
<br />
We are happy to have new leaders of the discussion, and the wide range of topics to which matroids are related mean that each week is a great chance for a new participant to drop in! If you would like to talk but need ideas, see the [[Matroids seminar/ideas]] page.<br />
<br />
To help develop an inclusive environment, a subset of the organizers will be available before the talk in the ninth floor lounge to informally discuss background material e.g., "What is a variety?" (this is especially for those coming from an outside area).<br />
<br />
'''Organizers''': Colin Crowley, Connor Simpson; Daniel Corey, Jose Israel Rodriguez<br />
<br />
{| cellpadding="8px" style="vertical-align:top; text-align:left; cellpadding:10px;"<br />
|1/18/2019<br />
|<br />
<div style="font-weight:bold;">[https://sites.google.com/site/dcorey2814/home Daniel Corey]</div><br />
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"><br />
<div><i>Introduction to matroids</i></div><br />
<div class="mw-collapsible-content"><br />
We'll cover the basic definitions and some examples, roughly following [http://web.ma.utexas.edu/users/sampayne/pdf/Math648Lecture3.pdf these notes].<br />
</div></div><br />
|-<br />
|1/25/2019 & 2/1/2019<br />
|<br />
<div style="font-weight:bold;">[https://www.math.wisc.edu/~jose/ Jose Israel Rodriguez]</div><br />
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"><br />
<div><i>Algebraic matroids in action</i></div><br />
<div class="mw-collapsible-content"><br />
We discuss algebraic matroids and their applications; see [https://arxiv.org/abs/1809.00865 Algebraic Matroids in Action].<br />
</div></div><br />
|-<br />
|2/8/2019<br />
|<br />
<div style="font-weight:bold;">[http://www.math.wisc.edu/~csimpson6/ Connor Simpson]</div><br />
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"><br />
<div><i>Proving the Heron-Rota-Welsh conjecture</i></div><br />
<div class="mw-collapsible-content"><br />
We outline the proof of the Heron-Rota-Welsh conjecture given by Adiprasito, Huh, and Katz in their paper [https://arxiv.org/abs/1511.02888 Hodge theory for combinatorial geometries]<br />
</div></div><br />
|-<br />
|2/15/2019<br />
|<br />
<div style="font-weight:bold;">Colin Crowley</div><br />
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"><br />
<div><i>Matroid polytopes</i></div><br />
<div class="mw-collapsible-content"><br />
We outline the original formulation of matroid polytopes as moment polytopes of subvarieties of the Grassmanian, following [http://www.math.ias.edu/~goresky/pdf/combinatorial.jour.pdf Combinatorial Geometries, Convex Polyhedra, and Schbert Cells].<br />
</div></div><br />
|-<br />
|2/22/2019<br />
|<br />
<div style="font-weight:bold;">[https://www.math.wisc.edu/~wang/ Botong Wang]</div><br />
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"><br />
<div><i>The Kazhdan-Lusztig polynomial of a matroid</i></div><br />
<div class="mw-collapsible-content"><br />
Classically, Kazdhan-Lusztig polynomials are associated to intervals of the Bruhat poset of a Coxeter group. We will discuss an analogue of Kazdhan-Lusztig polynomials for matroids, including results and conjectures from [https://arxiv.org/pdf/1611.07474.pdf these] [https://arxiv.org/pdf/1412.7408.pdf two] papers. <br />
</div></div><br />
|-<br />
|3/1/2019<br />
|<br />
<div style="font-weight:bold;">[https://math.berkeley.edu/~ceur/ Chris Eur]</div><br />
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"><br />
<div><i>TBD</i></div><br />
<div class="mw-collapsible-content"><br />
TBD <br />
</div></div><br />
|-<br />
|}</div>Csimpson6https://wiki.math.wisc.edu/index.php?title=Matroids_seminar&diff=16950Matroids seminar2019-02-16T20:23:02Z<p>Csimpson6: </p>
<hr />
<div>The matroids seminar & reading group meets '''10:00--10:45 on Fridays in Van Vleck 901''' in order to discuss matroids from a variety of viewpoints.<br />
In particular, we aim to<br />
* survey open conjectures and recent work in the area<br />
* compute many interesting examples<br />
* discover concrete applications<br />
<br />
We are happy to have new leaders of the discussion, and the wide range of topics to which matroids are related mean that each week is a great chance for a new participant to drop in! If you would like to talk but need ideas, see the [[Matroids seminar/ideas]] page.<br />
<br />
To help develop an inclusive environment, a subset of the organizers will be available before the talk in the ninth floor lounge to informally discuss background material e.g., "What is a variety?" (this is especially for those coming from an outside area).<br />
{| cellpadding="8px" style="vertical-align:top; text-align:left; cellpadding:10px;"<br />
|1/18/2019<br />
|<br />
<div style="font-weight:bold;">[https://sites.google.com/site/dcorey2814/home Daniel Corey]</div><br />
