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Valentin Blomer: Eigenvalue statistics of tori

Time: Wed 2019-04-03 11.00

Lecturer: Valentin Blomer (Universität Göttingen)

Location: SU, 306

We study the fine scale statistics of eigenvalues of
two-dimensional flat tori, in particular large gaps, small gaps and
correlations, and compare it to the Poisson model. From a number
theoretic point of view, this concerns the value distribution of
binary quadratic forms, and the proofs use various tools from
diophantine analysis and analytic number theory, including zero-free
regions of the Riemann zeta function, bounds for Kloosterman sums, and
properties of Fibonacci numbers. This is joint work with Radziwill and
also with Bourgain and Rudnick.

Belongs to: Department of Mathematics
Last changed: Mar 31, 2019