Zeta Functions and Applications to Twisted Conjugacy

Explore a 32-minute lecture on zeta functions and their applications to twisted conjugacy, delivered by Paula Lins at the International Centre for Theoretical Sciences as part of the Combinatorial Methods in Enumerative Algebra program. Delve into how algebraic counting problems generate integer sequences that are best understood through generating functions, examining classical zeta and L-functions including Dirichlet's zeta function, Witten's zeta function, and Hasse-Weil zeta functions. Learn about the role of zeta functions in asymptotic group theory and ring theory, with particular attention to their Euler product decompositions and rational local factors. Understand how these mathematical tools contribute to understanding underlying structures and their properties in algebraic systems, presented as part of a broader program aimed at connecting experts across related mathematical disciplines and training the next generation of researchers in enumerative algebra.