NTSGrad Fall 2021/Abstracts
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This page contains the titles and abstracts for talks scheduled in the Fall 2021 semester. To go back to the main GNTS page, click here.
Sep 14
| Hyun Jong Kim |
| What would Jordan do? |
| In his notes for students, Jordan has a list of general topics and references in number theory/algebraic geometry/arithmetic geometry that students in arithmetic geometry should be comfortable with after a certain point of time. I will introduce some language used in these general topics for beginners. |
Sep 21
| Peter YI WEI |
| The S-Unit equation: p-adic approaches |
| In this talk, I will go over the history of rational/integral points on curves. In particular, I will introduce a recent proof of the S-unit equation using p-adic period maps, given by Lawrence-Venkatesh. |
Sep 28
| TBA |
| TBA |
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Oct 5
| Yifan Wei |
| Lifting a smooth curve from char p to char 0 |
| Geometry over char p is fascinating or frustrating, depending on who you are. However varieties over char 0 could be enjoyed by geometers of all kinds. We will dicuss one way of lifting a smooth projective variety from char p to char 0. After applying our technique to curves we briefly mention the situation in higher dimensions. And if time permits, we discuss a non-liftable example by Serre. |
Oct 12
| TBA |
| TBA |
Oct 19
| TBA |
| TBA |
Oct 26
| Di Chen |
| Special values of zeta functions at positive even integers |
| I will introduce Euler's classical result over Q, Klingen-Siegel theorem over totally real number fields, and Zagier's theorems and conjectures over general number fields. I will give many examples and discuss their proofs. If time permits, I will discuss its relation with K-theory. |
Nov 2
| Jerry Y. Fu |
| Diophantine approximation: How I learned to stop worrying and love integral points |
| Diophantine approximation is a crucial tool in studying integral points and Schlickewei's theorem is a very useful theorem in proving finiteness theorems on integral points. In the first part of my talk I will show some elegant proof as applications of the subspace theorem such as Vojta's theorem, the S-unit equation, and then I will introduce main conjectures: Vojta, Mordell, Bombieri and Lang, and their relations to each other. |
Nov 9
| TBA |
| TBA |
Nov 16
| TBA |
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Nov 23
| TBA |
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Nov 30
| TBA |
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Dec 7
| TBA |
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Dec 14
| TBA |
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