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...
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...
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...
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 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...
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...
