Graduate Algebraic Geometry Seminar Spring 2022: Difference between revisions
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| bgcolor="#BCD2EE" align="center" | Title: | | bgcolor="#BCD2EE" align="center" | Title: An introduction to Tropicalization | ||
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| bgcolor="#BCD2EE" | Abstract: | | bgcolor="#BCD2EE" | Abstract: Tropicalization is a logarithmic process (functor) that takes embedded algebraic varieties to polyhedral complexes. The complexes that are in the image have some additional structure which leads to the definition of a tropical variety, the main object of study in tropical geometry. I'll talk about the first paper to use these ideas, and the problem that they were used to solve. | ||
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Revision as of 20:12, 3 March 2022
When: 4:30-5:30 PM Thursdays
Where: VV B231
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
Give a talk!
We need volunteers to give talks this semester. If you're interested, please fill out this form. 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.
Spring 2022 Topic Wish List
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
- Reductive groups and flag varieties
- Geothendieck '66, "On the de Rham Cohomology of Algebraic Varieties"
- Going from line bundles and divisors to vector bundles and chern classes
- A History of the Weil Conjectures
- Mumford & Bayer, "What can be computed in Algebraic Geometry?"
- A pre talk for any other upcoming talk
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 |
| February 10 | Everyone | Informal chat session |
| February 17 | Asvin G | |
| February 24 | Yu Luo | Riemann-Hilbert Correspondence |
| March 3 | ||
| March 10 | Colin Crowley | |
| March 24 | Caitlyn Booms | |
| March 31 | Ruofan | |
| April 7 | Alex Hof | |
| April 14 | ||
| April 21 | Connor Simpson | |
| April 28 | Karan | Using varieties to study polynomial neural networks |
| May 5 | Ellie Thieu |
February 10
| Everyone |
| Title: Informal chat session |
| Abstract: Bring your questions! |
February 17
| Asvin G |
| Title: TBD |
| Abstract: TBD |
February 24
| Yu LUO (Joey) |
| Title: Riemann-Hilbert Correspondence |
| Abstract: During the talk, I will start with "nonsingular" version of Riemann-Hilbert correspondence between flat vector bundles and local systems. Then I will introduce the regular singularity, then sketch the Riemann-Hilbert correspondence with regular singularity. If time permit, I will brief mention some applications.
\end{abstract} |
March 3
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| Abstract: |
March 10
| Title: An introduction to Tropicalization |
| Abstract: Tropicalization is a logarithmic process (functor) that takes embedded algebraic varieties to polyhedral complexes. The complexes that are in the image have some additional structure which leads to the definition of a tropical variety, the main object of study in tropical geometry. I'll talk about the first paper to use these ideas, and the problem that they were used to solve. |
March 17
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| Abstract: |
March 24
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March 31
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April 7
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April 14
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April 21
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April 28
| Karan |
| Title: Using varieties to study polynomial neural networks |
| Abstract: In this talk, I will exposit the work of Kileel, Trager, and Bruna in their 2019 paper "On the Expressive power of Polynomial Neural Networks". We will look at 1) what a polynomial neural network is and how we can interpret the output such networks as varieties, 2) why the dimension of this variety and the expressive power of this network are related, and 3) how the study of these varieties might tell us something about the architecture of the network. |
May 5
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