Number Theory over Function Fields - Lecture 5

Explore the fascinating world of number theory over function fields in this comprehensive lecture by Will Sawin from Columbia University. Delve into the deep analogy between ordinary integers and polynomials in one variable over finite fields, as well as between number fields and function fields of algebraic curves over finite fields. Discover how applying geometric techniques to classical number theory problems involving polynomials over finite fields leads to new insights. Learn about recent progress in this area, including connections to other mathematical disciplines. Examine how the circle method for counting Diophantine equation solutions relates to the topology of moduli spaces of curves in varieties. Investigate geometric approaches to Cohen-Lenstra heuristics and their generalizations, leading to new probabilistic results. Explore the connection between the analytic theory of automorphic forms over function fields and geometric Langlands theory. Gain a deeper understanding of this powerful approach to number theory that bridges multiple areas of mathematics.