Millimeter-wave surveys of the sky have the potential for
yielding a wealth of information about our universe from the first
instants of its existence to our own solar system. I will describe
how modern measurements of the cosmic microwave...
It may seem quite obvious that graphs carry a lot of geometric
structure. Don't we learn in algorithm classes how to solve
all-pairs-shortest-paths, minimum spanning trees etc.?
However, in this talk, I will try to impress on you the idea
that...
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...
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...
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...
