TopMath Talk with Vera Pazukhina: On discretizations and regularizations of gradient flows in Wasserstein-like spaces

„In this talk, we discuss how solutions to certain PDEs can be described within the framework of gradient flows. The most common approach involves obtaining them as limits of piecewise constant-in-time curves constructed by minimizing a problem that depends on the underlying metric and the driving functional. This may be combined with the requirement that the approximations are also piecewise constant in the spatial coordinates; in this case, the geometric structure of the tessellation becomes important. Part of this talk is dedicated to an approach that employs a hexagonal tessellation of a subset of R^2. Another topic is a time-discrete scheme that requires certain regularizations due to the possible loss of metric structure in some generalizations. Finally, we consider a method of obtaining solutions to certain PDEs using a time-continuous formulation in which the gradient flow structure is perturbed, but the underlying method remains based on a crucial variational principle.“

TopMath Talks

As part of the TopMath talks, TopMath students and doctoral students present parts of their research. They provide an understandable insight into their current area of interest, enabling students and staff from different research fields to broaden their mathematical background knowledge. The talks are open to the public and last about an hour, followed by discussion. You are cordially invited!