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Learn about conjugacy growth in groups through this 51-minute lecture presented by Gemma Crowe at the International Centre for Theoretical Sciences as part of the Combinatorial Methods in Enumerative Algebra program. Explore how algebraic counting problems generate integer sequences and their encoding through generating functions, with a focus on zeta functions in group theory. Discover the significance of Euler product decompositions and their rational local factors in understanding structural patterns. Gain insights into how various zeta functions, including Dirichlet's, Witten's, and Hasse-Weil, enumerate different mathematical structures from number fields to Lie group representations and rational points of algebraic varieties. Delivered as part of a broader program aimed at connecting experts across combinatorial areas and training young researchers in enumerative algebra, this lecture contributes to the understanding of asymptotic group theory and ring theory.
