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...
An inertial manifold is a positively invariant smooth
finite-dimensional manifold which contains the global attractor and
which attracts the trajectories at a uniform exponential rate. It
follows that the infinite-dimensional dynamical system is...
It is conjectured that every Reeb flow on a closed
three-manifold has either two, or infinitely many, simple periodic
orbits. I will survey what is currently known about this
conjecture. Then, I will try to explain some of the key ideas
behind...
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...
We'll discuss problems where bounds for L-functions have arisen
as inputs and where techniques for estimating them through their
integral representations have been useful (all of which have been
shaped and influenced by Peter Sarnak’s work).
