Polina Vytnova (Warwick)

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