Combinatorial Methods in Enumerative Algebra

Explore a lecture on combinatorial methods in enumerative algebra that delves into algebraic counting problems and their relationship with integer sequences and generating functions. Learn about classical zeta and L-functions, including Dirichlet's zeta function for number field ideal enumeration, Witten's zeta function for Lie group representation counting, and Hasse-Weil zeta functions for rational points of algebraic varieties over finite fields. Discover how zeta functions of groups and rings serve as essential tools in asymptotic group theory and ring theory, featuring Euler product decompositions with rational local factors. Delivered at the International Centre for Theoretical Sciences' Ramanujan Lecture Hall, this presentation is part of a broader program aimed at connecting experts across various mathematical disciplines and training young researchers in the dynamic field of enumerative algebra.