Event Category: Berkeley String-Math Seminar

Berkeley String-Math Seminar

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Abstract: [Joint work with Arvin Shahbazi-Moghaddam.] We prove a singularity theorem based on the covariant entropy bound. The theorem connects singularities to quantum information, and it eliminates the assumption of noncompactness from Penrose’s 1965 theorem. A quantum extension of our theorem further eliminates the null energy condition. It can be applied to an evaporating black hole, where it leads to … Read More

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Abstract: In almost all situations, the twist of a supersymmetric QFT has the structure of a holomorphic QFT. I’ll review general aspects of holomorphic QFT while drawing parallels to the familiar situation of chiral CFT. I will then define a holomorphic model which we propose describes the minimal twist of the six-dimensional superconformal theory associated to the Lie algebra sl(2). … Read More

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Abstract: In this talk I will explain how 3d mirror symmetry predicts an equivalence between 2-categories associated to dual pairs of hyperkahler quotients. The first 2-category is of an algebro-geometric flavor and was described by Kapustin/Rozansky/Saulina. The second category depends on symplectic topology and has a conjectural description in terms of the 3d generalized Seiberg-Witten equations. Both of these 2-categories are expected … Read More

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ABSTRACT: It was shown by M.Aganagic and A.Okounkov that the relative insertions in the quantum K-theory of Nakajima varieties are equivalent to non-singular descendent insertions. Among other things, this result leads to integral representation for solutions of qKZ equations and explicit description of the Bethe vectors.      From representation theoretic viewpoint, the result of Aganagic-Okoukov deals with the “slope” zero … Read More

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3d N=4 gauge theories admit two topological twists, “A” and “B”, which are expected to give rise to extended TQFT’s. Aspects of these TQFT’s are starting to be defined mathematically. My goal in this talk is to discuss recent developments in understanding line operators (the value of the TQFT’s on a circle), which are expected to form a dg braided … Read More

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Abstract: The goal of this talk will be to describe the relation between generators of Lagrangian Floer cohomology on a surface and functions on its mirror — both locally on building blocks such as cylinders, pairs of pants, and mirrors of pairs of pants, and globally on elliptic curves, higher genus surfaces, and their mirrors. The common theme throughout will be … Read More

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Abstract: The spectral decomposition of the Hilbert space of automorphic functions is a very old and central topic in number theory, and mathematics in general. In particular, the Eisenstein series produce automorphic functions on a group G from automorphic functions on its Levi subgroups and one is interested in spectrally decomposing them. I will review some classical as well as … Read More

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Abstract: I will explain how a recent “universal wall-crossing”framework of Joyce works in equivariant K-theory, which I view as amultiplicative refinement of equivariant cohomology. Enumerativeinvariants, possibly of strictly semistable objects living on the walls, are controlled by a certain (multiplicative version of) vertex lgebra structure on the K-homology groups of the ambient stack. In very special settings like refined Vafa-Witten … Read More

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Ozsváth-Szabó’s Heegaard Floer homology is a holomorphic curve analogue of the Seiberg-Witten Floer homology of closed 3-manifolds. Bordered Heegaard Floer homology is an extension of (one version of) Heegaard Floer homology to 3-manifolds with boundary, developed jointly with Ozsváth and Thurston. This talk is an overview of bordered Heegaard Floer homology. We will start by describing the structure and aspects … Read More