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.