# Video Lectures

### Gaussian multiplicative chaos: applications and recent developments

Nina Holden

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.

### Number theoretic aspects of multiplicative chaos

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 deviation estimates for Selberg’s central limit theorem, applications, and numerics

Emma Bailey

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...

### The Fyodorov-Hiary-Keating Conjecture

Louis-Pierre Arguin

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...

### A few results and conjectures on some product-ratio correlation functions of characteristic polynomials of beta-Hermite ensembles

Yan Fyodorov

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...

### Large sieve inequalities for families of L-functions

Matt Young

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...

### The distribution of values of zeta and L-functions

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...

### Opening Remarks and History of the math talks

Peter Sarnak, Jon Keating and Hugh Montgomery

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...

### Opening Remarks and History of the math talks

Peter Sarnak, Jon Keating and Hugh Montgomery

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...