****** This mini-course is part of the THU-PKU-BNU Probability Webinar series. ******

*** For more up-to-date information, please visit http://math0.bnu.edu.cn/~hehui/webinar.htm***

ABSTRACT

The theory of large deviations concerns the asymptotic behaviour of the probability of rare events under a sequence of probability measures. Schramm-Loewner evolution is a one-parameter family of random fractal non-selfcrossing curves that arise naturally as interfaces in two-dimentional conformally invariant systems. After explaining the basic ideas and results on LDP and SLE, we describe the large deviations of SLE in two regimes: when the parameter goes to 0 and to infinity. The rate functions of these LDPs are interesting in their own, especially from the point of view of geometric function theory. The LDPs of SLEs then allow us to derive several new results in geometric function theory, by giving probabilistic interpretation to deterministic objects.

SCHEDULE

9:00 - 10:30 am Beijing time, August 3, 5, 10, 12 (Mon Wed Mon Wed)

Aug 3

Tencent: 382 712 091

Zoom: 683 926 47011 (PIN: 583699)

Aug 5

Tencent: 140 192 150

Zoom: 694 678 95296 (PIN: 758495)

Aug 10

Tencent: 175 211 271

Zoom: 613 257 16599 (PIN: 352330)

Aug 12

Tencent: 196 507 842

Zoom: 648 833 71630 (PIN: 149231)

BRIEF BIO

Dr. Yilin Wang is currently a C.L.E. Moore Instructor at MIT. She obtained her Ph.D from ETH Zurich under Wendelin Werner in May 2019. From 2011 to 2015, she studied at École Normale Supérieure de Paris. Her research interests lie in the interface of complex analysis and probability theory. In particular. her current research aims to investigate the connections among random conformal geometry, geometric function theory, and Teichmueller theory. Her work has appeared in Inventiones mathematicae, International Mathematics Research Notices, and Annales Academiæ Scientiarum Fennicæ, etc. Wang was awarded NCCR SwissMAP Innovator Prize in 2018 and ETH Medal for her outstanding PhD thesis in 2020.