Takuya MURAYAMA

Takuya MURAYAMA

Department of Mathematics,
Graduate School of Science, Kobe University
Division : Applied Mathematics
Lecturer		 Building B, Room 425

Personal Website
Research Field : probability theory, complex analysis, Schramm-Loewner evolution
Research Summary : I am interested mainly in the theory of Schramm-Loewner evolution (SLE), which has a close relation to two-dimensional spin systems and quantum gravity and has been studied intensively since 2000. To analyze it successfully, one needs to integrate both the classical theory of conformal mappings including the Loewner differential equation and the stochastic methods based on Brownian motion. From such a background, now my interest has been growing to many different topics concerning connections between probability theory and complex analysis.
Primary Publications :
  1. T. Murayama, Chordal Komatu-Loewner equation for a family of continuously growing hulls, Stochastic Process. Appl. 129 (2019), 2968-2990.
  2. T. Murayama, On the slit motion obeying chordal Komatu-Loewner equation with finite explosion time, J. Evol. Equ. 20 (2020), 233-255.
  3. T. Amaba, R. Friedrich and T. Murayama, Univalence and holomorphic extension of the solution to ω-controlled Loewner-Kufarev equations, J. Differential Equations 269 (2020), 2697-2704.
  4. T. Murayama, On the continuity of half-plane capacity with respect to Caratheodory convergence, in: Dirichlet Forms and Related Topics, pp.379-399, Springer Proceedings in Mathematics & Statistics 394, Springer Nature Singapore Pte Ltd., Singapore, 2022.
  5. T. Murayama, Loewner chains and evolution families on parallel slit half-planes, J. Math. Anal. Appl. 526 (2023), Paper No. 127180, 51 pp.