Previous Conferences & Workshops

This is joint work with Michael Magee. We combine concepts from random matrix theory and free probability together with ideas from the theory of commutator length in groups and maps from surfaces, and establish new connections between the two. More...

The algorithm indicated in the title builds on Luks's classical framework and introduces new group theoretic and combinatorial tools. In the first talk we outline the algorithm and state the core group theoretic and algorithmic ingredients. Some of...

I will give an overview of my work with Antonio Lei, David Loeffler and Guido Kings about the construction of an Euler system for Rankin-Selberg convolutions of modular forms and its arithmetic applications. I will then discuss generalisations of...

In 2000 Eliashberg-Polterovich introduced the concept of positivity in contact geometry. The notion of a positive loop of contactomorphisms is central. A question of Eliashberg-Polterovich is whether $C^0$-small positive loops exist. We give a...

We discuss our results on global existence and convergence of solutions to the gradient flow equation for the Yang-Mills energy functional over a closed, four-dimensional, Riemannian manifolds: If the initial connection is close enough to a minimum...

Stochastic quantization equations are evolutionary PDEs driven by space-time white noises. They are proposed by physicists in the 80s as the natural dynamics associated to the (Euclidean) quantum field theories. We will discuss the recent progress...

I will talk about convex-cocompact representations of finitely generated free group $F_g$ into $\mathrm{PSL}(2,\mathbb C)$. First I will talk about Schottky criterion. There are many ways of characterizes Schottky group. In particular, convex hull...

I want to sketch some algebraic and geometric tools to solve a variety of extremal problems surrounding Minkowski sums of polytopes and colorful simplicial depth.

Mock modular forms were first formally defined in the literature by Zagier in 2007, though their roots trace back to the mock theta functions, curious power series described by Ramanujan in his last letter to Hardy in 1920. As the overarching theory...