Event Category: Berkeley String-Math Seminar

Berkeley String-Math Seminar

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An early highlight of quantum topology was the observation that the Jones polynomial — and many other knot and link invariants — arise from braided monoidal categories of quantum group representations. In hindsight, this can be understood as underlying reason for the existence  of associated topological quantum field theories (TQFTs) in 3 and 4 dimensions. Not much later, Khovanov discovered … Read More

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Abstract:Schur quantization refers to a particular type of representation of the quantized algebras of functions on Coulomb branches of vacua of N=2, d=4 supersymmetric quantum field theories,  providing a quantum theoretical interpretation of the Schur indices. My talk will describe how the  Schur quantization encodes key aspects of the low energy physics of the underlying theory, and how it provides a new quantization of … Read More

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Abstract: Khovanov homology is a powerful link invariant which has numerous applications. It is powerful not only because it is a strong invariant, but also it is functorial and has many relations with other invariants. In 2018, Stoffregen-Zhang realized that there is a spectral sequence from the Khovanov homology of a periodic link to the annular Khovanov homology of its … Read More

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Abstract: Perverse schobers refer to perverse sheaves of (enhanced) triangulated categories, as introduced by Kapranov-Schechtman. Though their general theory remains conjectural, there exists a robust theory of perverse schobers on surfaces with boundary. In the talk, we will discuss how such perverse schobers naturally arise from cosheaves of Fukaya categories of Lefschetz fibrations constructed by Ganatra-Pardon-Shende. For instance, in the … Read More

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We count holomorphic curves in complex 3-space with boundaries on three special Lagrangian solid tori. The count is valued in the HOMFLYPT skein module of the union of the tori. Using 1-parameter families of curves at infinity, we derive three skein valued operator equations which must annihilate the count, and which dequantize to a mirror of the geometry. We show … Read More

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Abstract: The cohomological Hall algebra of a quiver can serve as model of an algebra of BPS states of a 4d N = 2 theory. We investigate modules for the CoHA which arise from (anti-)involutions of the underlying quiver, and find that the cohomology of moduli stacks of objects with classical type structure groups (e.g. for orthosymplectic quivers) gives a … Read More

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Mirror symmetry aims at equivalences of Fukaya categories (A-side) and categories of coherent sheaves (B-side). Deformed mirror symmetry aims at matching deformations of A-side and B-side. In this talk, I explain how to do it in case of mirror symmetry for punctured surfaces. We start by constructing gentle algebras and matrix factorizations, which serve as A-side and B-side. Then we … Read More

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Abstract:  Let X_0 be a rational surface with a cyclic quotient singularity (1,a)/r.  Kawamata constructed a remarkable vector bundle K_0 on X_0 such that the finite-dimensional algebra End(K_0), called the Kalck-Karmazyn algebra, “absorbs” the singularity of X_0 in a categorical sense.  If we deform over an irreducible component of the versal deformation space of X_0 (as described by Kollár and Shepherd-Barron), … Read More