School of Mathematics

Hurwitz moduli spaces of covers of curves of degree d are classical and well studied objects if one assumes that d! is invertible and hence no wild ramification phenomena occur. There were very few attempts to study the wild case. In the most...

A convex toric domain  is a 4-dimensional subset of , defined as the preimage of a bounded convex region  in the positive quadrant of  under the moment map. We consider how geometric features of  such as the curviness of its boundary and its affine...

In this talk, I will focus on simultaneous non-vanishing results for Dirichlet L-functions at the central point 1/2. Specifically, I will describe non-vanishing results (conditional on GRH) for two L-functions associated to Dirichlet characters in...

Many geometric spaces carry natural collections of special submanifolds that encode their internal symmetries. Examples include abelian varieties and their sub-abelian varieties, locally symmetric spaces with their totally geodesic subspaces, period...

The geodesic flow (for the hyperbolic metric) of an infinite Riemann surface is ergodic if and only if Brownian motion is recurrent, which is also equivalent to the divergence of the Poincaré series. Surfaces with ergodic geodesic flows are most...

Ricci solitons are the self-similar solutions to the Ricci flow, which is the heat equation for Riemannian metrics, and they model singularity formation. We survey various estimates for Ricci solitons in dimension 4. This is mainly the work of...

A classical construction of Mitsumatsu, later generalized by Hozoori, associates to any (oriented) Anosov flow on a closed 3-manifold M a Liouville structure on the thickening [−1,1]×M. This construction also extends to suitable taut foliations.

From...

The study of Turán numbers of graphs and hypergraphs is a rich problem in extremal combinatorics. The Turán problem asks, given a fixed forbidden (hyper)graph F, what is the maximum number of edges in an F-free (hyper)graph in terms of the number of...

We describe the obstruction to lift Frobenius on certain Shimura varieties and apply this to the theory of companion forms for classical modular forms (Gross, Coleman-Voloch, Faltings-Jordan) and also in higher dimension.

Since Hironaka's famous resolution of singularities in characteristics zero in 1964, it took about 40 years of intensive work of many mathematicians to simplify the method, describe it using conceptual tools and establish its functoriality. However...