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Mathematical Physics

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

Seminar Series Events/Videos

TBA
Nov 27 2017 - 2:00pm
Room #: 394
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TBA
Jan 22 2018 - 2:00pm
Room #: 394
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Monday Nov 13, 2017
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Making perturbative quantum field theory (QFT) mathematically rigorous is an important step towards understanding how the non-perturbative framework should look like. Recently, two approaches have been developed to address this issue: perturbative algebraic quantum field theory (pAQFT) and the factorization algebras approach developed by Costello and Gwilliam. The former works primarily in Lorentzian signature, while the later in Euclidean, but there are many formal parallels between them.

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Monday Nov 06, 2017
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In this talk I will define the quantum K-theory of Nakajima quiver varieties and show its connection to representation theory of quantum groups and quantum integrable systems on the examples of the Grassmannian and the flag variety. In particular, the Baxter operator will be identified with operators of quantum multiplication by quantum tautological classes via Bethe equations. Quantum tautological classes will also be constructed and, time permitting, an explicit universal combinatorial formula for them will be shown.
Based on joint works with P.Koroteev, A.Smirnov and A.Zeitlin

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Monday Oct 16, 2017
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It is easy to prove that d-dimensional complex Hilbert space can contain at most d^2 equiangular lines.  But despite considerable evidence and effort, sets of this size have only been proved to exist for finitely many d.  Such sets are relevant in quantum information theory, where they define optimal quantum measurements known as SIC-POVMs (Symmetric Informationally Complete Positive Operator-Valued Measures).  They also correspond to complex projective 2-designs of the minimum possible cardinality.   Numerical evidence points to their existence for all d as orbits of finite Heisenberg gro

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Wednesday Oct 11, 2017
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I will talk about a recent proof, joint with M. Gröchenig and D. Wyss, of a conjecture of Hausel and Thaddeus which predicts the equality of suitably defined Hodge numbers of moduli spaces of Higgs bundles with SL(n)- and PGL(n)-structure. The proof, inspired by an argument of Batyrev, proceeds by comparing the number of points of these moduli spaces over finite fields via p-adic integration.

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Wednesday Oct 04, 2017

Geometric invariant theory (GIT) is an essential tool for constructing moduli spaces in algebraic geometry. Its advantage, that the construction is very concrete and direct, is also in some sense a draw-back, because semistability in the sense of GIT is often more complicated to describe than related intrinsic notions of semistability in moduli problems. Recently a theory has emerged which treats the results and structures of geometric invariant theory in a broader context.

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Monday Oct 02, 2017
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Moore and Tachikawa conjecture that there exists a functor from the category of 2-bordisms to a certain category whose objects are algebraic groups and morphisms between $G$ and $H$ are given by affine symplectic varieties with an action of $G\times H$.  I will explain a proof of this conjecture due to Ginsburg and Kazhdan, and its relation to Coulomb branches of certain quiver gauge theories which allows to make interesting calculations.

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Monday Sep 25, 2017
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I'll do my best to explain my approach to the BFN construction of (quantum) Coulomb branches.  This approach is based on viewing the BFN algebra as an endomorphism algebra in a larger category that's easier to present (and which we can draw some pretty pictures for).  In particular, this approach is helpful in understanding the representation theory of this algebra, and in constructing and analyzing tilting generators on Coulomb branches.

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Monday Sep 25, 2017
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He will discuss relations between Virasoro and Kac-Moody conformal blocks, character varieties and quantum groups, and AGT.

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Wednesday Jul 19, 2017
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The talk is based on my recent work with Ryan Aziz. We find a dual version of a previous double-bosonisation theorem whereby each finite-dimensional braided-Hopf algebra in the category of corepresentations of a coquasitriangular Hopf algebra gives a new larger coquasitriangular Hopf algebra, for example taking c_q[SL_2] to c_q[SL_3] for these quantum groups reduced at certain odd roots of unity.

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Monday Jun 12, 2017
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We use the cluster structure on the Grassmannian and the combinatorics of plabic graphs to exhibit a new aspect of mirror symmetry for Grassmannians in terms of polytopes.

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