On Random Polynomials and Counting Number Fields: Fourier Analysis Meets Arith... - Theresa Anderson

Workshop on Dynamics, Discrete Analysis and Multiplicative Number Theory
2:00pm – 3:00pm Simonyi Hall 101 and Remote Access
Topic: On Random Polynomials and Counting Number Fields: Fourier Analysis Meets Arithmetic Statistics
Speaker: Theresa Anderson
Affiliation: Carnegie Mellon University
Date: February 27 2023
Behaviors of objects of algebraic interest, such as polynomials, elliptic curves and number fields -- many of which are still unknown -- fall into the field of arithmetic statistics.. By bringing in Fourier analysis to interplay with a wide variety of number theoretic techniques, we were recently able to improve our counting tools. Today I'll discuss predicting random polynomials and determining how many number fields of a given degree there are, both using these techniques in different ways.