My work involves analysis, probability and some aspects of geometry such as Riemannian geometry and geometric group theory. I study different aspects of heat diffusion on manifolds from the point of view of both partial differential equations and stochastic processes. I am mainly interested in th...
My work involves analysis, probability and some aspects of geometry such as Riemannian geometry and geometric group theory. I study different aspects of heat diffusion on manifolds from the point of view of both partial differential equations and stochastic processes. I am mainly interested in those properties that relate to the large-scale geometry of the underlying space. Potential theory and functional analysis often provide the framework and tools to study these properties.