# Coincidences between homological densities, predicted by arithmetic - 2 of 2

Speaker: Benson Farb

Date: Thu, Jun 13, 2019

Location: PIMS, University of British Columbia

Conference: Workshop on Arithmetic Topology

Subject:

Class: Scientific

### Abstract:

In this talk I'll describe some remarkable coincidences in topology that were found only by applying Weil's (number field)/(f unction field) analogy to some classical density theorems in analytic number theory, and then computing directly. Unlike the finite field case, here we have only analogy; the mechanism behind the coincidences remains a mystery. As a teaser: it seems that under this analogy the (inverse of the) Riemann zeta function at $(n+1)$ corresponds to the 2-fold loop space of $P^n$. This is joint work with Jesse Wolfson and Melanie Wood.

This is the second lecture in a two part series: part 1