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...
Ethiopia is unique in the world for the incomparable prominence
of the cross in the life of its Orthodox Christian population.
Crosses of unparalleled intricacy and sophistication are
extensively used in religious and magic rituals, as well as
in...
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...
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...
I will talk about recent work towards a conjecture of Gonek
regarding negative shifted moments of the Riemann zeta function. I
will explain how to obtain asymptotic formulas when the shift in
the Riemann zeta function is big enough, and how we can...
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...
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...
