Laplacians, metrics and boundaries of simplicial complexes and Dirichlet spaces

Applicants Professor Dr. Matthias Keller; Professor Dr. Daniel Lenz; Dr. Marcel Schmidt
Subject Area Mathematics
Term from 2020 to 2025
Project identifier Deutsche Forschungsgemeinschaft (DFG) - Project number 441844630
 

Project Description

The project studies the interplay between analysis and geometry mediated by Laplacians. Its starting point is the investigation of discrete spaces and, in particular, graphs.The geometry comes about via intrinsic metrics and boundaries. The analytic side is present via spectral theory, potential theory and harmonic functions.The project is naturally divided in two parts: These deal with higher order Laplacians on simplicial complexes and harmonic functions of Laplacians arising from Dirichlet spaces respectively.
DFG Programme Priority Programmes
Subproject of SPP 2026:  Geometry at Infinity