Modul:   MAT074  Talks in mathematical physics

Gluing formulas for heat kernels

Talk by Dr. Konstantin Walter Wernli

Speaker invited by: Prof. Dr. Alberto Cattaneo

Date: 16.12.24  Time: 13.30 - 14.30  Room: Y27H25

Motivated by heat kernel renormalization of perturbative quantum field theory, we study the cutting and gluing behaviour of the heat kernel on a Riemannian manifold \( M \) which is cut along a compact hypersurface \( \gamma \) into two Riemannian manifolds \( M_1\), \(M_2\). Under a certain assumption on \( (M,\gamma) \) (which we conjecture to be true for all Riemannian manifolds), we prove a gluing formula for the heat kernel which involves only the heat kernels on \( M_1, M_2 \) and \( \gamma \). This is a joint work with Pavel Mnev, arxiv:2404.00156