Prof. Sir John Ball (University of Oxford) Some Recent Mathematical Developments in Liquid Crystals
The understanding of liquid crystal behaviour has traditionally been an area with a fertile interaction between science and mathematics. The lecture will describe different theories of liquid crystals and some recent results concerning their predictions and the connection between them.
Dr. Melina Freitag (University of Bath) Balanced Truncation Model Order Reduction for Stochastically Controlled Linear Systems
When solving linear stochastic differential equations numerically, usually a high order spatial discretisation is used.
Balanced truncation (BT) is a well-known projection technique in the deterministic framework which reduces the order of a control system and hence reduces computational complexity. In this talk we give an introduction to model order reduction by balanced truncation and then consider a differential equation where the control is replaced by a noise term. We provide theoretical tools such as stochastic concepts for reachability and observability, which are necessary for balancing related model order reduction of linear stochastic differential equations with additive L’evy noise. Moreover, we derive error bounds for BT and provide numerical results for a specific example which support the theory. This is joined work with Martin Redmann (WIAS Berlin).
Prof. Zoubin Ghahramani (University of Cambridge) Probabilistic machine learning: foundations and frontiers
Probabilistic modelling provides a mathematical framework for understanding what learning is, and has therefore emerged as one of the principal approaches for designing computer algorithms that learn from data acquired through experience. I will review the foundations of this field, from basics to Bayesian nonparametric models and scalable inference. I will then highlight some current areas of research at the frontiers of machine learning, leading up to topics such as probabilistic programming, Bayesian optimisation, the rational allocation of computational resources, and the Automatic Statistician.
Prof. Beatrice Pelloni (Heriot-Watt University) Beyond integrability: the far-reaching consequences of thinking about boundary conditions
In this talk, I will outline results obtained in the last fifteen years, motivated by the original aim to include boundary conditions into the celebrated Inverse Scattering Transform, which is in essence a nonlinear Fourier transform. The talk will revisit the Fourier transform on R, embedding it in a general way of thinking about integral transform that relies on a formulation in the complex domain (called a Riemann-Hilbert formulation) and start from this idea to describe a generalised approach, now known as the unified transform, or Fokas transform. This circle of ideas has produced unexpected and very general results for the rigorous inversion of integral transform, for the solution of linear boundary value problems, for the study of nonselfadjoint differential operators, as well as for the original nonlinear problems. I will describe the key ideas and some of the most unexpected results.
10:40 Plenary talk 1 Prof. Zoubin Ghahramani (University of Cambridge) (MR2)
11:25 Plenary talk 2 Prof. Sir John Ball (University of Oxford) (MR2)
12:20 Plenary talk 3 Prof. Beatrice Pelloni (Heriot-Watt University) (MR2)
14:15 Plenary talk 4 Dr. Melina Freitag (University of Bath) (MR4)
15:00-15:15 Etienne Fodor (University of Cambridge) (MR4)
15:15-15:30 Francois-Xavier Briol (University of Warwick) (MR4)
15:30-15:45 Panayiota Katsamba (University of Cambridge) (MR4)
15:45-16:10 Tea Break
16:10-16:25 Cristiana De Filippis (University of Oxford) (MR4)
16:25-16:40 Oliver Crook (University of Cambridge) (MR4)
16:40-16:55 Thomas Crawford (Naked Scientists) (MR4)
16:55-17:10 Matt Colbrook (University of Cambridge) (MR4)
17:10-17:25 Alastair Gregory (Imperial College London) (MR4)
17:25-17:40 Imanol Pérez (University of Oxford) (MR4)