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Staff Introduction
Many "critical phenomena", important in statistical physics and probability theory, are conjectured or already known to be conformally invariant. In two dimension, this invariance can be regarded as the invariance under conformal mappings in complex analysis. "SchrammLoewner evolution" (SLE) was introduced as a stochastic process which has such a conformal invariance. SLE is the random timeevolution of a family of conformal mappings; in view of complex analysis, it is described by the Loewner differential equation. This equation was originally employed to prove the Bieberbach conjecture, but there are many other possible applications in physics and mathematics, including SLE, integrable systems, HeleShaw flow, and noncommutative probability. Under these backgrounds, I'm studying SLE and the Loewner equation from both probabilistic and complexanalytic points of view.
Keywords  stochastic analysis, geometric function theory, SchrammLoewner evolution 

Faculty , Department  Faculty of Mathematics , Department of Mathematical Sciences 