# Mathematical Physics

This series consists of talks in the area of Mathematical Physics.

## Seminar Series Events/Videos

Currently there are no upcoming talks in this series.

## Moonshine, topological modular forms, and 576 fermions.

Thursday Sep 22, 2016
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I will report on progress understanding the 576-fold periodicity in TMF in terms of conformal field theoretic constructions. Sporadic finite groups and their cohomology will play a role.

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## Monodromy of the Casimir connection and Coxeter categories

Thursday Sep 08, 2016
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A Coxeter category is a braided tensor category which carries an action of a generalised braid group $B_W$ on its objects. The axiomatics of a Coxeter category and the data defining the action of $B_W$ are similar in flavor to the associativity and commutativity constraints in a monoidal category, but arerelated to the coherence of a family of fiber functors.

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## Learning Seminar on Maulik-Okounkov

Thursday Jun 23, 2016
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## Learning seminar on Maulik-Okounkov

Tuesday Jun 07, 2016
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## Integrable systems and vacua of N=2* theories

Thursday Jun 02, 2016
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## Gluing in factorization homology via quantum Hamiltonian reduction

Thursday May 26, 2016
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Topological factorization homology is an invariant of manifolds which enjoys a hybrid of the structures in topological field theory, and in singular homology. These invariants are especially interesting when we restrict attention to the factorization homology of surfaces, with coefficients in braided tensor categories. In this talk, I would like to explain a technique, related to Beck monadicity, which allows us to compute these abstractly defined categories, as modules for explicitly computable, and in many cases well-known, algebras.

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## The A model and Lagrangian cobordisms

Thursday May 26, 2016

Physically, there's no reason to expect that the A model (as encoded by Gromov-Witten invariants and the Fukaya category) should be related to the theory of cobordisms between D branes. However, it seems that for the A model on convex symplectic targets, the theory of Lagrangian cobordisms detects many invariants of the Fukaya category, and may even recover it--put another way, it seems one can enrich the algebraic structures of the A model as being linear over cobordism spectra.

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## Cluster Theory is the Moduli Theory of A-branes in 4-manifolds

Thursday May 19, 2016
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We'll explain the slogan of the title: a cluster variety is a space associated to a quiver, and which is built out of algebraic tori.

They appear in a variety of contexts in geometry, representation theory, and physics. We reinterpret the definition as: from a quiver (and some additional choices) one builds an exact symplectic 4-manifold from which the cluster variety is recovered as a component in its moduli space of Lagrangian branes. In particular, structures from cluster algebra govern the classification of exact Lagrangian surfaces in Weinstein 4-manifolds.

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## The classification of chiral WZW models

Tuesday Apr 05, 2016
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I will explain how to axiomatize the notion of a chiral WZW model using the formalism of VOAs (vertex operator algebras). This class of models is in almost bijective correspondence with pairs (G,k), where G is a connected (not necessarily simply connected) Lie group and k in H^4(BG,Z) is a degree four cohomology class subject to a certain positivity condition. To my surprise, I have found a couple extra models which satisfy all the defining properties of chiral WZW models, but which don't come from pairs (G,k) as above.

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## Quiver varieties and elliptic quantum groups

Thursday Mar 17, 2016
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