Random Conformal Geometry of Coulomb Gas Formalism
|분야||2017 Math Colloquium|
|날짜||2017-03-24||시간||15:50 ~ 18:00|
|장소||Math Sci Bldg 404||초청자||Kunwoo Kim|
|TOPIC||Random Conformal Geometry of Coulomb Gas Formalism|
|소개 및 안내사항||Title: Random Conformal Geometry of Coulomb Gas Formalism
Abstract: Several cluster interfaces in 2D critical lattice models have been proven to have conformally invariant scaling limits, which are described by SLE(Schramm-Loewner evolution) process, a family of random fractal curves. As the remarkable achievements of complex analytic/probabilistic methods, Lawler-Schramm-Werner's work and Smirnov's work will be discussed. The main ingredient of these methods is to find SLE martingale-observables. After presenting the precise relation between SLE and conformal field theory, I will describe some SLE martingale-observables in terms of correlation functions in a family of statistical fields generated by background charge modification of the Gaussian free field. This talk is based on joint work with N. Makarov.