School of Mathematics

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).

Since work of Montgomery and Katz-Sarnak, the eigenvalues of random matrices have been used to model the zeroes of the Riemann zeta function and other L-functions. Keating and Snaith extended this to also model the distribution of values of the L...

I’ll speak about new joint work with Rachel Greenfeld and Marina Iliopoulou in which we address some classical questions concerning the size and structure of integer distance sets. A subset of the Euclidean plane is said to be an integer distance...

I'll discuss spectral gaps in the following contexts:
- d-regular graphs
- locally symmetric spaces e.g. hyperbolic manifolds
- finite dimensional unitary representations of discrete groups e.g. free groups, surface groups
 

Of particular interest are...