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"><br />
<div><i>Introduction to matroids</i></div><br />
<div class="mw-collapsible-content"><br />
We'll cover the basic definitions and some examples, roughly following [http://web.ma.utexas.edu/users/sampayne/pdf/Math648Lecture3.pdf these notes].<br />
</div></div><br />
|-<br />
|1/25/2019 & 2/1/2019<br />
|<br />
<div style="font-weight:bold;">[https://www.math.wisc.edu/~jose/ Jose Rodriguez]</div><br />
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"><br />
<div><i>Algebraic matroids in action</i></div><br />
<div class="mw-collapsible-content"><br />
We discuss algebraic matroids and their applications; see [https://arxiv.org/abs/1809.00865 Algebraic Matroids in Action].<br />
</div></div><br />
|-<br />
|2/8/2019<br />
|<br />
<div style="font-weight:bold;">[http://www.math.wisc.edu/~csimpson6/ Connor Simpson]</div><br />
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"><br />
<div><i>Proving the Heron-Rota-Welsh conjecture</i></div><br />
<div class="mw-collapsible-content"><br />
We outline the proof of the Heron-Rota-Welsh conjecture given by Adiprasito, Huh, and Katz in their paper [https://arxiv.org/abs/1511.02888 Hodge theory for combinatorial geometries]<br />
</div></div><br />
|-<br />
|2/15/2019<br />
|<br />
<div style="font-weight:bold;">Colin Crowley</div><br />
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"><br />
<div><i>Matroid polytopes</i></div><br />
<div class="mw-collapsible-content"><br />
We outline the original formulation of matroid polytopes as moment polytopes of subvarieties of the Grassmanian, following [http://www.math.ias.edu/~goresky/pdf/combinatorial.jour.pdf Combinatorial Geometries, Convex Polyhedra, and Schbert Cells].<br />
</div></div><br />
|-<br />
|2/22/2019<br />
|<br />
<div style="font-weight:bold;">[https://www.math.wisc.edu/~wang/ Botong Wang]</div><br />
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"><br />
<div><i>The Kazhdan-Lusztig polynomial of a matroid</i></div><br />
<div class="mw-collapsible-content"><br />
Classically, Kazdhan-Lusztig polynomials are associated to intervals of the Bruhat poset of a Coxeter group. We will discuss an analogue of Kazdhan-Lusztig polynomials for matroids, including results and conjectures from [https://arxiv.org/pdf/1611.07474.pdf these] [https://arxiv.org/pdf/1412.7408.pdf two] papers. <br />
</div></div><br />
|-<br />
|}</div>Csimpson6https://wiki.math.wisc.edu/index.php?title=Matroids_seminar&diff=16949Matroids seminar2019-02-16T20:20:13Z<p>Csimpson6: </p>
<hr />
<div>The matroids seminar & reading group meets '''10:00--10:45 on Fridays in Van Vleck 901''' in order to discuss matroids from a variety of viewpoints.<br />
In particular, we aim to<br />
* survey open conjectures and recent work in the area<br />
* compute many interesting examples<br />
* discover concrete applications<br />
<br />
We are happy to have new leaders of the discussion, and the wide range of topics to which matroids are related mean that each week is a great chance for a new participant to drop in! If you would like to talk but need ideas, see the [https://www.math.wisc.edu/wiki/index.php/Matroids_seminar/ideas ideas page].<br />
<br />
To help develop an inclusive environment, a subset of the organizers will be available before the talk in the ninth floor lounge to informally discuss background material e.g., "What is a variety?" (this is especially for those coming from an outside area).<br />
{| cellpadding="8px" style="vertical-align:top; text-align:left; cellpadding:10px;"<br />
|1/18/2019<br />
|<br />
<div style="font-weight:bold;">[https://sites.google.com/site/dcorey2814/home Daniel Corey]</div><br />
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"><br />
<div><i>Introduction to matroids</i></div><br />
<div class="mw-collapsible-content"><br />
We'll cover the basic definitions and some examples, roughly following [http://web.ma.utexas.edu/users/sampayne/pdf/Math648Lecture3.pdf these notes].<br />
</div></div><br />
|-<br />
|1/25/2019 & 2/1/2019<br />
|<br />
<div style="font-weight:bold;">[https://www.math.wisc.edu/~jose/ Jose Rodriguez]</div><br />
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"><br />
<div><i>Algebraic matroids in action</i></div><br />
<div class="mw-collapsible-content"><br />
We discuss algebraic matroids and their applications; see [https://arxiv.org/abs/1809.00865 Algebraic Matroids in Action].<br />
</div></div><br />
|-<br />
|2/8/2019<br />
|<br />
<div style="font-weight:bold;">[http://www.math.wisc.edu/~csimpson6/ Connor Simpson]</div><br />
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"><br />
<div><i>Proving the Heron-Rota-Welsh conjecture</i></div><br />
<div class="mw-collapsible-content"><br />
