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
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...
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
Stochastic Gradient Descent (SGD) is the de facto optimization
algorithm for training neural networks in modern machine learning,
thanks to its unique scalability to problem sizes where the data
points, the number of data points, and the number of...