Geometric microlocal analysis meets discrete geometryOberseminar Global Analysis and Operator Algebras

by Boris Vertman (Uni Oldenburg)

Tuesday Jun 23, 2026, 2:15 PM → 3:45 PM Europe/Berlin

Endenicher Allee 60/1-008 (Mathezentrum)

Melrose’s geometric microlocal analysis involves the concept of blowing up
submanifolds to resolve non-uniform operator kernel behaviour. This technique has
been central to the analysis of singular spaces, but was previously disconnected
from discrete geometry. We introduce a new framework that applies Melroses's blowup
techniques to scaling limits of discrete surfaces to study the discrete heat kernel
as the discretization mesh size goes to zero. This proves a full asymptotics of the
determinant on discrete surfaces beyond the example of regular lattices that has
been the best possible result so far.