Event Category: Berkeley String-Math Seminar

Berkeley String-Math Seminar

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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

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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

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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

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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

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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.

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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

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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

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Abstract: In the first part of the talk, I will recall Kazhdan-Lusztig’s geometric realization of the affine Hecke algebra H_q as well as Bezrukavnikov’s categorification of the statement. One of the fundamental tools of the theory is the so-called asymptotic affine Hecke algebra introduced by Lusztig (it can be thought of as a “limit” of H_q as “q goes to … Read More

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Abstract: To each compact, orientable surface S whose connected components have non-empty boundary, we define a dg category whose objects are neatly embedded 1-manifolds in S. In the case when S is a disk, this recovers the so-called “Bar-Natan category”: the natural setting for Khovanov’s celebrated categorification of the Jones polynomial. We expect that these dg categories form part of the … Read More

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ABSTRACT: Given a Riemann surface C and a central charge c, one can define the notion of Virasoro conformal block. Virasoro conformal blocks capture universal features of conformal field theory on C. I will describe a new scheme for constructing Virasoro conformal blocks at central charge c=1, by relating them to simpler “abelian” objects, namely conformal blocks for the Heisenberg … Read More