学术报告 报告题目：From Hopf Algebras to Machine learning via Rough Paths
报 告 人：Terry Lyons 教授（英国牛津大学）
报告时间：2016年12月01日（星期四）上午10:00-11:30
报告地点：4号楼4131室
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数学学院
2016年11月24日
报告摘要：
Rough path theory aims to build an effective calculus that can model the interactions between complex oscillatory (rough) evolving systems. At its mathematical foundations, it is a combination of analysis blended with algebra
that goes back to LC Young, and to KT Chen. Key to the theory is the essential need to incorporate additional non-commutative structure into areas of mathematics we thought were stable. At its high points, there are the regularity structures of Martin Hairer that allow robust meaning to be given to numerous core nonlinear stochastic pdes
describing evolving interfaces in physics.
Classic results, by Clark, Cameron and Dickinson, demonstrate that a nonlinear approach to the data is essential.Rough path theory lives up to this challenge and can be viewed as providing fundamentally more efficient ways of approximately describing complex data; approaches that, after penetrating the basic ideas, are computationally tractable and lead to new scalable ways to regress, classify, and learn functional relationships from data. One non-mathematical application that is already striking is the use of signatures on a daily basis in the online recognition of
Chinese Handwriting on mobile phones.
报告人简介：
Terry Lyons is the Wallis Professor of Mathematics of Oxford university，a Fellow of the Royal Society,
President-Designate of the London Mathematical Society, and one of the UK’s leading mathematicians, having
made a number of contributions to stochastic analysis. He has been named Schramm Lecturer for 2014 by the
Institute of Mathematical Statistics. 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). Lyons 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). His research interests are focused on Rough Paths, Stochastic Analysis, and
Applications. He is also interested in developing mathematical tools that can be used to effectively model and
describe high dimensional systems that exhibit randomness. He was President of the UK Learned Society for
Mathematics, the London Mathematical Society.