regular seminar Rene Schilling (TU Dresden)
at: 15:00 - 16:00 KCL, Strand room: S4.29 abstract: | We discuss necessary and sufficient criteria for certain Fourier multiplication operators to satisfy the Liouville property (bounded harmonic functions are a.s. constant) and the local continuation property (bounded functions, that are harmonic and identically zero on a domain, are a.s. zero on the whole space). Since the operators generate stochastic processes, there is also a probabilistic interpretation of these findings. Keywords: |
colloquium Dan Crisan (Imperial College)
at: 14:30 - 15:30 KCL, Strand room: BH(SE) 2.09. abstract: | Onwards from the mid-twentieth century, the stochastic filtering problem has caught the attention of thousands of mathematicians, engineers, statisticians, and computer scientists. Its applications span the whole spectrum of human endeavour, including satellite tracking, credit risk estimation, human genome analysis, and speech recognition. Stochastic filtering has engendered a surprising number of mathematical techniques for its treatment and has played an important role in the development of new research areas, including stochastic partial differential equations, stochastic geometry, rough paths theory, and Malliavin calculus. It also spearheaded research in areas of classical mathematics, such as Lie algebras, control theory, and information theory. The aim of this paper is to give a brief historical account of the subject followed by a recent filtering application to data assimilation for geophysical fluid dynamics models. Keywords: Mathematical analysis, stochastic analysis |
regular seminar Michael Wemyss (Glasgow)
at: 15:00 - 16:00 KCL, Strand room: S4.29 abstract: | Motivated by various contraction conjectures, categorical statements, and classification theorems, and also by the seemingly insatiable urge to rewrite all of mathematics using only the letter C, I will describe the full A_infty structure associated to a general (-3,1)-curve inside a smooth CY 3-fold. This sounds complicated, but it turns out to be combinatorial and easy. Of course, most of the talk will be about background, and the motivation for considering these questions, including the analytic classification of 3-fold flops using noncommutative data. This is all joint work with Gavin Brown. Keywords: |
regular seminar Alex Watson (University College London)
at: 15:00 - 16:00 KCL, Strand room: S4.29 abstract: | The Wiener-Hopf factorisation of a Lévy process has two forms. The first describes how the process makes new maxima and minima, by decomposing it into two so-called 'ladder processes'. The second expresses its characteristic exponent as the product of two functions related to the ladder processes. Since the latter is analytic in nature, the question naturally arises: is such a decomposition unique? The answer has been known for killed Lévy processes since at least Rogozin's work in 1966, but appears to have remained open in general. We show that, indeed, uniqueness holds in all cases. This gives a solid foundation to the 'theory of friendship', which allows one to construct a Lévy process with known Wiener-Hopf factorisation. The results also hold for random walks. Joint work with Leif Döring (Mannheim), Mladen Savov (Sofia) and Lukas Trottner (Aarhus). Keywords: Lévy processes, Wiener-Hopf Factorisation |