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