Seminar| Institute of Mathematical Sciences
Time: January 6th, 7th and 9th, 2025,15:00-17:00
Location: IMS, RS408
Speaker:Xi Geng, Melbourne University
Abstract:The signature transform is a fundamental transformation which maps a multidimensional rough path into a sequence of global quantities defined in terms of iterated path integrals. In recent years, the signature transform has been broadly used as a basic tool in data science applications. In this mini-course, we will study the basic mathematical theory of the signature transform. After discussing some of its basic mathematical properties such as Chen's identity and the shuffle product formula, we will prove the fundamental signature uniqueness theorem, which asserts that every rough path is uniquely determined by its signature up to treelike equivalence. We will also discuss the powerful technique of path developments and its applications to some important open problems in rough path theory.
Short Bio of the speaker:
耿曦，2011年本科毕业于中山大学数学系，随后赴牛津大学师从钱忠民教授，于2016年获得博士学位。期间2014-2016年在Terry Lyons教授的指导下从事博士后研究，毕业后2016-2019年在卡耐基梅隆大学继续从事博士后研究。从2019年2月至今，于墨尔本大学数学与统计学院任教。主要的研究领域是粗糙路径分析和随机分析。
Xi Geng got his Bachelor degree in Mathematics at Sun Yat-sen University in 2011 and Ph.D. degree from University of Oxford in 2016 under the supervision of Prof. Zhongmin Qian and Prof. Terry Lyons. From 2016 to 2019 he was a postdoc at CMU.
He is currently a senior lecturer at the School of Mathematics and Statistics, Melbourne University. His main research areas include rough path analysis and stochastic analysis.