Sixth and higher moments of L-functions are important and
challenging problems in analytic number theory. In this talk, I
will discuss my recent joint works with Xiannan Li, Kaisa
Matom\"aki and Maksym Radziw\il\l on an asymptotic formula of
the...
In 2018 Keating, Rodgers, Roditty-Gershon and Rudnick
established relationships of the mean-square of sums of the divisor
function $d_k(f)$ over short intervals and over arithmetic
progressions for the function field $\mathbb{F}_q[T]$ to
certain...
I will explain how to construct the Ruelle invariant of a
symplectic cocycle over an arbitrary measure preserving flow. I
will provide examples and computations in the case of Hamiltonian
flows and Reeb flows (in particular, for toric domains). As...
I will give an introduction to Gaussian multiplicative chaos and
some of its applications, e.g. in Liouville theory. Connections to
random matrix theory and number theory will also be briefly
discussed.
Multiplicative chaos is the general name for a family of
probabilistic objects, which can be thought of as the random
measures obtained by taking the exponential of correlated Gaussian
random variables. Multiplicative chaos turns out to be
closely...
Large sieve inequalities are useful and flexible tools for
understanding families of L-functions. The quality of the
bound is one measure of our understanding of the corresponding
family. For instance, they may directly give rise to good
bounds...
I will survey recent progress on understanding the value
distribution of zeta and L-functions. In particular I will
discuss the problem of moments of the zeta function on the critical
line, and central values of L-functions, where the last
twenty...
On April 6, 1972 a young graduate student named Hugh Montgomery
and the world-renowned mathematical physicist Freeman Dyson had a
conversation in the tearoom at the Institute for Advanced Study
which led to a fusion of two disparate fields and an...
