Event Category: Berkeley String-Math Seminar

Berkeley String-Math Seminar

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Abstract:  Many interesting varieties can be realized as the Coulomb branch of a 3d N=4 gauge theory, and this realization can give us some very interesting information.  One of the most familiar varieties that appears this way is the cotangent bundle of the Grassmannian of k-planes in C^n.  I’ll explain this realization as a special case of the more general … Read More

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Abstract: In this talk I will start with introducing a new presentation of deformed double current algebra of type gl_k, denoted by A^{(k)}, which is motivated from the study of M2 branes in the twisted M-theory. Then I will explain how to find an algebra embedding from A^{(k)} to the mode algebra of W^{(k)}_\infty, which is a matrix-extended generalization of … Read More

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This is the first of two talks. I will give an overview on algebraic categorification of tensors products of type A quantum group representations emphasising the role of (categorified) skew Howe duality. The results are in principle not new, but the focus will be on explaining the advantages and disadvantages of the existing approaches. In particular I like to illustrate … Read More

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Starting from braided monoidal categories of quantum group representations and categorification results one comes to the question whether categorification can be used to construct a corresponding braided monoidal 2-category. In this talk we start from the observation that the Hecke algebras for all symmetric groups taken together form a braided monoidal category that controls all quantum link invariants of type … Read More

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This talk is based on joint work in progress with Mina Aganagic, Spencer Tamagni and Peng Zhou. We’ll discuss work in progress toward a homological mirror symmetry statement. The A side is the k-fold symmetric product of a double cover of the cylinder ramified at n points. The B side is a matrix factorization category on the k-th horizontal hilbert scheme … Read More

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Abstract: The affine Hecke category, defined using affine Soergel bimodules, categorifies the affine Hecke algebra. I will compare the derived horizontal trace of the affine Hecke category with the elliptic Hall algebra, and with the derived category of the commuting stack. In particular, I will describe certain explicit generators for the trace category and some categorical commutation relations between these. … Read More

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3d mirror symmetry is a duality for certain hyperkähler manifolds. This talk will explore its connections with 2d mirror symmetry, as a 3d analog of ‘Mirror Symmetry is T-duality’ by Strominger, Yau, and Zaslow, which described 2d mirror symmetry via 1d dualities. Based on joint works with Naichung Conan Leung.

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Abstract: The correspondence of AGT sets up, in part, a connection between six-dimensional superconformal theories and 2d CFT. We will give a mathematical construction of 2d CFT from 6d SCFT which involves recent progress in our understanding of the holomorphic twist 6d superconformal symmetry. We then turn to the question of enhancement of familiar structures in 2d CFT to 6d … Read More

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Abstract: Symplectic geometry plays a crucial role in string theory through the lens of mirror symmetry, a duality that connects it to complex geometry. This connection is formalized in M. Kontsevich’s celebrated 1994 ICM conjecture on homological mirror symmetry (HMS), providing a powerful algebraic framework to study these dualities. While HMS has been established for mirrors of Calabi-Yau and Fano … Read More