Workshop on Topological Aspects of Quantum Field Theories
(14  18 Jan 2013)
~ Abstracts ~
Supersymmetric sigma models, elliptic cohomology and the Witten genus Dan BerwickEvans, 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 Khomology of CWcomplexes Alan Carey, Australian National University, Australia
I will outline an approach to constructing the twisted Khomology groups of CWcomplexes using generalised BaumDouglas cycles. This is work in progress with Paul Baum and BaiLing 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 betagamma 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 ChernSimons theory Urs Schreiber, Utrecht University, The Netherlands
I give an introduction to the natural formulation of ChernSimonstype quantum field theory by "extended" ("multitiered") 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 ChernSimons theory".
(ncatlab.org/schreiber/show/A+higher+stacky+perspective+on+ChernSimons+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 RaySinger 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 nontrivial 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 Ktheory and as Bfields in string theories. The second lecture will present a systematical approach to nonabelian gerbes and connections on them. Here, one objective is to explain how the choice of different "structure 2groups" and "structure bigroupoids" leads naturally to various versions of (differential) Ktheory twistings that recently appeared in the literature. The third lecture will be about geometric string structures, their formulation in terms of connections on nonabelian 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 JeanMichel Bismut and Xiaonan Ma on the asymptotics of the RaySinger analytic torsion. Our results generalize the corresponding result due to Mueller on closed hyperbolic 3manifolds.
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