NTSGrad Fall 2024/Abstracts

This page contains the titles and abstracts for talks scheduled in the Fall 2024 semester. To go back to the main GNTS page for the semester, click here.

9/10

Ivan Aidun

Rational Points on Curves, an Introduction to Arithmetic Geometry

Arithmetic geometry is an area of number theory that uses geometry to answer questions about when multivariable polynomials have integer or rational solutions. Already, even the simplest case, finding rational points on curves, offers many interesting facets worth exploring. In this talk I'll introduce several facets of the world of finding points on curves. Although I won't be able to discuss any topic in great depth, I hope to say at least a little bit about: finding points everywhere locally, why are elliptic curves groups, and why does the genus of a curve affect the rational points.

9/17

Amin Idelhaj

Random Walk on Groups

I'll give a random walk through some topics surrounding random walk on finite groups: Fourier analysis, spectral gaps, isoperimetric inequalities, and expander graphs.

9/24

Chenghuang Chen

Exponential Sums in Analytic Number Theory

I will mainly focus on van der Corput's B process for exponential sums in order to fit Thursday's NTS talk. If I have enough time, I will also talk about some related concepts in Montgomery's book "Ten Lectures on the Interface of Analytic Number Theory and Harmonic Analysis".

10/1

Eiki Norizuki

Hodge Numbers of Birational Calabi-Yau Manifolds

This is a prep talk for Thursday's NTS talk. In 1995, Kontsevich introduced motivic integration to prove that Hodge numbers of Birational Calabi-Yau Manifolds are equal. There is an alternative proof using other tools and I will try to outline some of the ingredients of this approach. I may talk about classical Hodge theory, Weil conjectures, p-adic integrations and p-adic Hodge theory.