Workshop on Topological Aspects of Quantum Field Theories
(14 - 18 Jan 2013)
~ Abstracts ~
Supersymmetric sigma models, elliptic cohomology and the Witten genus
Dan Berwick-Evans, University of California at Berkeley, USA
We will explain a geometric model for elliptic cohomology over the complex numbers motivated by the physics of supersymmetric sigma models. This leads to a construction of the Witten genus, which we can interpret as a sort of volume form on a mapping space. Our approach shares many features with the work of Stolz and Teichner on TMF and of Costello on the Witten genus.
« Back... Twisted K-homology of CW-complexes
Alan Carey, Australian National University, Australia
I will outline an approach to constructing the twisted K-homology groups of CW-complexes using generalised Baum-Douglas cycles. This is work in progress with Paul Baum and Bai-Ling Wang.
« Back... Scanning and the homotopy type of bordism categories
Søren Galatius, Stanford University, USA
The lectures will discuss some methods for understanding the cohomology of moduli spaces of manifolds. I will survey some developments from the last decade and discuss some new results.
« Back... Factorization algebras
Owen Gwilliam, University of California at Berkeley, USA
The overall goal of these lectures is to explain how chiral differential operators relate to Costello's recent work on the Witten genus. The first lecture will introduce and motivate factorization algebras, which were invented by Beilinson and Drinfeld to capture some of the structure of chiral conformal field theory but have since appeared in topology as well. In the second lecture, we will explain why the observables of free quantum field theories are factorization algebras. We will also discuss the issues in extending this construction to interacting field theories. Finally, the last lecture will outline how these ideas and techniques apply to the curved beta-gamma system, recovering chiral differential operators and the Witten genus.
« Back... Topological field theories and the homotopy groups of spheres.
Michael Hopkins, Harvard University, USA
I will describe the relationship between the stable homotopy groups of spheres and topological quantum field theories, and some of the questions it engenders.
« Back... Higher Chern-Simons theory
Urs Schreiber, Utrecht University, The Netherlands
I give an introduction to the natural formulation of Chern-Simons-type quantum field theory by "extended" ("multi-tiered") Lagrangians given by maps of higher differential moduli stacks. Then I discuss applications to various problems in quantum field theory. This will proceed roughly along the lines of the text "A higher stacky perspective on Chern-Simons theory".
(ncatlab.org/schreiber/show/A+higher+stacky+perspective+on+Chern-Simons+theory) with Domenico Fiorenza and Hisham Sati.
« Back... Variants of analytic torsion and relation to TQFT
Mathai Varghese, The University of Adelaide, Australia
I will talk about variants of Ray-Singer analytic torsion that require pseuododifferential operators for their definition, and will relate them to TQFT. This is joint work with Siye Wu
« Back... Higher string topology via Hochschild homology
Nathalie Wahl, University of Copenhagen, Denmark
We construct universal operations in Hochschild homology and use them to define non-trivial higher degree operations on the homology of the free loop space of a manifold associated to surfaces of any genus and any number of boundary components. These operations, which are parametrized by Sullivan diagrams, can be seen as part of a "compactified" topological conformal field theory.
« Back... Gerbes with connections
Konrad Waldorf, Universität Regensburg, Germany
The first lecture will be an introduction to abelian bundle gerbes and connections on them, focussing on higher algebra aspects and the roles that gerbes play as twistings of K-theory and as B-fields in string theories. The second lecture will present a systematical approach to non-abelian gerbes and connections on them. Here, one objective is to explain how the choice of different "structure 2-groups" and "structure bigroupoids" leads naturally to various versions of (differential) K-theory twistings that recently appeared in the literature. The third lecture will be about geometric string structures, their formulation in terms of connections on non-abelian gerbes, and their relation to geometric spin structures on the loop space.
« Back... Asymptotics of analytic torsion
Weiping Zhang, Nankai University, China
We describe a joint work with Jean-Michel Bismut and Xiaonan Ma on the asymptotics of the Ray-Singer analytic torsion. Our results generalize the corresponding result due to Mueller on closed hyperbolic 3-manifolds.
« Back...
|