Please email Katie Weeks (k.weeks@imperial.ac.uk) to be put on the waiting list for this talk. Tea and cakes will be served in the SCR from 16.45.
Stochastic analysis is the branch of mathematics that looks at understanding and modelling systems that behave randomly.
One of its most celebrated results is the Feynman-Kac representation formula, first established in the 1940s for the heat equation, and extended since to many other equations. This formula provides a link between macroscopic models and the microscopic phenomena often governed by randomness and uncertainty.
Such study of the microscopic world can enable us to gain insights into the working of the macroscopic world, with applications including tracking moving vehicles, pricing financial options under constraints and filtering the solution of the Navier-Stokes equation.
Based on current research, it would appear that a mathematical model for predicting the future behaviour of very large groups, akin to the fictional science psychohistory in Isaac Asimov’s books, may not be too far-fetched.
Biography
Dan Crisan is Professor of Mathematics at Imperial. He has always been fascinated by the rigour of Mathematical Analysis and its countless applications.
Raised in Romania, Dan moved to Edinburgh in 1991 where he studied for a PhD in Stochastic Analysis. He first came to Imperial in 1995 as a postdoctoral fellow. After a brief spell at the Statistical Laboratory in Cambridge, he returned to Imperial in 2000, where he was awarded a Governors’ Lectureship. Since then he has assiduously promoted stochastic analysis in the Department of Mathematics, across the College and beyond.
Dan’s research covers a variety of areas including stochastic filtering, particle algorithms, Monte Carlo methods, stochastic partial differential equations, forward-backward stochastic differential equations and Malliavin calculus. He is particularly interested in studying macroscopic models such as solutions of partial differential equations through their microscopic and stochastic counterparts.