# Mathematical Physics

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

## Seminar Series Events/Videos

Jan 23 2017 - 2:00pm
Room #: 301
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Apr 10 2017 - 2:00pm
Room #: 394
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## Vertex algebras and quantum master equation.

Wednesday Jan 18, 2017
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We study the effective BV quantization theory for chiral deformation of two dimensional conformal field theories. We establish an exact correspondence between renormalized quantum master equations for effective functionals and Maurer-Cartan equations for chiral vertex operators. The generating functions are proven to be quasi-modular forms. As an application, we construct an exact solution of quantum B-model (BCOV theory) in complex one dimension that solves the higher genus mirror symmetry conjecture on elliptic curves.

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## BV formalism and derived symplectic geometry

Monday Jan 16, 2017
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We will describe a formulation of the Batalin-Vilkovisky formalism using derived symplectic geometry.  In this setting, the classical master equation of the BV formalism describes a space of coisotropic structures.  Using this approach, we resolve a conjecture of Felder-Kazhdan regarding BRST cohomology.  Time permitting, we will also describe applications of these ideas to more general quantization problems.

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## Convex Polytopes for the Central Degeneration of the Affine Grassmannian

Monday Jan 09, 2017
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The affine Grassmannian is the analog of the Grassmannian for the loop group. They are very important objects in mathematical physics and the Geometric Langlands program. In this talk, I will explain my recent work on the central degeneration of semi-infinite orbits, Iwahori orbits and Mirkovic-Vilonen cycles in the affine Grassmannian. I will also use lots of convex polytopes to illustrate my results. In addition, I will explain the connections between my work and other parts of geometric representation theory and combinatorial algebraic geometry.

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## Topological recursion and deformation quantization.

Thursday Dec 08, 2016
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About a decade ago Eynard and Orantin proposed a powerful computation algorithm
known as topological recursion. Starting with a spectral curve" and some initial data"
(roughly, meromorphic differentials of order one and two) the topological recursion produces by induction
a collection of symmetric meromorphic differentials on the spectral curves parametrized by
pairs of non-negative integers (g,n) (g should be thought of as a genus and n as the number of punctures).

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## Periods, Motives, and graphical interpretations thereof

Monday Dec 05, 2016
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Integral values of zeta functions are important not only for what they say about other values of their respective functions, but also for what they say about transcendence degree questions for appropriate extensions of the rationals or other number fields.  They  also appear in some recent computations relevant to particle physics.
In this talk we will give a quick introduction to the theory of periods and motives, relate said theory to special values of zeta functions, and discuss a graphical definition of the associated category of motives.

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## The Coherent Satake Category, Clusters, and Wilson-'t Hooft Operators

Thursday Dec 01, 2016
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We discuss recent work showing that in type A_n the category of equivariant perverse coherent sheaves on the affine Grassmannian categorifies the cluster algebra associated to the BPS quiver of pure N=2 gauge theory. Physically, this can be understood as a statement about line operators in this theory, following ideas of Gaiotto-Moore-Neitzke, Costello, and Kapustin-Saulina -- in short, coherent IC sheaves are the precise algebro-geometric counterparts of Wilson-'t Hooft line operators.

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## Quantum groups from character varieties

Thursday Nov 10, 2016
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Quantum groups from character varieties

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## Mathematical Physics Seminar

Thursday Nov 03, 2016
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## Wigner-Eckart theorem and Jordan-Schwinger representation for infinite-dimensional representations of the Lorentz group

Thursday Oct 27, 2016
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The Wigner-Eckart theorem is a well known result for tensor operators of SU(2) and, more generally, any compact Lie group. I will show how it can be generalised to arbitrary Lie groups, possibly non-compact. The result relies on the knowledge of recoupling theory between finite-dimensional and arbitrary admissible representations, which may be infinite-dimensional; the particular case of the Lorentz group will be studied in detail.

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## On the mathematics of étale gerbes inspired by physics

Thursday Oct 13, 2016
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For a finite group G, a G-gerbe over a space B can be thought of as a fiber bundle over B with fibers the classifying orbifold BG. Hellerman-Henriques-Pantev-Sharpe studied conformal field theories on G-gerbes. Given a G-gerbe Y-> B, they constructed a disconnected space \widehat{Y} endowed with a locally constant U(1) 2-cocycle c. They conjectured that a CFT on Y is equivalent to a CFT on \widehat{Y} twisted by the "B-field" c.

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## RECENT PUBLIC LECTURE

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Speaker: Molly Shoichet