Geometry of random tilings via complex structures and the Beltrami equation
发布时间：2026年08月26日
浏览次数：136
发布者: Ruixin Li
主讲人： Kari Astala (University of Helsinki)
活动时间： 从 2026-09-08 16:00 到 17:00
场地： 北京国际数学研究中心，镜春园78号院（怀新园）77201室
Abstract:
Under suitable boundary restrictions, scaling limits of random planar tilings present surprising geometric features: One observes definite deterministic and disordered (or frozen and liquid) limit configurations with interesting geometric properties. In this talk we explain how the geometry of these limit configurations can be understood and described in quite detail via suitable degenerate Beltrami differential equations and the complex structures they provide.
Bio-Sketch:
Kari Astala received his mathematical education in Helsinki, Finland and obtained PhD in 1980. He was a Professor at Jyväskylä University 1995-2002, and since 2002 he has been a Professor at University of Helsinki. His research concentrates on the interaction of PDE's and complex analysis, for instance on quasiconformal structures at various instances. He has (co)-authored more than 80 research publications, including the research monograph "Elliptic partial differential equations and quasiconformal mappings in the plane" by Princeton University Press. He was awarded the Salem Prize 1994 and the Finnish Cultural Foudation Prize 2011. Also, he was invited speaker at ICM in 1994 and at ECM in 1996 and in 2012.
Under suitable boundary restrictions, scaling limits of random planar tilings present surprising geometric features: One observes definite deterministic and disordered (or frozen and liquid) limit configurations with interesting geometric properties. In this talk we explain how the geometry of these limit configurations can be understood and described in quite detail via suitable degenerate Beltrami differential equations and the complex structures they provide.
Bio-Sketch:
Kari Astala received his mathematical education in Helsinki, Finland and obtained PhD in 1980. He was a Professor at Jyväskylä University 1995-2002, and since 2002 he has been a Professor at University of Helsinki. His research concentrates on the interaction of PDE's and complex analysis, for instance on quasiconformal structures at various instances. He has (co)-authored more than 80 research publications, including the research monograph "Elliptic partial differential equations and quasiconformal mappings in the plane" by Princeton University Press. He was awarded the Salem Prize 1994 and the Finnish Cultural Foudation Prize 2011. Also, he was invited speaker at ICM in 1994 and at ECM in 1996 and in 2012.
