Academic Report of School of Mathematical Sciences [2026] No. 092

(Series Report for High-Level University Construction No. 1351)

Title：An introduction to the path signature theory

Speaker：Assistant Professor Wang Shi (ShanghaiTech University)

Time：14:30-15:30, Sept. 21, 2026

Location：Room 1420, Huiwen Building, Yuehai Campus

Abstract: The  signature  map  sends  a  BV  curve  in  R^n  to  a formal  series  in  its  tensor  algebra,  by  using  the  iterated integral method.  I  will  first  briefly  survey  the  theory  of  signature map developed  by  K.T.  Chen,  and  then  introduce  the  general  signature inversion problem. Finally, I will discuss recent joint work with Chong Liu on how to use rational approximation to explicitly recover an axial increasing curve from its signature.

Speaker Profile：Wang Shi is an Assistant Professor, Research Fellow, and Ph.D. advisor at the Institute of Mathematical Sciences, ShanghaiTech University. His research interests include differential geometry, geometric topology, geometric group theory, and dynamical systems. He has published numerous papers in leading journals such as J. Eur. Math. Soc., Math. Ann., Geom. Topol., and Adv. Math. He has served as principal investigator on a National Natural Science Foundation of China Outstanding Young Scientist Fund Project (Overseas) and a National Key Research and Development Program project (Young Scientist).

Faculty and students are welcome to attend!

Invited by: Zhou Ze

School of Mathematical Sciences

September 15, 2026