Professor Terry Lyons FLSW FRSE FRS, Wallis Professor of Mathematics, Mathematical Institute, University of Oxford
Abstract: It often happens that measurements have redundant information over and above the invariants of interest; we might measure a rigid object in cartesian co-ordinates although we are only interested in the shape. Representing in an invariant way that does not carry redundant information about its embedding can significantly enhance many processes. If there is a representation where the invariance are highly nonlinear this cleaning can be challenging and the ever changing clutter adds noise and degrades learning processes. One critical and ignored symmetry occurs when we sample a stream of data, often we care little about how the path was sampled or parametrised, and we just care about the trajectory (in space time). This is an infinite dimensional set of symmetries, and if the sampling changes with each observation, or the data comprises rare tranisents, or has missing data. The induced noise can be very considerable. Recent mathematics introduces a transform the signature that describes streamed data faithfully without introducing a parametrisation. It has considerable benefits in terms of dimension reduction etc.
Bio: Professor Terry Lyons is the Wallis Professor of Mathematics at the University of Oxford; he was a founding member (2007) of, and then Director (2011-2015) of, the Oxford Man Institute of Quantitative Finance; he was the Director of the Wales Institute of Mathematical and Computational Sciences (WIMCS; 2008-2011). He came to Oxford in 2000 having previously been Professor of Mathematics at Imperial College London (1993-2000), and before that he held the Colin Maclaurin Chair at Edinburgh (1985-93). Prof Lyons’ long-term research interests are all focused on Rough Paths, Stochastic Analysis, and applications – particularly to Finance and more generally to the summarising of large complex data. More specifically, his interests are in developing mathematical tools that can be used to effectively model and describe high dimensional systems that exhibit randomness. Prof Lyons is involved in a wide range of problems from pure mathematical ones to questions of efficient numerical calculation.