Reflection Factorizations of Singer Cycles in Linear and Unitary Groups

Explore a 49-minute lecture from the Combinatorial Methods in Enumerative Algebra program that delves into reflection factorizations of Singer cycles in linear and unitary groups. Learn from Joel Brewster Lewis as part of an international program organized by experts from the University of Galway, Australian National University, IMSc Chennai, IIT Kanpur, and Bielefeld University. Gain insights into algebraic counting problems, integer sequences, and generating functions while understanding how zeta functions serve as tools in asymptotic group theory and ring theory. Discover how these mathematical concepts connect to Dirichlet's zeta function, Witten's zeta function, and Hasse-Weil zeta functions, which encode various mathematical structures from number fields to rational points of algebraic varieties. Delivered at the Ramanujan Lecture Hall at ICTS Bengaluru, this lecture is part of a broader program aimed at training young researchers in enumerative algebra and fostering connections between combinatorial areas and zeta functions of groups and rings.