To study the asymptotic behavior of orbits of a dynamical
system, one can look at orbit closures or invariant measures. When
the underlying system has a homogeneous structure, usually coming
from a Lie group, with appropriate assumptions a wide...
the special values of Dirichlet L-functions have long been a
source of fascination and frustration. From Euler's solution in
1734 of the Basel problem to Apery's proof in 1978 that
zeta(3...
Cohen, Lenstra, and Martinet have given highly influential
conjectures on the distribution of class groups of number fields,
the finite abelian groups that control the factorization in number
fields. Malle, using tabulation of class groups of number...
The Higher order Fourier uniformity conjecture asserts that on
most short intervals, the Mobius function is asymptotically uniform
in the sense of Gowers; in particular, its normalized Fourier
coefficients decay to zero. This conjecture is known
to...
What is the densest lattice sphere packing in the d-dimensional
Euclidean space? In this talk we will investigate this question as
dimension d goes to infinity and we will focus on the lower bounds
for the best packing density, or in other words on...
Discrete subgroups of PSL(2,C) are called Kleinian groups and
they are fundamental groups of complete oriented hyperbolic
3-manifolds/orbifolds. Except for countably many conjugacy classes,
all Kleinian groups have infinite co-volume in PSL(2, C).
The Mobius function is one of the most important arithmetic
functions. There is a vague yet well known principle regarding its
randomness properties called the “Mobius randomness law". It
basically states that the Mobius function should be...
Bounds for Dirichlet polynomials play an important role in
several questions connected to the distribution of primes. For
example, they can be used to bound the number of zeroes of the
Riemann zeta function in vertical strips, which is relevant
to...
Bounds for Dirichlet polynomials play an important role in
several questions connected to the distribution of primes. For
example, they can be used to bound the number of zeroes of the
Riemann zeta function in vertical strips, which is relevant
to...
