Graduate Algebraic Geometry Seminar Spring 2023: Difference between revisions
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Revision as of 20:38, 27 February 2023
When: 4:15-5:15 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 |
| January 31 | Mahrud Sayrafi | Bounding the Multigraded Regularity of Powers of Ideals |
| February 1 | John Cobb | Introduction to Intersection Theory |
| February 8 | Yiyu Wang | An introduction to Macpherson's Chern classes |
| February 15 | Alex Hof | Normal Cones in Algebraic Geometry |
| February 22 | Maya Banks | Syzygies of Projective Varieties |
| March 1 | Asvin G | TBD |
| March 8 | Asvin G | Introduction to P1 plus one point |
| March 22 | Kevin Dao | Remarks on the Enriques-Kodaira Classification |
| March 29 | Peter Yi Wei | TBD |
| April 5 | Colin Crowley (Maybe) | TBD |
| April 12 | Asvin G | Introduction to P1 minus no point |
| April 19 | Asvin G | Introduction to P1 minus one point |
| April 26 | Asvin G | Introduction to P1 minus two points |
| May 3 | Asvin G | Introduction to P1 minus three points |
January 31
| Mahrud Sayrafi |
| Title: Bounding the Multigraded Regularity of Powers of Ideals |
| Abstract: Building on a result of Swanson, Cutkosky-Herzog-Trung and Kodiyalam described the surprisingly predictable asymptotic behavior of Castelnuovo--Mumford regularity for powers of ideals on a projective space P^n: given an ideal I, there exist integers d and e such that for large enough n the regularity of I^n is exactly dn+e.
Through a medley of examples we will see why asking the same question about an ideal I in the total coordinate ring S of a smooth projective toric variety X is interesting. After that I will summarize the ideas and methods we used to bound the region reg(I^n) as a subset of Pic(X) by proving that it contains a translate of reg(S) and is contained in a translate of Nef(X), with each bound translating by a fixed vector as n increases. Along the way will see some surprising behavior for multigraded regularity of modules. This is joint work with Juliette Bruce and Lauren Cranton Heller. |
February 1
| John Cobb |
| Title: Introduction to Intersection Theory |
| Abstract: In this |
February 8
| Yiyu Wang |
| Title: An introduction to Macpherson's Chern classes |
| 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. |
February 15
| Alex Hof |
| Title: Normal Cones in Algebraic Geometry |
| 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. |
February 22
| Maya Banks |
| Title: Syzygies of Projective Varieties |
| 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. |
March 1
| Asvin G |
| Title: TBD |
| Abstract: |
March 8
| Title: |
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March 22
| Kevin Dao |
| Title: Remarks on the Enriques-Kodaira Classification |
| Abstract: |
March 29
| Peter Yi Wei |
| Title: TBD |
| Abstract: |
April 5
| Colin Crowley (Maybe) |
| Title: TBD |
| Abstract: |
April 12
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April 19
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April 26
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May 3
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