[geometry-ml:03428] MS seminars at Kavli IPMU -- Oleksandr Tsymbaliuk (Aug 7) and Alexander Voronov (Aug 9)

[Todor Milanov]

Dear all,

I would like to announce the following two MS seminars at Kavli IPMU

1) Speaker: Oleksandr Tsymbaliuk (Yale)
Date:	Tue, Aug 07, 2018, 13:15 - 14:45
Place:	Seminar Room A

Title:	Coulomb branches, shifted quantum algebras and modified q-Toda systems

Abstract: In the recent series of papers by Braverman-Finkelberg-Nakajima a mathematical construction of the Coulomb branches of 3d N=4 quiver gauge theories was proposed (the latter are supposed to be symplectic dual to the corresponding well-understood Higgs branches). They can be also realized as slices in the affine Grassmannian and therefore admit a multiplication. 

In the current talk, we shall discuss the quantizations of these Coulomb branches and their K-theoretic analogues, and the (conjectural) down-to-earth realization of these quantizations via shifted Yangians and shifted quantum affine algebras. Those admit a coproduct quantizing the aforementioned multiplication of slices. In type A, they also act on equivariant cohomology/K-theory of parabolic Laumon spaces. 

As another interesting application, the shifted quantum affine algebras in the simplest case of sl(2) give rise to a new family of 3^{n-2} q-Toda systems of sl(n), generalizing the well-known one due to Etingof and Sevostyanov. If time permits, we shall explain how to obtain 3^{rk(g)-1} modified q-Toda systems for any simple Lie algebra g. 

This talk is based on the joint works with M. Finkelberg and R. Gonin.


2) Speaker:	Alexander Voronov (U of Minnesota)
Date:	Thu, Aug 09, 2018, 15:30 - 17:00
Place:	Seminar Room B

Title:	Quantizing Deformation Theory

Abstract: Classical deformation theory is based on the Classical Master Equation (CME), a.k.a. the Maurer-Cartan Equation: dS + 1/2 [S,S] = 0. Physicists have been using a quantized CME, called the Quantum Master Equation (QME), a.k.a. the Batalin-Vilkovisky (BV) Master Equation: dS + h \Delta S + 1/2 {S,S} = 0. The CME is defined in a differential graded (dg) Lie algebra, whereas the QME is defined in a space V[[h]] of formal power series or V((h)) of formal Laurent series with values in a dg-BV-algebra V or a bi-dg-Lie algebra. A generalization of classical deformation theory based on the QME may be thought of as quantized deformation theory. Examples include cohomological field theory and string-field theory. Quantum deformation functor and its representability will also be discussed in the talk.

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Todor Eliseev Milanov
Associate Professor 
Kavli IPMU,  Japan

todor.milanov ＠ ipmu.jp