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# 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.

## Geometric Langlands and symplectic duality

Thursday Dec 03, 2015
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I will review the possible role in Geometric Langlands
of N=4 boundary conditions in four-dimensional supersymmetric Yang Mills theory.
The action of S-duality on such boundary conditions can be understood
in terms of symplectic duality.

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## Holomorphic Floer Quantization

Thursday Nov 19, 2015
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## The AGT conjecture for gauge theories on A-type ALE spaces, K-theoretic/Cohomological Hall algebras and sheaves on stacks

Thursday Nov 12, 2015
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K-theoretical/Cohomological Hall algebras, associated with the stack of zero-dimensional sheaves on $\mathbb{C}^2$, play a prominent role in the proof, given by Schiffmann and Vasserot, of the AGT conjecture for

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## Representations of truncated shifted Yangians and symplectic duality

Thursday Oct 29, 2015
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We study the representation theory of truncated shifted Yangians. These algebras arise as quantizations of slices to Schubert varieties in the affine Grassmannian. We will describe the combinatorics of their highest weights, which is encoded in Nakajima's monomial crystal. We also prove Hikita's conjecture in this context.

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## Basic aspects of 3d N=4 theories and symplectic duality

Thursday Oct 15, 2015
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I'll discuss the two topological twists of 3d N=4 theories, and explain how to understand them in the AKSZ/BV formalism, and how they relate to twists of 4d N =2 theories.  Symplectic duality then takes the form of an equivalence between 3d N=4 theories which interchanges the two topological twists.  I'll also introduce monopole operators and explain the role they play in symplectic duality.

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## Half-BPS boundary conditions in 3d N=4 theories

Thursday Oct 08, 2015
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## Boundaries and D-modules in 3d N=4 theories

Thursday Oct 01, 2015
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After a quick review of the Higgs and Coulomb branches of 3d N=4 theories, I'll introduce some simple classes of boundary conditions and explain how they lead to (pairs of) modules for certain (pairs of) quantum algebras. I will focus on abelian theories, for which the relevant boundary conditions/modules can be described using the geometry of (pairs of) hyperplane arrangements. From this, the simplest examples of symplectic-dual modules will arise.

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## Introduction to symplectic duality

Thursday Sep 24, 2015
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## The standard model from non-commutative geometry: what? why? what's new?

Wednesday May 27, 2015
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## The Standard Model as an extension of the noncommutative algebra of forms

Tuesday May 26, 2015
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## RECENT PUBLIC LECTURE

### Erik Verlinde: A new view on gravity and the dark side of the cosmos

Speaker: Erik Verlinde