The next APDE seminar will take place Wednesday, Nov 28, in 740 Evans from 3-4pm.

Title: Illusions: curves of zeros of Selberg zeta functions

Abstract: It is well known (since 1956) that the Selberg Zeta function

for compact surfaces satisfies the “Riemann Hypothesis”: any zero in the

critical strip 0<R(s)<1 is either real or Im(s)=1/2. The question of

location and distribution of the zeros of the Selberg Zeta function

associated to a noncompact hyperbolic surface attracted attention of the

mathematical community in 2014 when numerical experiments by

D. Borthwick showed that for certain surfaces zeros seem to lie on

smooth curves. Moreover, the individual zeros are so close to each other

that they give a visual impression that the entire curve is a zero set.

We will give an overview of the computational methods used, present

recent results, justifying these observations as well as state open

conjectures.