We outline the proof of the Heron-Rota-Welsh conjecture given by Adiprasito, Huh, and Katz in their paper [https://arxiv.org/abs/1511.02888 Hodge theory for combinatorial geometries]<br />
</div></div><br />
|-<br />
|2/15/2019<br />
|<br />
<div style="font-weight:bold;">Colin Crowley</div><br />
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"><br />
<div><i>Matroid polytopes</i></div><br />
<div class="mw-collapsible-content"><br />
We outline the original formulation of matroid polytopes as moment polytopes of subvarieties of the Grassmanian, following [http://www.math.ias.edu/~goresky/pdf/combinatorial.jour.pdf Combinatorial Geometries, Convex Polyhedra, and Schbert Cells].<br />
</div></div><br />
|-<br />
|2/22/2019<br />
|<br />
<div style="font-weight:bold;">[https://www.math.wisc.edu/~wang/ Botong Wang]</div><br />
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"><br />
<div><i>The Kazhdan-Lusztig polynomial of a matroid</i></div><br />
<div class="mw-collapsible-content"><br />
Classically, Kazdhan-Lusztig polynomials are associated to intervals of the Bruhat poset of a Coxeter group. We will discuss an analogue of Kazdhan-Lusztig polynomials for matroids, including results and conjectures from [https://arxiv.org/pdf/1611.07474.pdf these] [https://arxiv.org/pdf/1412.7408.pdf two] papers. <br />
</div></div><br />
|-<br />
|}</div>Csimpson6https://wiki.math.wisc.edu/index.php?title=Matroids_seminar/ideas&diff=16948Matroids seminar/ideas2019-02-16T20:17:47Z<p>Csimpson6: </p>
<hr />
<div>Looking to come talk at matroids seminar? Don't know what to talk about? Look no further! This page houses the world's finest selection of matroid-related talk ideas that we'd like to hear.<br />
Feel free to pile on your own ideas.<br />
<br />
* Kashyap, Navin; Soljanin, Emina; Vontobel, Pascal [https://www.birs.ca/workshops/2009/09w5103/report09w5103.pdf Applications of Matroid Theory & Combinatorial Optimization to Information and Coding theory]<br />
* Matroids in coding theory<br />
* Matroids in combinatorial optimization<br />
* Matroids in information theory<br />
* The same set of authors wrote a series of three papers called “Log-Concave Polynomials I, II, & III”: they develop basis counting algorithms & prove the strongest version of Mason's conjecture<br />
** LCP I: “First nontrivial deterministic basis-counting algorithm for general matroids” https://arxiv.org/abs/1807.00929<br />
** LCP II: Randomized algorithm for basis-counting. They also prove a 30-year-old conjecture about the exchange graph of the bases https://arxiv.org/abs/1811.01816<br />
** LCP III: The self-contained proof of Mason’s conjecture. This one is very short. https://arxiv.org/abs/1811.01600</div>Csimpson6https://wiki.math.wisc.edu/index.php?title=Matroids_seminar/ideas&diff=16947Matroids seminar/ideas2019-02-16T20:17:23Z<p>Csimpson6: </p>
<hr />
<div>Looking to come talk at matroids seminar? Don't know what to talk about? Look no further! This page houses the world's finest selection of matroid-related talk ideas that we'd like to hear.<br />
Feel free to pile on your own ideas.<br />
<br />
* Kashyap, Navin; Soljanin, Emina; Vontobel, Pascal [https://www.birs.ca/workshops/2009/09w5103/report09w5103.pdf Applications of Matroid Theory & Combinatorial Optimization to Information and Coding theory]<br />
* Matroids in coding theory<br />
* Matroids in combinatorial optimization<br />
* Matroids in information theory<br />
* The same set of authors wrote a series of three papers called “Log-Concave Polynomials I, II, & III”: they develop basis counting algorithms & prove the strongest version of Mason's conjecture<br />
** LCP I: “First nontrivial deterministic basis-counting algorithm for general matroids” https://arxiv.org/abs/1807.00929<br />
** Randomized algorithm for basis-counting. They also prove a 30-year-old conjecture about the exchange graph of the bases https://arxiv.org/abs/1811.01816<br />
** The self-contained proof of Mason’s conjecture. This one is very short. https://arxiv.org/abs/1811.01600</div>Csimpson6https://wiki.math.wisc.edu/index.php?title=Matroids_seminar/ideas&diff=16946Matroids seminar/ideas2019-02-16T20:16:42Z<p>Csimpson6: </p>
<hr />
<div>Looking to come talk at matroids seminar? Don't know what to talk about? Look no further! This page houses the world's finest selection of matroid-related talk ideas that we'd like to hear.<br />
Feel free to pile on your own ideas.<br />
<br />
* Kashyap, Navin; Soljanin, Emina; Vontobel, Pascal [https://www.birs.ca/workshops/2009/09w5103/report09w5103.pdf Applications of Matroid Theory & Combinatorial Optimization to Information and Coding theory]<br />
* Matroids in coding theory<br />
* Matroids in combinatorial optimization<br />
* Matroids in information theory<br />
