Graduate Algebraic Geometry Seminar Fall 2023: Difference between revisions

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{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table
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| bgcolor="#A6B658" align="center" style="font-size:125%" | John Cobb
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| bgcolor="#BCD2EE" align="center" |Title: Introduction to Intersection Theory
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| bgcolor="#BCD2EE" |Abstract: In this <s>advertisement</s> talk, I'd like to talk about some methods used in enumerative geometry. I'll define what a Chow ring is, count some things with it, and tell you why you should read "3264 and all that" this semester with me.
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| bgcolor="#A6B658" align="center" style="font-size:125%" | Yiyu Wang
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| bgcolor="#BCD2EE" align="center" |Title: An introduction to Macpherson's Chern classes
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| bgcolor="#BCD2EE" |Abstract: In this talk, I will start from a formula of the Euler characteristic number of a degree d smooth hypersurface in P^n and discuss how to generalize this formula to the singular case. This naturally leads to the notion of the Chern classes of a singular space. I will briefly introduce Macpherson's Chern classes which is a natural generalization of the ordinary Chern class and how to calculate these classes.
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| bgcolor="#A6B658" align="center" style="font-size:125%" |Alex Hof
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| bgcolor="#BCD2EE" align="center" |Title: Normal Cones in Algebraic Geometry
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| bgcolor="#BCD2EE" |Abstract: In this talk, we'll go over the definition of the normal cone of a closed subscheme, explore the geometric intuition behind it via a construction called the Rees algebra, and explain how it can be used to give geometric characterizations of apparently algebraic notions such as flatness and depth.
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| bgcolor="#A6B658" align="center" style="font-size:125%" |Maya Banks
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| bgcolor="#BCD2EE" align="center" |Title: Syzygies of Projective Varieties
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| bgcolor="#BCD2EE" | Abstract: The general slogan for the study of syzygies in geometry is that "geometric information about a projective variety is reflected in its sygygies." In this talk, we'll discuss some of the early results that kick-started this idea, such as Castelnuovo-Mumford regularity, quadric generation of varieties in P^n, and Green's Linear Syzygy Theorem. I'll go over all of the basic definitions and hopefully do lots of examples---in particular, this talk should be accessible to someone taking the intro Algebraic Geometry sequence.
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| bgcolor="#A6B658" align="center" style="font-size:125%" |Asvin G
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| bgcolor="#BCD2EE" align="center" |Title: TBD
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| bgcolor="#A6B658" align="center" style="font-size:125%" |Kevin Dao
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| bgcolor="#BCD2EE" align="center" |Title: Enriques-Kodaira Classification and its Influence on MMP
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| bgcolor="#BCD2EE" |Abstract: There is always more to say than there is time to say it. Let this abstract be an overly optimistic summary. I’ll tell you what the EK classification is, how it is achieved, the relevant development of birational algebraic geometry, and then point towards  the difficulties in higher dimensions. I’ll also indicate, where possible and from what I know, the technical tools that are ubiquitous to the topic. If there is time, I will indicate a few problems and directions in either (a) the classification of (non-algebraic) surfaces, (b) rational curves on varieties, (c) major results of the MMP itself.
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| bgcolor="#A6B658" align="center" style="font-size:125%" |Peter Yi Wei
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| bgcolor="#BCD2EE" align="center" |Title: TBD
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| bgcolor="#A6B658" align="center" style="font-size:125%" |Dima Arinkin
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| bgcolor="#BCD2EE" align="center" |Title: Hitchin Fibration
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| bgcolor="#A6B658" align="center" style="font-size:125%" |Yunfan He
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| bgcolor="#BCD2EE" align="center" |Title: Variation of Hodge structure
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| bgcolor="#BCD2EE" |Abstract: I will review a little bit of the classic Hodge theory, and talk about how to generalize to the relative version.
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| bgcolor="#A6B658" align="center" style="font-size:125%" |Jacob Wood
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| bgcolor="#A6B658" align="center" style="font-size:125%" |Brian Hepler
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| bgcolor="#A6B658" align="center" style="font-size:125%" |Sun Woo Park
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| bgcolor="#BCD2EE" align="center" |Title: Introduction to Newton Polygon
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Revision as of 16:00, 31 August 2023

When: 4:30-5:30 PM on Wednesday.

Where: Van Vleck B119

Toby the OFFICIAL mascot of GAGS!!

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
September 13
September 20
September 27
October 4
October 11
October 18
October 25
November 1
November 8
November 15
November 22
November 29
December 6
December 13

September 13

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September 20

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September 27

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October 4

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October 11

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October 18

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October 25

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November 1

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November 8

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November 15

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November 22

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November 29

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December 6

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December 13

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Past Semesters

Spring 2023

Fall 2022

Spring 2022

Fall 2021

Spring 2021

Fall 2020

Spring 2020

Fall 2019

Spring 2019

Fall 2018

Spring 2018

Fall 2017

Spring 2017

Fall 2016

Spring 2016

Fall 2015

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