Seminars Sorted by Series

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...

Abstract: 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...

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.

Rank-one non-Hermitian deformations of  tridiagonal beta-Hermite Ensembles have been introduced by R. Kozhan several years ago. For a fixed N and beta>0 the joint probability density of N complex eigenvalues  was shown to have a form of a...

In 2012, Fyodorov, Hiary & Keating and Fyodorov & Keating proposed a series of conjectures describing the statistics of large values of zeta in short intervals of the critical line. In particular, they relate these statistics to the ones of log...

Selberg’s celebrated central limit theorem shows that the logarithm of the zeta function at a typical point on the critical line behaves like a complex, centered Gaussian random variable with variance $\log\log T$. This talk will present recent...

Montgomery's pair correlation conjecture ushered a new paradigm into the theory of the Riemann zeta function, that of the occurrence of Random Matrix Theory statistics, as developed in part by Dyson, into the theory. A parallel development was the...

We introduce a new zero-detecting method which is sensitive to the vertical distribution of zeros of the zeta function. This allows us to show that there are few ‘half-isolated’ zeros. If we assume that the zeros of the zeta function are restricted...

In 2005, Conrey, Farmer, Keating, Rubinstein, and Snaith formulated a 'recipe' that leads to precise conjectures for the asymptotic behavior of integral moments of various families of $L$-functions. They also proved exact formulas for moments of...

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...

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...