Avscon the Schur topology

Abstract

The aim of the course is to lead to an understanding of homogenisation processes in an operator-theoretic sense. In fact, using solely operator-theoretic means not referring to the particular form of the coefficients, we will identify an operator topology on the level of coefficients that will fully capture the convergence involved in the context of homogenisation. One upshot of this perspective will be that we will obtain homogenisation results for time-dependent partial differential equations (almost) for free.

This is part of the Avscon Lecture series 2025; Avscon (= A very short course on..) comprises each year of 4 short lecture courses accessible to B.Sc. students or higher; details and registration can be found at https://www.marcus-waurick.de/avscon ; this course on homogenisation and related things has 37 pages