* The same set of authors wrote a series of three papers called “Log-Concave Polynomials I, II, & III”. In first two, they (lightly but crucially) apply results from Hodge Theory of Combo Geo & Botong and June Huh’s paper to develop new basis counting algorithms (I think this was a problem that Jose brought up at our first meeting). In the final one provides “a self-contained proof of Mason’s strongest conjecture”, a result that strengthens the log-concavity result of Hodge Theory for Combo Geo<br />
** LCP I: “First nontrivial deterministic basis-counting algorithm for general matroids” https://arxiv.org/abs/1807.00929<br />
** Randomized algorithm for basis-counting. They also prove a 30-year-old conjecture about the exchange graph of the bases https://arxiv.org/abs/1811.01816<br />
** The self-contained proof of Mason’s conjecture. This one is very short. https://arxiv.org/abs/1811.01600</div>Csimpson6https://wiki.math.wisc.edu/index.php?title=Matroids_seminar/ideas&diff=16945Matroids seminar/ideas2019-02-16T20:15:28Z<p>Csimpson6: Created page with "Looking to come talk at matroids seminar? Don't know what to talk about? Look no further! This page houses the world's finest selection of matroid-related talk ideas that we'd..."</p>
<hr />
<div>Looking to come talk at matroids seminar? Don't know what to talk about? Look no further! This page houses the world's finest selection of matroid-related talk ideas that we'd like to hear.<br />
Feel free to pile on your own ideas.<br />
<br />
* Kashyap, Navin; Soljanin, Emina; Vontobel, Pascal [https://www.birs.ca/workshops/2009/09w5103/report09w5103.pdf Applications of Matroid Theory & Combinatorial Optimization to Information and Coding theory]<br />
* Matroids in coding theory<br />
* Matroids in combinatorial optimization<br />
* Matroids in information theory<br />
* The same set of authors wrote a series of three papers called “Log-Concave Polynomials I, II, & III”. In first two, they (lightly but crucially) apply results from Hodge Theory of Combo Geo & Botong and June Huh’s paper to develop new basis counting algorithms (I think this was a problem that Jose brought up at our first meeting). In the final one provides “a self-contained proof of Mason’s strongest conjecture”, a result that strengthens the log-concavity result of Hodge Theory for Combo Geo<br />
** LCP I: “First nontrivial deterministic basis-counting algorithm for general matroids” https://arxiv.org/abs/1807.00929<br />
** Randomized algorithm for basis-counting. They also prove a 30-year-old conjecture about the exchange graph of the bases https://arxiv.org/abs/1811.01816</div>Csimpson6https://wiki.math.wisc.edu/index.php?title=Matroids_seminar&diff=16944Matroids seminar2019-02-16T20:01:57Z<p>Csimpson6: </p>
<hr />
<div>The matroids seminar & reading group meets '''10:00--10:45 on Fridays in Van Vleck 901''' in order to discuss matroids from a variety of viewpoints.<br />
In particular, we aim to<br />
* survey open conjectures and recent work in the area<br />
* compute many interesting examples<br />
* discover concrete applications<br />
<br />
We are happy to have new leaders of the discussion, and the wide range of topics to which matroids are related mean that each week is a great chance for a new participant to drop in!<br />
<br />
To help develop an inclusive environment, a subset of the organizers will be available before the talk in the ninth floor lounge to informally discuss background material e.g., "What is a variety?" (this is especially for those coming from an outside area).<br />
{| cellpadding="8px" style="vertical-align:top; text-align:left; cellpadding:10px;"<br />
|1/18/2019<br />
|<br />
<div style="font-weight:bold;">[https://sites.google.com/site/dcorey2814/home Daniel Corey]</div><br />
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"><br />
<div><i>Introduction to matroids</i></div><br />
<div class="mw-collapsible-content"><br />
We'll cover the basic definitions and some examples, roughly following [http://web.ma.utexas.edu/users/sampayne/pdf/Math648Lecture3.pdf these notes].<br />
</div></div><br />
|-<br />
|1/25/2019 & 2/1/2019<br />
|<br />
<div style="font-weight:bold;">[https://www.math.wisc.edu/~jose/ Jose Rodriguez]</div><br />
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"><br />
<div><i>Algebraic matroids in action</i></div><br />
<div class="mw-collapsible-content"><br />
We discuss algebraic matroids and their applications; see [https://arxiv.org/abs/1809.00865 Algebraic Matroids in Action].<br />
</div></div><br />
|-<br />
|2/8/2019<br />
|<br />
<div style="font-weight:bold;">[http://www.math.wisc.edu/~csimpson6/ Connor Simpson]</div><br />
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"><br />
<div><i>Proving the Heron-Rota-Welsh conjecture</i></div><br />
