摘要：In probability theory, universality is the phenomenon where random processes converge to a common limit despite microscopic differences. For instance, the random walk, under mild conditions, converges to the same Brownian motion seen from afar, no matter the law of each independent step. This phenomenon underlies the appearance of the random simple curve, called SLE, as the universal scaling limit of interfaces in conformally invariant 2D systems. On the other hand, the family of simple curves has a Kähler structure, where we can study the geometric relations between curves. We will explain how these two worlds are tied together and show some applications of this link. 

嘉宾简介：Yilin Wang is working on topics at the interface of Complex analysis and Probability theory. Her current research focuses on themes that aim at enlightening the connections among Random conformal geometry, Geometric function theory, and Teichmüller theory.

After graduating in 2019 with a Ph.D. from Eidgenössische Technische Hochschule (ETH) of Zurich, under the supervision of Wendelin Werner (Fields Medal 2006), Yilin Wang worked at Massachusetts Institute of Technology (MIT) as C.L.E. Moore Instructor. In 2022, she joined IHES as the first junior professor.

She was awared Maryam Mirzakhani New Frontiers Prize at 2022.