Causal optimal transport and the related adapted Wasserstein distance have recently been popularized as a more appropriate alternative to the classical Wasserstein distance in the context of stochastic analysis and mathematical finance. In this talk, we establish some interesting consequences of causality for transports on the space of continuous functions between the laws of stochastic differential equations.
 

We first characterize bicausal transport plans and maps between the laws of stochastic differential equations. As an application, we are able to provide necessary and sufficient conditions for bicausal transport plans to be induced by bi-causal maps. Analogous to the classical case, we show that bicausal Monge transports are dense in the set of bicausal couplings between laws of SDEs with unique strong solutions and regular coefficients.

 This is a joint work with Rama Cont.

Kaufman constructed a family of Fourier-decaying measures on the set of badly approximable numbers. Pollington and Velani used these to show that Littlewood’s conjecture holds for a full-dimensional set of pairs of badly approximable numbers. We construct analogous measures that have implications for inhomogeneous diophantine approximation. In joint work with Agamemnon Zafeiropoulos and Evgeniy Zorin, our idea is to shift the continued fraction and Ostrowski expansions simultaneously.

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.

TBD

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