[線上同步] SLE and Conformal Restriction Property
卓冠宇先生國立中央大學數學系 11:00 – 11:50 鴻經館 M107
開放線上聽演講：
(1) https://meet.google.com/afn-gzmo-btm
(2) 開啟google meet並輸入下列代碼：afn-gzmo-btm
Abstract：
Schramm-Loewner Evolution (SLEκ) was introduced by Oded Schramm in 2000 to study the asymptotic behavior (scaling limit) of loop-erased random walks for κ=2 and uniform spanning trees for κ=8. A well-known application of SLE is that the Hausdorff dimension of the outer boundary of a planar Brownian motion is almost surely 4/3, which was conjectured by Benoit Mandelbrot and proved by Gregory F. Lawler, Oded Schramm, and Wendelin Werner by showing that the outer boundary of a planar Brownian motion has the same law as an SLE6. In this talk, I will introduce the development of SLE, and a series of measures defined on the space of curves in the complex plane, including Brownian excursion measures, Boundary bubble measures, and Loop measures. We obtain an expression for the Radon-Nikodym derivative of dipolar SLEκ in a domain with respect to dipolar SLEκ in a subdomain for 0<κ≤8/3.