<div class="mw-collapsible-content"><br />
We outline the proof of the Heron-Rota-Welsh conjecture given by Adiprasito, Huh, and Katz in their paper [https://arxiv.org/abs/1511.02888 Hodge theory for combinatorial geometries]<br />
</div></div><br />
|-<br />
|2/15/2019<br />
|<br />
<div style="font-weight:bold;">Colin Crowley</div><br />
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"><br />
<div><i>Matroid polytopes</i></div><br />
<div class="mw-collapsible-content"><br />
We outline the original formulation of matroid polytopes as moment polytopes of subvarieties of the Grassmanian, following [http://www.math.ias.edu/~goresky/pdf/combinatorial.jour.pdf Combinatorial Geometries, Convex Polyhedra, and Schbert Cells].<br />
</div></div><br />
|-<br />
|2/22/2019<br />
|<br />
<div style="font-weight:bold;">[https://www.math.wisc.edu/~wang/ Botong Wang]</div><br />
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"><br />
<div><i>The Kazhdan-Lusztig polynomial of a matroid</i></div><br />
<div class="mw-collapsible-content"><br />
Classically, Kazdhan-Lusztig polynomials are associated to intervals of the Bruhat poset of a Coxeter group. We will discuss an analogue of Kazdhan-Lusztig polynomials for matroids, including results and conjectures from [https://arxiv.org/pdf/1611.07474.pdf these] [https://arxiv.org/pdf/1412.7408.pdf two] papers. <br />
</div></div><br />
|-<br />
|}</div>Csimpson6https://wiki.math.wisc.edu/index.php?title=Matroids_seminar&diff=16943Matroids seminar2019-02-16T19:58:28Z<p>Csimpson6: </p>
<hr />
<div>The matroids seminar & reading group meets '''10:00--10:45 on Fridays in Van Vleck 901''' in order to discuss matroids from a variety of viewpoints.<br />
In particular, we aim to<br />
* survey open conjectures and recent work in the area<br />
* compute many interesting examples<br />
* discover concrete applications<br />
<br />
We are happy to have new leaders of the discussion, and the wide range of topics to which matroids are related mean that each week is a great chance for a new participant to drop in!<br />
<br />
To help develop an inclusive environment, a subset of the organizers will be available before the talk in the ninth floor lounge to informally discuss background material e.g., "What is a variety?" (this is especially for those coming from an outside area).<br />
{| cellpadding="8px" style="vertical-align:top; text-align:left; cellpadding:10px;"<br />
|1/18/2019<br />
|<br />
<div style="font-weight:bold;">[https://sites.google.com/site/dcorey2814/home Daniel Corey]</div><br />
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"><br />
<div><i>Introduction to matroids</i></div><br />
<div class="mw-collapsible-content"><br />
We'll cover the basic definitions and some examples, roughly following [http://web.ma.utexas.edu/users/sampayne/pdf/Math648Lecture3.pdf these notes].<br />
</div></div><br />
|-<br />
|1/25/2019 & 2/1/2019<br />
|<br />
<div style="font-weight:bold;">[https://www.math.wisc.edu/~jose/ Jose Rodriguez]</div><br />
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"><br />
<div><i>Algebraic matroids in action</i></div><br />
<div class="mw-collapsible-content"><br />
We discuss algebraic matroids and their applications; see [https://arxiv.org/abs/1809.00865 Algebraic Matroids in Action].<br />
</div></div><br />
|-<br />
|2/8/2019<br />
|<br />
<div style="font-weight:bold;">[http://www.math.wisc.edu/~csimpson6/ Connor Simpson]</div><br />
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"><br />
<div><i>Proving the Heron-Rota-Welsh conjecture</i></div><br />
<div class="mw-collapsible-content"><br />
We outline the proof of the Heron-Rota-Welsh conjecture given by Adiprasito, Huh, and Katz in their paper [https://arxiv.org/abs/1511.02888 Hodge theory for combinatorial geometries]<br />
</div></div><br />
|-<br />
|2/15/2019<br />
|<br />
<div style="font-weight:bold;">Colin Crowley</div><br />
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"><br />
<div><i>Matroid polytopes</i></div><br />
<div class="mw-collapsible-content"><br />
We outline the original formulation of matroid polytopes as moment polytopes of subvarieties of the Grassmanian, following [http://www.math.ias.edu/~goresky/pdf/combinatorial.jour.pdf Combinatorial Geometries, Convex Polyhedra, and Schbert Cells].<br />
</div></div><br />
|-<br />
|2/22/2019<br />
|<br />
<div style="font-weight:bold;">[https://www.math.wisc.edu/~wang/ Botong Wang]</div><br />
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"><br />
<div><i>The Kazhdan-Lusztig polynomial of a matroid</i></div><br />
<div class="mw-collapsible-content"><br />
