题目：Connecting Schramm-Loewner evolution to Teichmuller theory  

报告人：王艺霖，法国高等科学研究所（Institut des Hautes Études Scientifiques, IHES）

时间：2023年5月4日（周四）15:00-16:00

地点：东区第五教学楼5406教室

https://us06web.zoom.us/j/8784574760

Password：111111

摘要：In this introductory lecture, I will show how ideas in probabilistic theory gives rise to a natural quantity, and show it to be linked to objects in Teichmuller theory. More specifically, we study the Loewner energy for Jordan curves which is first introduced as the action functional of Schramm-Loewner evolution (SLE), a family of random fractal curves modeling interfaces in 2D statistical mechanics. On the other hand, we show that the Loewner energy coincides with the universal Liouville action introduced by Takhtajan and Teo, which is a Kahler potential for the Weil-Petersson metric on Universal Teichmueller space. This unexpected link suggests that more geometric structures are hidden underneath the probabilistic theory of SLE. I will give an overview of the link between SLE and Kahler geometry of Universal Teichmuller space and a first glimpse into the territory the link has opened up to.