Graduate Algebraic Geometry Seminar Fall 2023
When: 4:30-5:30 PM on Wednesday.
Where: Van Vleck B119
Who: All undergraduate and graduate students interested in algebraic geometry, commutative algebra, and related fields are welcome to attend.
Why: The purpose of this seminar is to learn algebraic geometry and commutative algebra by giving and listening to talks in a informal setting. Sometimes people present an interesting paper they find. Other times people give a prep talk for the 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.
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@g-groups.wisc.edu by sending an email to gags+subscribe@g-groups.wisc.edu. If you prefer (and are logged in under your wisc google account) the list registration page is here.
Organizers: John Cobb, Yu (Joey) Luo
Give a talk!
We need volunteers to give talks this semester. Beginning graduate students are particularly encouraged to give a talk, since it's a great way to get your feet wet with the material. If you would like some talk ideas, see the list on the main page. Sign up here.
Wishlist
This was assembled using input from an interest form at the beginning of the semester. Choose one and you will have the rare guarantee of having one interested audience member. Feel free to add your own.
- Hilbert Schemes
- Geothendieck '66, "On the de Rham Cohomology of Algebraic Varieties"
- A History of the Weil Conjectures
- A pre talk for any other upcoming talk
- Weil Conjectures, GAGA theorems, surfaces of general type, moduli spaces, moduli of curves, mixed characteristics (stuff), elliptic curves, abelian varieties, hyperelliptic curves, resolution of singularities, minimal model program (stuff).
Being an audience member
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:
- Do Not Speak For/Over the Speaker
- Ask Questions Appropriately
Talks
| Date | Speaker | Title | Abstract |
| September 13 | Peter Wei | Introduction to the Cartier Isomorphism (Pretalk) | This is a preparatory talk for Josh Mundinger's talk on Friday. We discuss the Cartier isomorphism. |
| September 20 | |||
| September 27 | Yifan Wei | p-torsions in the p-adic land and de Rham cohomology | Following Tate, we will try to visualize an elliptic curve over Cp, specifically, the p-adic disk near identity. Logarithm in the p-adic land provides a nice linearization to the problem, and we'll explore what this all means. If time permits, I'll sketch the proof of Hodge-Tate decomposition. (You know something like this is coming.) |
| October 4 | Owen Goff | TBA | TBA |
| October 11 | TBA | TBA | TBA |
| October 18 | Alex Hof | Why Does Normalization Resolve Singularities in Codimension 1? | We review the definition of the normalization of an algebraic variety, discuss the geometric intuition for it, and explain why normalizing removes codimension-1 singularities. This talk is intended to be accessible to people taking first-semester algebraic geometry. |
| October 25 | Jack Messina | Variations of Hodge Structure and Hodge Modules | This talk aims to introduce Hodge modules. We will start with the classical variation of Hodge structure, and then cover some background on perverse sheaves and D-modules. From here, we can introduce pure Hodge modules. We end by mentioning mixed Hodge modules and the Saito vanishing theorem. |
| November 1 | Yiyu Wang | ||
| November 8 | John Cobb | Likelihood Geometry | Maximum likelihood estimation (MLE) is a fundamental task in statistics. June Huh and Bernd Sturmfels wrote a long paper that explores how characteristics of the MLE problem for algebraic statistical models are reflected in the geometry of the likelihood correspondence, a variety that ties together observed data and their maximum likelihood estimators. I’ll define these objects, frame some questions (with partial answers) about them, and give some cool facts coming from algebraic statistics. This will be adapted from a much shorter talk, so there will be plenty of time for tangents and questions! |
| November 15 | Peter Wei | Pretalk for Purnaprajna Bangere's talk | |
| November 22 | Thanksgiving Break | ||
| November 29 | Yanbo Chen | An Introduction to Homotopy Theory | The Brown Representability theorem tells us that each generilized cohomology theory is representable, then use the suspension theorem, we get a sequence of spaces and some relations between them. This is a simple model for spectrum in algebraic topology. In this talk we will discuss this notion, give some geometric examples and explore one important problem: how to get a ``good'' category for spectra. |
| December 9 | Kevin Dao | Introduction to D-Modules | On the basics of the theory of D-Modules and how it gets used. |
| December 13 | Maya Banks | Intro to weighted projective space |