Classically, Kazdhan Lusztig polynomials are associated to intervals of the Bruhat poset of a Coxeter group. We will discuss an analogue of Kazdhan-Lusztig polynomials for matroids, including results and many conjectures from [https://arxiv.org/pdf/1611.07474.pdf these] [https://arxiv.org/pdf/1412.7408.pdf two] papers. <br />
</div></div><br />
|-<br />
|}</div>Csimpson6https://wiki.math.wisc.edu/index.php?title=Matroids_seminar&diff=16942Matroids seminar2019-02-16T19:48:49Z<p>Csimpson6: </p>
<hr />
<div>The matroids seminar & reading group meets '''10:00--10:45 on Fridays in Van Vleck 901''' in order to discuss matroids from a variety of viewpoints.<br />
In particular, we aim to<br />
* survey open conjectures and recent work in the area<br />
* compute many interesting examples<br />
* discover concrete applications<br />
<br />
We are happy to have new leaders of the discussion, and the wide range of topics to which matroids are related mean that each week is a great chance for a new participant to drop in!<br />
<br />
To help develop an inclusive environment, a subset of the organizers will be available before the talk in the ninth floor lounge to informally discuss background material e.g., "What is a variety?" (this is especially for those coming from an outside area).<br />
{| cellpadding="8px" style="vertical-align:top; text-align:left; cellpadding:10px;"<br />
|1/18/2019<br />
|<br />
<div style="font-weight:bold;">[https://sites.google.com/site/dcorey2814/home Daniel Corey]</div><br />
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"><br />
<div><i>Introduction to matroids</i></div><br />
<div class="mw-collapsible-content"><br />
We'll cover the basic definitions and some examples, roughly following [http://web.ma.utexas.edu/users/sampayne/pdf/Math648Lecture3.pdf these notes].<br />
</div></div><br />
|-<br />
|1/25/2019 & 2/1/2019<br />
|<br />
<div style="font-weight:bold;">[https://www.math.wisc.edu/~jose/ Jose Rodriguez]</div><br />
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"><br />
<div><i>Algebraic matroids</i></div><br />
<div class="mw-collapsible-content"><br />
We talk about algebraic matroids, matroid polytopes, and their connection to algebraic geometry.<br />
</div></div><br />
|-<br />
|2/8/2019<br />
|<br />
<div style="font-weight:bold;">[http://www.math.wisc.edu/~csimpson6/ Connor Simpson]</div><br />
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"><br />
<div><i>Proving the Heron-Rota-Welsh conjecture</i></div><br />
<div class="mw-collapsible-content"><br />
We outline the proof of the Heron-Rota-Welsh conjecture given by Adiprasito, Huh, and Katz in their paper [https://arxiv.org/abs/1511.02888 Hodge theory for combinatorial geometries]<br />
</div></div><br />
|-<br />
|2/15/2019<br />
|<br />
<div style="font-weight:bold;">Colin Crowley</div><br />
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"><br />
<div><i>Matroid polytopes</i></div><br />
<div class="mw-collapsible-content"><br />
We outline the original formulation of matroid polytopes as moment polytopes of subvarieties of the Grassmanian, following [http://www.math.ias.edu/~goresky/pdf/combinatorial.jour.pdf Combinatorial Geometries, Convex Polyhedra, and Schbert Cells].<br />
</div></div><br />
|-<br />
|}</div>Csimpson6https://wiki.math.wisc.edu/index.php?title=Matroids_seminar&diff=16941Matroids seminar2019-02-16T19:47:39Z<p>Csimpson6: </p>
<hr />
<div>The matroids seminar & reading group meets '''10:00--10:45 on Fridays in Van Vleck 901''' in order to discuss matroids from a variety of viewpoints.<br />
In particular, we aim to<br />
* survey open conjectures and recent work in the area<br />
* compute many interesting examples<br />
* discover concrete applications<br />
<br />
We are happy to have new leaders of the discussion, and the wide range of topics to which matroids are related mean that each week is a great chance for a new participant to drop in!<br />
<br />
To help develop an inclusive environment, a subset of the organizers will be available before the talk in the ninth floor lounge to informally discuss background material e.g., "What is a variety?" (this is especially for those coming from an outside area).<br />
{| cellpadding="8px"<br />
|- style="vertical-align:top; text-align:left; cellpadding:10px;"<br />
|1/18/2019<br />
|<br />
<div style="font-weight:bold;">[https://sites.google.com/site/dcorey2814/home Daniel Corey]</div><br />
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"><br />
<div><i>Introduction to matroids</i></div><br />
<div class="mw-collapsible-content"><br />
We'll cover the basic definitions and some examples, roughly following [http://web.ma.utexas.edu/users/sampayne/pdf/Math648Lecture3.pdf these notes].<br />
</div></div><br />
|-<br />
|1/25/2019 & 2/1/2019<br />
|<br />
<div style="font-weight:bold;">[https://www.math.wisc.edu/~jose/ Jose Rodriguez]</div><br />
