# Algebra/Topology Seminar

Speaker: Ronno Das

Title: Stability of zeta statistics

Abstract: Many natural families of varieties, for example spaces arising from Bertini problems or zero cycles, demonstrate stability of both point counts over finite fields and motivic zeta functions. However, neither of these two forms of stability implies the other. We provide a generalized common framework for the two forms of stability and prove that the stronger property of Hadamard convergence'' is satisfied by many examples arising from zero cycles. We also conjecture that any natural'' sequence of zeta functions that converges to the same Hadamard function in both the point count and weight topologies satisfies Hadamard convergence. This talk is based on joint work with Margaret Bilu and Sean Howe.