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Abstracts for Geometry and Quantum Field Theory

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Non-abelian bundle gerbes

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Speaker: 
Danny Stevenson
Affiliation: 
Glasgow
Date: 
Fri, 2010-06-25 09:30 - 10:30
Location: 
MPIM Lecture Hall
Parent event: 
Geometry and Quantum Field Theory

In this talk we will give an introduction to so-called `non-abelian cohomology'. Building on the talk of Michael Murray we will explain why bibundle gerbes parametrize non-abelian cohomology. We will comment on the existence of bibundle gerbes and describe their classifying theory. If time permits we will describe some examples.
This is joint work with Michael Murray and David Roberts.

Differential K-theory: Axioms, Models and Operations

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Speaker: 
Ulrich Bunke
Affiliation: 
Regensberg
Date: 
Fri, 2010-06-25 11:00 - 12:00
Location: 
MPIM Lecture Hall
Parent event: 
Geometry and Quantum Field Theory

The Weak Heat Kernel Expansion and the Quantum Double Suspension

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Speaker: 
Partha Sarathi Chakraborty
Affiliation: 
IMS, Chennai
Date: 
Fri, 2010-06-25 14:00 - 14:30
Location: 
MPIM Lecture Hall
Parent event: 
Geometry and Quantum Field Theory

We are interested in producing spectral triples that satisfy the hypothesis of the local index formula namely regularity and finiteness of the dimension spectrum. We begin with showing that  the weak heat kernel expansion is stable under quantum double suspension and the usual heat kernel expansion implies weak heat kernel expansion. Therefore quantum double suspending ordinary compact spin manifolds  we get spectral triples that satisfy weak heat kernel expansion. We further show that weak heat kernel expansion implies regularity and finiteness of the dimension spectrum.

Markov measures and extended zeta functions

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Speaker: 
Anna Maria Paolucci
Date: 
Fri, 2010-06-25 14:30 - 15:00
Location: 
MPIM Lecture Hall
Parent event: 
Geometry and Quantum Field Theory

We find new representations of $q$-families of algebras. These algebras are built on generators and relations. They are C*-algebras and their representations are a part of non-commutative harmonic analysis. Our approach is amenable to applications in problems from dynamics and mathematical physics: We introduce a deformation parameter $q$, and an associated family of $q$-relations where the number $q$ is a "quantum-deformation," and also a parameter in a scale of (Riemann-Ruelle) zeta functions.

Higher dimensional infinitesimal groupoids of manifolds

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Speaker: 
Dennis Borisov
Affiliation: 
Yale
Date: 
Fri, 2010-06-25 15:30 - 16:00
Location: 
MPIM Lecture Hall
Parent event: 
Geometry and Quantum Field Theory

The construction (by Kapranov) of the space of infinitesimal paths on a manifold is extended to include higher dimensional infinitesimal objects, encoding contractions of infinitesimal loops. This full infinitesimal groupoid is shown to have the algebra of polyvector fields as its non-linear cohomology.

Renormalized integrals and a path integral representation of the heat kernel

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Speaker: 
Christian Bär
Affiliation: 
Potsdam
Date: 
Fri, 2010-06-25 16:00 - 16:30
Location: 
MPIM Lecture Hall
Parent event: 
Geometry and Quantum Field Theory

We propose a concept of renormalized integrals which generalizes integrals on measure spaces. This is a suitable framework for defining path integrals without having to construct an actual measure on path space. We show how this works for the heat kernel of a Laplace type operator on a compact Riemannian manifold. The hope is that this approach can circumvent problems with the standard approach using Wiener measure when one wants to deal with the Schrödinger equation instead of the heat equation.

 

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