Organized by Mina Aganagic, Dima Galakhov, Vivek Shende and Andrey Smirnov
Mondays, 2:003:00, 402 Le Conte Hall.
Schedule of talks for Fall 2016:
Sep 12  Mina Aganagic  Two mathematical applications of little string theory 
Sep 19  Vivek Shende  Categories and moduli spaces associated to singular Lagrangians 
Sep 26  Andrei Negut  qdeformed Walgebras, Ext operators and the AGTW relations 
Oct 3  Dmitry Galakhov  The twodimensional LandauGinzburg approach to link homology 
Oct 10  No Seminar  
Oct 17  Lotte Hollands  Opers, spectral networks and the T[3] theory 
Oct 24  Michael Viscardi  Equivariant quantum cohomology and the geometric Satake equivalence 
Oct 31 
Pavel Putrov  Resurgence in ChernSimons theory 
Nov 7  Nikita Nekrasov  How I learned to stop worrying and to love both instantons and antiinstantons 
Nov 14  Andrey Smirnov  Quantum Ktheory and NekrasovShatashvili conjecture 
Nov 21  No Seminar  
Nov 28  No Seminar  
Dec 5  Tudor Dimofte (2:304) and Alexander Braverman (45) 
TBA

A note to the speakers:
This is a research seminar, intended for mathematicians and physicists. For the speaker to successfully reach the audience in both fields, it is important to explain, as clearly as possible: the motivations for the work, questions addressed, key ideas.
The audience may fail to appreciate the glory of the result, otherwise.
The seminar archive can be found: here
Abstracts
Sep 12
I will describe two mathematical applications of little string theory. The first leads to a variant of AGT correspondence that relates qdeformed
W algebra conformal blocks to Ktheoretic instanton counting. This correspondence can be
proven for any simply laced Lie algebra. The second leads to a variant of quantum Langlands
correspondence which relates qdeformed conformal blocks of an affine Lie algebra and a W algebra, associated to a
Langlands dual pair of Lie algebras. The proof of the correspondence for simply laced Lie algebras involves, in
a crucial way, the recently discovered elliptic stable envelopes. This is based on joint works with Nathan
Haouzi and with Edward Frenkel and Andrei Okounkov.
Sep 19
I describe certain categories which arise from the consideration of singular Lagrangian
geometries in symplectic manifolds, in 4 and 6 dimensions. These are (mathematically) the Fukaya category of a
neighborhood of the singular space; presumably in physics, some category of branes. I will explain how moduli spaces
usually associated with irregular singularities, cluster varieties, knot homology, and various other subjects arise in this manner, and then pose
some questions regarding the connection to branetiling, higher genus effects, and quantization.
Sep 26
I will present a construction of the qdeformed Walgebra of gl_r and its Verma module, that does not
use the free field realization or screening charges. The upshot is that our method allows us to directly
compute the commutation relations between the CarlssonOkounkov Ext operator on the moduli space of rank r
sheaves and the defining currents of the qdeformed Walgebra. This implies a geometric representation theory
interpretation of the AGTW relations.
Oct 3
We describe rules for computing a homology theory of knots and links in R^3. It is derived from the theory
of framed BPS states bound to domain walls separating twodimensional LandauGinzburg models with (2,2) supersymmetry.
We illustrate the rules with some sample computations, obtaining results consistent with Khovanov homology.
We show that of the two LandauGinzburg models discussed in this context by Gaiotto and Witten one,
(the socalled YangYangLandauGinzburg model) does not lead to topological invariants of links while the other,
based on a model with target space equal to the universal cover of the moduli space of SU(2) magnetic monopoles,
will indeed produce a topologically invariant theory of knots and links.
Oct 17
In this seminar I will explain how certain partition functions of fourdimensional quantum field theories,
such as the nonLagrangian T[3] theory, have a geometric interpretation as generating functions of socalled opers.
This will reveal close ties to spectral networks and the exact WKB method. (This is joint work with Andy Neitzke.)