NCG seminar at SISSA

[Emanuele Tuillier Illingworth]

"NON-COMMUTATIVE GEOMETRY" SEMINAR

Monday 7 December 2015 at 11:30AM
Venue: Department of Mathematics, Trieste University, Seminar Room - 
Third Floor bld H2bis

Prof. Teoman Turgut (Boğaziçi University, Istanbul)
"Heat kernel approach to singular problems"

Abstract.
We discuss the bound state spectrum of a particle moving on a Riemannian 
manifold
under the influence of delta function potentials. We show that the 
renormalization can be naturally accomplished by the heat kernel 
approach. A slight generalization to the Klein-Gordon type particles are 
also presented. Currently there is some interest on particles captured 
by curves, modeled by singular interactions supported on such curves, we 
present a generalization to our approach to circles embedded into a 
Riemannian manifold. We also discuss the renormalization group flows of 
these systems. If time permits a more ambitious generalization to 
interacting bosons on a two dimensional manifold will be presented.