Graduate Algebraic Geometry Seminar Fall 2017
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 | Semiorthogonal Decomposition for Algebraic Varieties |
| 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 | TBD | TBD |
| April 20 | TBD | TBD |
| April 27 | TBD | TBD |
| 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: Semiorthogonal Decomposition for Algebraic Varieties |
|
Abstract: I will explain some results from Bondal and Orlov's article of the same name. One interpretation of what it should mean to "compute" a triangulated category is to give a full exceptional sequence, or failing that a semiorthogonal decomposition into two categories that you are willing to pretend to understand. Bondal and Orlov did this for the intersection of two quadrics and for blowups. The strategy is to express one of the terms in the semiorthogonal decomposition as the image of a Fourier-Mukai transform. This is useful because they have a theorem (this is probably the "main content" of the paper) that lets you guarantee that the FM transform is full and faithful. |
February 10
| Ed Dewey |
| Title: Semiorthogonal Decompositions for Algebraic Varieties |
|
Abstract: I will explain some results from Bondal and Orlov's article of the same name. One interpretation of what it should mean to "compute" a triangulated category is to give a full exceptional sequence, or failing that a semiorthogonal decomposition into two categories that you are willing to pretend to understand. Bondal and Orlov did this for the intersection of two quadrics and for blowups. The strategy is to express one of the terms in the semiorthogonal decomposition as the image of a Fourier-Mukai transform. This is useful because they have a theorem (this is probably the "main content" of the paper) that lets you guarantee that the FM transform is full and faithful. |
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
| TBD |
| Title: TBD |
|
Abstract: TBD |
April 20
| TBD |
| Title: TBD |
|
Abstract: TBD |
April 27
| TBD |
| Title: TBD |
|
Abstract: TBD |
May 4
| TBD |
| Title: TBD |
|
Abstract: TBD |
May 11
| TBD |
| Title: TBD |
|
Abstract: TBD |