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"><br />
<div><i>Algebraic matroids</i></div><br />
<div class="mw-collapsible-content"><br />
We talk about algebraic matroids, matroid polytopes, and their connection to algebraic geometry.<br />
</div></div><br />
|-<br />
|2/8/2019<br />
|<br />
<div style="font-weight:bold;">[http://www.math.wisc.edu/~csimpson6/ Connor Simpson]</div><br />
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"><br />
<div><i>Proving the Heron-Rota-Welsh conjecture</i></div><br />
<div class="mw-collapsible-content"><br />
We outline the proof of the Heron-Rota-Welsh conjecture given by Adiprasito, Huh, and Katz in their paper [https://arxiv.org/abs/1511.02888 Hodge theory for combinatorial geometries]<br />
</div></div><br />
|-<br />
|2/15/2019<br />
|<br />
<div style="font-weight:bold;">Colin Crowley</div><br />
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"><br />
<div><i>Matroid polytopes</i></div><br />
<div class="mw-collapsible-content"><br />
We outline the original formulation of matroid polytopes as moment polytopes of subvarieties of the Grassmanian, following [http://www.math.ias.edu/~goresky/pdf/combinatorial.jour.pdf Combinatorial Geometries, Convex Polyhedra, and Schbert Cells].<br />
</div></div><br />
|-<br />
|}</div>Csimpson6https://wiki.math.wisc.edu/index.php?title=Matroids_seminar&diff=16940Matroids seminar2019-02-16T19:30:01Z<p>Csimpson6: </p>
<hr />
<div>The matroids seminar & reading group meets '''10:00--10:45 on Fridays in Van Vleck 901''' in order to discuss matroids from a variety of viewpoints.<br />
In particular, we aim to<br />
* survey open conjectures and recent work in the area<br />
* compute many interesting examples<br />
* discover concrete applications<br />
<br />
We are happy to have new leaders of the discussion, and the wide range of topics to which matroids are related mean that each week is a great chance for a new participant to drop in!<br />
<br />
To help develop an inclusive environment, a subset of the organizers will be available before the talk in the ninth floor lounge to informally discuss background material e.g., "What is a variety?" (this is especially for those coming from an outside area).<br />
{| cellpadding="8px"<br />
|- style="vertical-align:top; text-align:left; cellpadding:10px;"<br />
|1/18/2019<br />
|<br />
<div style="font-weight:bold;">Daniel Corey</div><br />
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"><br />
<div><i>Introduction to matroids</i></div><br />
<div class="mw-collapsible-content"><br />
We'll cover the basic definitions and some examples, roughly following [http://web.ma.utexas.edu/users/sampayne/pdf/Math648Lecture3.pdf these notes].<br />
</div></div><br />
|-<br />
|}</div>Csimpson6https://wiki.math.wisc.edu/index.php?title=Matroids_seminar&diff=16939Matroids seminar2019-02-16T18:44:55Z<p>Csimpson6: </p>
<hr />
<div>The matroids seminar & reading group meets '''10:00--10:45 on Fridays in Van Vleck 901''' in order to discuss matroids from a variety of viewpoints.<br />
In particular, we aim to<br />
* survey open conjectures and recent work in the area<br />
* compute many interesting examples<br />
* discover concrete applications<br />
<br />
We are happy to have new leaders of the discussion, and the wide range of topics to which matroids are related mean that each week is a great chance for a new participant to drop in!<br />
<br />
To help develop an inclusive environment, a subset of the organizers will be available before the talk in the ninth floor lounge to informally discuss background material e.g., "What is a variety?" (this is especially for those coming from an outside area).<br />
<br />
{| cellpadding="8";<br />
! style="text-align:left;"| Date<br />
! style="text-align:left;"| Speaker/title/abstract<br />
|-<br />
|2/3/2018 || Speakername || Talk title what am i about<br />
|}<br />
<br />
<div class="toccolours mw-collapsible" style="width:400px; overflow:auto;"><br />
<div style="font-weight:bold;line-height:1.6;">Lorem ipsum sample</div><br />
<div class="mw-collapsible-content"><br />
This text is collapsible. {{Lorem}}<br />
</div></div></div>Csimpson6https://wiki.math.wisc.edu/index.php?title=Matroids_seminar&diff=16938Matroids seminar2019-02-16T18:43:49Z<p>Csimpson6: </p>
<hr />
<div>The matroids seminar & reading group meets '''10:00--10:45 on Fridays in Van Vleck 901''' in order to discuss matroids from a variety of viewpoints.<br />
In particular, we aim to<br />
* survey open conjectures and recent work in the area<br />
* compute many interesting examples<br />
* discover concrete applications<br />
<br />
We are happy to have new leaders of the discussion, and the wide range of topics to which matroids are related mean that each week is a great chance for a new participant to drop in!<br />
