Deep Gaussian processes have proved remarkably successful as a tool for various statistical inference tasks. This success relates in part to the flexibility of these processes and their ability to capture complex, non-stationary behaviours. 

In this talk, we will introduce the general framework of deep Gaussian processes, in which many examples can be constructed, and demonstrate their superiority in inverse problems including computational imaging and regression.

 We will discuss recent algorithmic developments for efficient sampling, as well as recent theoretical results which give crucial insight into the behaviour of the methodology.

 

We discuss timelike surfaces of finite size in general relativity and the initial boundary value problem. We consider obstructions with the standard Dirichlet problem, and conformal version with improved properties. The ensuing dynamical features are discussed with general cosmological constant.

In this talk I will discuss the representation theory of truncated current Lie algebras in prime characteristic. I will first give an introduction to modular representation theory for general restricted Lie algebras and introduce the Kac-Weisfeiler conjectures. Then I will introduce a family of Lie algebras known as truncated current Lie algebras, and discuss their representation theory and its relationship with the representation theory of reductive Lie algebras in positive characteristic.

We will give a relaxed introduction to some of the most classical dynamical systems - Anosov flows. These flows were highly influential in the development of ideas which the audience might be more familiar with. For example, Anosov flows give rise to exponential group growth and taut foliations, both of which we will discuss. Finally, we will talk about some recent work obstructing Anosov flows and their combinatorial analogs - veering triangulations

Property (T) was introduced by Kazhdan in the sixties to show that lattices in higher rank semisimple Lie groups are finitely generated. We will discuss some classical examples of groups that satisfy this property, with a particular focus on SL(3, R).

Graph braid groups are similar to braid groups, except that they are defined as ‘braids’ on a graph, rather than the real plane. We can think of graph braid groups in terms of the discrete configuration space of a graph, which is a CW-complex. One can compute a presentation of a graph braid group using Morse theory. In this talk I will give a few examples on how to compute these presentations in terms of generating circuits of the graph. I will then go through a detailed example of a graph that gives a one-ended braid group.

For a hyperbolic knot there are two types of invariants, the hyperbolic invariants coming from the geometric structure and the classical invariants coming from the topology or combinatorics. It has been observed in many different cases that these seemingly different types of invariants are in fact related. I will give examples of these relationships and discuss in particular a link by Stoimenow between the determinant and volume.  

The Ivanov conjecture is equivalent to the statement that every covering map of surfaces has the so-called Putman-Wieland property. I will discuss my recent work with Vlad Marković, where we prove it for asymptotically all coverings as the degree grows. I will give some overview of our main tool: spectral geometry, which is related to objects like the heat kernel of a hyperbolic surface, or Cheeger connectivity constant.