Monday, February 7, 2022 - 4:00pm
Wen-Ching Winnie Li
Penn State University
Prime numbers are a central topic in number theory. They have inspired the study of many subjects in mathematics. For a finite graph or simplicial complex, closed geodesics play the role of primes. In this survey talk we shall explore the distribution of these primes through the associated zeta functions. The results are products of rich interplay between number theory and combinatorics. When the associated zeta function satisfies the Riemann Hypothesis, the underlying combinatorial object has nice properties. As such, it has interesting applications, which will also be discussed.