<br />
To help develop an inclusive environment, a subset of the organizers will be available before the talk in the ninth floor lounge to informally discuss background material e.g., "What is a variety?" (this is especially for those coming from an outside area).<br />
<br />
{|<br />
! style="text-align:left;"| Date<br />
! style="text-align:left;"| Speaker/title/abstract<br />
|-<br />
|2/3/2018 || Speakername || Talk title what am i about<br />
|}<br />
<br />
<div class="toccolours mw-collapsible" style="width:400px; overflow:auto;"><br />
<div style="font-weight:bold;line-height:1.6;">Lorem ipsum sample</div><br />
<div class="mw-collapsible-content"><br />
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</div></div></div>Csimpson6https://wiki.math.wisc.edu/index.php?title=Matroids_seminar&diff=16937Matroids seminar2019-02-16T18:42:48Z<p>Csimpson6: </p>
<hr />
<div>The matroids seminar & reading group meets '''10:00--10:45 on Fridays in Van Vleck 901''' in order to discuss matroids from a variety of viewpoints.<br />
In particular, we aim to<br />
* survey open conjectures and recent work in the area<br />
* compute many interesting examples<br />
* discover concrete applications<br />
<br />
We are happy to have new leaders of the discussion, and the wide range of topics to which matroids are related mean that each week is a great chance for a new participant to drop in!<br />
<br />
To help develop an inclusive environment, a subset of the organizers will be available before the talk in the ninth floor lounge to informally discuss background material e.g., "What is a variety?" (this is especially for those coming from an outside area).<br />
<br />
{|<br />
! style="text-align:left;"| Date<br />
! Speaker/title/abstract<br />
|-<br />
|2/3/2018 || Speakername || Talk title what am i about<br />
|}<br />
<br />
<div class="toccolours mw-collapsible" style="width:400px; overflow:auto;"><br />
<div style="font-weight:bold;line-height:1.6;">Lorem ipsum sample</div><br />
<div class="mw-collapsible-content"><br />
This text is collapsible. {{Lorem}}<br />
</div></div></div>Csimpson6https://wiki.math.wisc.edu/index.php?title=Matroids_seminar&diff=16936Matroids seminar2019-02-16T18:42:09Z<p>Csimpson6: </p>
<hr />
<div>The matroids seminar & reading group meets '''10:00--10:45 on Fridays in Van Vleck 901''' in order to discuss matroids from a variety of viewpoints.<br />
In particular, we aim to<br />
* survey open conjectures and recent work in the area<br />
* compute many interesting examples<br />
* discover concrete applications<br />
<br />
We are happy to have new leaders of the discussion, and the wide range of topics to which matroids are related mean that each week is a great chance for a new participant to drop in!<br />
<br />
To help develop an inclusive environment, a subset of the organizers will be available before the talk in the ninth floor lounge to informally discuss background material e.g., "What is a variety?" (this is especially for those coming from an outside area).<br />
<br />
{|<br />
! style="text-align:left;"| Date<br />
! Speaker/title/abstract<br />
|-<br />
|Speakername || Talk title what am i about<br />
|}<br />
<br />
<div class="toccolours mw-collapsible" style="width:400px; overflow:auto;"><br />
<div style="font-weight:bold;line-height:1.6;">Lorem ipsum sample</div><br />
<div class="mw-collapsible-content"><br />
This text is collapsible. {{Lorem}}<br />
</div></div></div>Csimpson6https://wiki.math.wisc.edu/index.php?title=Matroids_seminar&diff=16932Matroids seminar2019-02-16T18:16:05Z<p>Csimpson6: matroids seminar organizational page</p>
<hr />
<div>The matroids seminar & reading group meets '''10:00--10:45 on Fridays in Van Vleck 901''' in order to discuss matroids from a variety of viewpoints.<br />
In particular, we aim to<br />
* survey open conjectures and recent work in the area<br />
* compute many interesting examples<br />
* discover concrete applications<br />
<br />
At the reading group website URL TBD one can find a list of possible topics to discuss this semester. We are happy to have new leaders of the discussion. <br />
Because of the wide range of topics, each week is a new chance for a new participant to drop in. <br />
To help develop an inclusive environment, a subset of the organizers will be available before the talk in the ninth floor lounge to informally discuss background material e.g., "What is a variety?" (this is especially for those coming from an outside area). <br />
<br />
<div class="toccolours mw-collapsible" style="width:400px; overflow:auto;"><br />
<div style="font-weight:bold;line-height:1.6;">Lorem ipsum sample</div><br />
<div class="mw-collapsible-content"><br />
This text is collapsible. {{Lorem}}<br />
</div></div></div>Csimpson6