Stochastic Komatu-Loewner Evolutions

2019/03/25 Mon 13:00 - 15:00
2019/03/29 Fri 13:00 - 15:00
2019/04/05 Fri 10:00 - 12:00
2019/04/12 Fri 13:00 - 15:00
2019/04/17 Wed 13:00 - 15:00
127 Conference Room, Building No.3
Room 110, Building No.3
Zhenqing Chen
University of Washington

Loewner equation is a differential equation for conformal mappings that can be used to describe evolution of a family of simply connected planar domains. It was introduced by C. Loewner in 1923 in his work on the Bieberbach conjecture. Oded Schramm observed and conjectured in 2000 that scaling limit of many two-dimensional lattice models in statistical physics can be described by Loewner evolutions with Brownian motions as the driving function. Many of these conjectures are latter confirmed in a series of joint work by G. Lawler, O. Schramm and W. Werner and by S. Smirnov.

On the other hand, Y. Komatu extended Loewner equation to circularly slit annuli in 1950 but in the left derivative sense. The aim of this series of lectures is to survey some recent progress in the study of Komatu-Loewner evolutions and its stochastic counterpart in the canonical slit domains, with emphasis on probabilistic methods.

  • Lecture 1: Conformal mapping and Brownian motion with darning
  • Lecture 2: Komatu-Loewner differential equations for multiply connected domains
  • Lecture 3: Induced slit motions and Komatu-Loewner evolution
  • Lecture 4: Stochastic Komatu-Loewner differential equation
  • Lecture 5: SKLE and SLE

Poster (PDF)

*Lectures will take place at Room 110 in March and at 127 Conference Room in April.

[NOTE] This series of lectures will be video-recorded and made available online.
Please note that anyone in the front rows of the room can be captured by a video camera.