Event Category: Berkeley String-Math Seminar

Berkeley String-Math Seminar

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Khovanov showed, more than 20 years ago, that Jones polynomial emerges as an Euler characteristic of a homology theory. The knot categorification problem is to find a uniform description of this theory, for all gauge groups, which originates from physics, or from geometry. In these lectures, I will describe two solutions to this problem, which originate in string theory, and … Read More

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Khovanov showed, more than 20 years ago, that Jones polynomial emerges as an Euler characteristic of a homology theory. The knot categorification problem is to find a uniform description of this theory, for all gauge groups, which originates from physics, or from geometry. In these lectures, I will describe two solutions to this problem, which originate in string theory, and … Read More

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Khovanov showed, more than 20 years ago, that Jones polynomial emerges as an Euler characteristic of a homology theory. The knot categorification problem is to find a uniform description of this theory, for all gauge groups, which originates from physics, or from geometry. In these lectures, I will describe two solutions to this problem, which originate in string theory, and … Read More

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Khovanov showed, more than 20 years ago, that Jones polynomial emerges as an Euler characteristic of a homology theory. The knot categorification problem is to find a uniform description of this theory, for all gauge groups, which originates from physics, or from geometry. In these lectures, I will describe two solutions to this problem, which originate in string theory, and … Read More

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We introduce the notions of (G,q)-opers and Miura (G,q)-opers, where G is a simply-connected complex simple Lie group, and prove some general results about their structure. We then establish a one-to-one correspondence between the set of (G,q)-opers of a certain kind and the set of nondegenerate solutions of a system of Bethe Ansatz equations. Additionally we associate to a (G,q)-oper … Read More

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Abstract: Given a 3d N=4 supersymmetric quantum field theory, there is an associated Coulomb branch, which is an important reflection of the A-twist of this theory. In the case of gauge theories, this Coulomb branch has a description due to Braverman-Finkelberg-Nakajima; I’ll discuss how we can generalize this geometric description in order to construct non-commutative resolutions of Coulomb branches (giving … Read More

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Fix a Calabi-Yau 3-fold X. Its DT invariants count stable bundles and sheaves on X. The generalised DT invariants of Joyce-Song count semistable bundles and sheaves on X. I will describe work with Soheyla Feyzbakhsh showing these generalised DT invariants in any rank r can be written in terms of rank 1 invariants. By the MNOP conjecture these rank 1 … Read More

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Abstract: We study the Borel summation of the Gromov-Witten potential for the resolved conifold. The Stokes phenomena associated to this Borel summation are shown to encode the Donaldson-Thomas invariants of the resolved conifold, having a direct relation to the Riemann-Hilbert problem formulated by T. Bridgeland. There exist distinguished integration contours for which the Borel summation reproduces previous proposals for the non-perturbative … Read More