Operators on Singular Manifolds

30.08.2016, 11:00  –  Haus 9, Raum 2.22
Arbeitsgruppenseminar Analysis

Xiaojing Lyu

We study the interplay between analysis on manifolds with  singularities and complex analysis and develop new structures of  operators based on the Mellin transform and tools for iterating the  calculus for higher singularities. We refer to the idea of  interpreting boundary value problems (BVPs) in terms of  pseudo-differential operators with a principal symbolic hierarchy,  taking into account that BVPs are a source of cone and edge operator  algebras. The respective cone and edge pseudo-differential algebras in  turn are the starting point of higher corner theories. In addition  there are deep relationships between corner operators and complex  analysis. This will be illustrated by numerous examples.