Graduate Algebraic Geometry Seminar Spring 2016
When: Wednesdays 4:00pm
Where:Van Vleck B139
Who: YOU!!
Why: The purpose of this seminar is to learn algebraic geometry by giving and listening to talks in a informal setting. Talks are typically accessible to beginning graduate students and take many different forms. Sometimes people present an interesting paper they find. Other times people give a prep talk for the Friday Algebraic Geometry Seminar. Other times people give a series of talks on a topic they have been studying in-depth.
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 here.
Give a talk!
We need volunteers to give talks this semester. If you're interested contact DJ, or just add yourself to the list (though in that case we might move your talk later without your permission). Beginning graduate students are particularly encouraged to give a talk, since it's a great way to get your feet wet with the material.
Wish List
If there is a subject or a paper which you'd like to see someone give a talk on, add it to this list. If you want to give a talk and can't find a topic, try one from this list.
- 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)
- A careful explanation of the correspondence between graded modules and sheaves on projective varieties.
- Braverman and Bezrukavnikov: geometric Langlands correspondence for D-modules in prime characteristic: the GL(n) case (Note: this title sounds tough but prime characteristic makes things easier)
- Homological projective duality
- The orbit method (for classifying representations of a Lie group)
- Kaledin: geometry and topology of symplectic resolutions
- Kashiwara: D-modules and representation theory of Lie groups (Note: Check out that diagram on page 2!)
- Geometric complexity theory, maybe something like arXiv:1508.05788.
Spring 2016
| Date | Speaker | Title (click to see abstract) |
| January 20 | Jay Yang | Tropical Geometry II |
| January 27 | Jay Yang | Tropical Geometry III |
| February 3 | Ed Dewey | Derived Category of Projective Space |
| February 10 | Ed Dewey | More Derived Category of Projective Space |
| February 17 | TBD | TBD |
| February 24 | DJ Bruce | Divisors and Stuff I |
| March 2 | DJ Bruce | Divisors and Stuff II |
| March 9 | DJ Bruce | Divisors and Stuff III |
| March 16 | TBD | TBD |
| March 23 | N/A | No GAGS This Week |
| March 30 | Daniel Hast | Jacobians, path integrals, and fundamental groups of curves I |
| April 6 | Daniel Hast | Jacobians, path integrals, and fundamental groups of curves II |
| April 13 | Jason Steinberg | Something Something Shimura Varieties |
| April 20 | Quinton Westrich | Projective Duality |
| April 27 | Zachary Charles | Polynomial systems, toric geometry, and Newton polytopes |
| May 4 | TBD | TBD |
| May 11 | TBD | TBD |
January 20
| Jay Yang |
| Title: Tropical Geometry II |
|
Abstract: Previously we discussed the basic definitions of tropical geometry, and the connection to algebraic geometry. Now we use this to count curves through points on P^2. This is a well known result initially proven without the use of tropical tools. But using tropical tools we can give a proof that relies on the combinatorics of lattice paths. I will begin with a review of some facts from tropical geometry that we need for this proof. |
January 27
| TBD |
| Title: TBD |
|
Abstract: TBD |
February 3
| Ed Dewey |
| Title: Derived Category of Projective Space |
|
Abstract: I will talk about the derived category of projective space, covering mostly the same material that Andrei did at the end of his homological algebra course, but at a more leisurely pace. My main reference is the Skimming. |
February 10
| Ed Dewey |
| Title: More Derived Category of Projective Space |
|
Abstract: I will explain in what sense we now "know" the derived category of projective space from Beilinson's result. There is a very nice answer in terms of quivers but I got distracted by another, much less efficient but maybe more flexible approach using dg categories, so that is what we will do. If my understanding permits, we will also talk about the derived category of a projective space bundle. |
February 17
| TBD |
| Title: TBD |
|
Abstract: TBD |
February 24
| DJ Bruce |
| Title: Divisors and Stuff I |
|
Abstract: TBD |
March 2
| DJ Bruce |
| Title: Divisors and Stuff II |
|
Abstract: TBD |
March 9
| DJ Bruce |
| Title: Divisors and Stuff III |
|
Abstract: TBD |
March 16
| TBD |
| Title: TBD |
|
Abstract: TBD |
March 23
| No Seminar This Week |
| Title: N/A |
|
Abstract: Enjoy your break! |
March 30
| Daniel Hast |
| Title: Jacobians, path integrals, and fundamental groups of curves I |
|
Abstract: TBD |
April 6
| Daniel Hast |
| Title: Jacobians, path integrals, and fundamental groups of curves II |
|
Abstract: TBD |
April 13
| Jason Steinberg |
| Title: Something Something Shimura Varieties |
|
Abstract: |
April 20
| Quinton Westrich |
| Title: Projective Duality |
|
Abstract: Intro to discriminants and duals of projective varieties. My field will be C. |
April 27
| Zachary Charles |
| Title: Polynomial systems, toric geometry, and Newton polytopes |
|
Abstract: While the Bezout bound generically gives us the number of roots of a polynomial system in projective space, often much more can be said about specific systems in affine space. Kushnirenko's Theorem (and later Bernstein's theorem) gives better bounds for "sparse" systems of polynomials. These bounds are based on the volume of Newton polytopes. I will prove Kushnirenko's theorem using ideas from toric geometry, commutative algebra, and the geometry of polytopes. If time permits we will give applications of this theorem to power systems. |
May 4
| TBD |
| Title: TBD |
|
Abstract: TBD |
May 11
| TBD |
| Title: TBD |
|
Abstract: TBD |