中科院数学与系统科学研究院

数学研究所

中科院华罗庚数学重点实验室

华罗庚青年数学论坛

学术报告

报告人：王艺霖 博士（Massachusetts Institute of Technology）

题  目：From Schramm-Loewner evolutions to Weil-Petersson quasicircles

时  间：2021.09.14（星期二），09:00-11:00

地  点：腾讯会议：572 683 516

摘  要：From the overview lecture, we saw that the Loewner energy for Jordan curves connects Schramm-Loewner svolutions to Weil-Petersson Teichmueller space through the large deviations principle as the SLE parameter goes to 0. In these two hours, I will introduce in more detail the class of Weil-Petersson quasicircles and the associated Weil-Petersson Teichmueller space.
---------------------------------------------------------------------
  报告人：王艺霖 博士（Massachusetts Institute of Technology）

题  目：From Schramm-Loewner evolutions to Weil-Petersson quasicircles（II）

时  间：2021.09.16（星期四），09:00-11:00

地  点：腾讯会议：161 199 555

摘  要：In this lecture, I will show how ideas from random conformal geometry inspire many new results for Weil-Petersson quasicircles. As a notable example, we introduce another Loewner-Kufarev energy, a quantity defined for measures on the cylinder $S^1 \times \mathbb R$ which arises in the context of large deviations of SLEs when the parameter goes to infinity. Through the SLE duality we speculate a duality between Loewner and Loewner-Kufarev energies. We prove this duality using only deterministic analytic tools and show that the Loewner-Kufarev chain driven by a finite LK-energy measure generates a foliation whose leaves are all Weil-Petersson quasicircles. This is a joint work with Fredrik Viklund (KTH).