Abstract: Solving the heat equation (d/dt - A)u = 0 with initial condition u(0) = u_0 gives rise to the semigroup exp(tA) for t > 0. This semigroup is constructed from the resolvent (A - z)^{-1} by means of a Cauchy integral. In this talk, we will highlight some aspects of this procedure for various operators A, starting from matrices (ode's), passing to elliptic differential operators on closed manifolds, and, finally, manifolds with conic singularities.

Refreshments will be served compliments of the Division of Mathematics & Natural Science.