NTSGrad Spring 2023/Abstracts

This page contains the titles and abstracts for talks scheduled in the Fall 2023 semester. To go back to the main GNTS page for the semester, click here.

1/24

Tunus Tuncbilek

The classification of Lie algebras and their representations

I will introduce simple Lie algebras over C and classify them, up to isomorphism, using their Dynkin diagrams and root systems. I will also talk about more advanced results from the literature on Lie algebra representations.

1/31

John Yin

Bilu’s Equidistribution Theorem

Bilu’s Equidistribution Theorem says that any sequence of points with decreasing height is equidistributed on the unit circle. We will show the proof of this and discuss related works if time permits.

2/7

No Talk!

2/14

Hyun Jong Kim

Bounded Height Problem for Dynamically Defined Sets

I will give a survey talk about one of the projects that Laura DeMarco has proposed for the upcoming Arizona Winter School in March. Namely, the problem aims to show that the set of orbit collisions via families of self maps of $\mathbb{P}^1$ defined over $\overline{\mathbb{Q}}$ has bounded height. Notes to this talk are available at https://github.com/hyunjongkimmath/GNTS_spring_2023_presentation_notes

2/21

Yiyu Wang

The Local Monodromy Theorem and the Monodromy-Weight Conjecture

In this talk, I will introduce the celebrated local monodromy theorem in the topology and rephrase it in a number-theoretical way which is due to Grothendieck. I will explain what it means from the topological and Hodge theoretical point of view. This theorem naturally leads to the notion of mondromy filtration, and the Monodromy-Weight conjecture asserts that it coincides with the weight filtration.

2/28

Eiki Norizuki

$o$-minimal structures in number theory

$o$-minimality is an area of model theory that has had applications to many areas including number theory and arithmetic geometry. I will give a gentle introduction to what an $o$-minimal structure is and try to state some results in number theory that can be framed in terms of $o$-minimality. In particular, it can be used to address some problems in point-counting (Pila-Wilkie's theorem) and transcendence number theory (Schanuel's Conjecture). No particular prior knowledge is assumed and it should be accessible to anyone.

3/21

TBA

3/28

TBA

4/4

TBA

4/11

TBA

4/18

TBA

4/25

TBA

5/2

TBA