Abstract: “We link several constructions of vertex operator algebras (VOA) in supersymmetric QFT. One is the SCFT/VOA correspondence of Beem et al, identifying VOA inside the protected sector of a 4d N=2 SCFT. Using the Omega-background approach to the SCFT/VOA, and compactifying the 4d theory on the infinite cigar geometry, we relate this to the construction of boundary VOAs in … Read More
Abstract: My talk is based on the joint project with Lev Rozansky. I will explain how we rigorously construct 3D TQFT, which is a KRS theory with targets Hilbert scheme of points on a plane. Defects in the last theory encode a knot in the three-space and we rediscover the HOMFLY-PT homology of a link as a part of the … Read More
Abstract: We revisit supersymmetric localization with monopole operators in 3D N=4 gauge theories, arriving at a new point of view on their quantized Coulomb branch algebras. Our construction agrees with and recovers the existing mathematical definition. We apply the machinery to define a nonabelian analog of shift operators in enumerative theory of quasimaps, and illustrate the construction in detail for … Read More
The talk will consist of two parts. In the first, longer, part I will review the basics of quantum toroidal algebras and their representation theory focusing on the simplest example of type gl(1). I will also discuss the identification between the representations of the algebra and branes of Type IIB string theory, how brane interactions manifest themselves in this setup … Read More
Abstract: There exists a well-known similarity between the Kloosterman sum in number theory and the Bessel differential equation. This connection was explained by B. Dwork in 70s by discovering the Frobenius structures in the p-adic theory of the Bessel differential equation. In my talk I will speculate that this connection extends to the equivariant quantum differential equations for a wide … Read More
Abstract. I will explain how to associate a spectral network to a Demazure weave via Floer theory. Specifically, the talk will present how spectral networks, as introduced by Gaiotto-Moore-Neitzke, arise when computing J-holomorphic strips associated to augmentations of Lagrangian fillings of Legendrian links. In particular, this provides a Floer-theoretical description of Stokes lines in higher rank and with arbitrary irregular Stokes … Read More
Abstract: The count of microstates for supersymmetric black holes is typically obtained from a supersymmetric index in weakly-coupled string theory. I will explain how to find the saddles of the gravitational path integral corresponding to this index in a general theory of supergravity in asymptotically flat space. Such saddles exhibit a new attractor mechanism which explains the agreement between the string … Read More
Abstract: There is a hope that some of the technology developed for counting curves may be also applicable to certain number-theoretic counting problems. While the exact contours of this hope remain a bit vague at the moment, I will focus on a handful of actual mathematical statements proven in our ongoing joint work with David Kazhdan.
Abstract: I’ll recall some basics about Slodowy slices, generalized slices in the affine Grassmannian, and quantizations thereof called W-algebras and Yangians, respectively, as well as their analogues for affine Lie algebras which are naturally described using the theory of vertex algebras. Then I’ll explain a construction of vertex algebras associated to divisors in toric Calabi-Yau threefolds, which include affine W-algebras … Read More
Abstract: The “Algebra of the Infrared” refers to a collection of homotopical algebra structures (discovered by Gaiotto-Moore-Witten) that one associates to a massive two-dimensional N=(2,2) quantum field theory (subject to certain constraints). This provides a powerful framework for working out the category of boundary conditions of such QFTs. Specializing to the example of massive Landau-Ginzburg models, one is lead to a … Read More