Event Category: Berkeley String-Math Seminar

Berkeley String-Math Seminar

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Abstract : I will report an on-going joint project with Hanany and Finkelberg. We identify Coulomb branches of orthosymplectic quiver gauge theories with orthosymplectic bow varieties. Then we use this identification to realize closures of nilpotent orbits for SO, and more as Coulomb branches.

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In the third talk, we discuss how quasimaps can be used to translate S-duality of Vafa-Witten invariants of Curve x Curve’ to a duality of quasimap invariants of moduli spaces of Higgs bundles on Curve. This provides an enumerative realization of Kapustin-Witten’s dimensional reduction in the case of SL and PGL.                

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Abstract : I will report an on-going joint project with Hanany and Finkelberg. We identify Coulomb branches of orthosymplectic quiver gauge theories with orthosymplectic bow varieties. Then we use this identification to realize closures of nilpotent orbits for SO, and more as Coulomb branches. (continuation).

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Abstract: Donaldson-Thomas theory associates integers (which are virtual counts of sheaves) to a Calabi-Yau threefold X. The simplest example is that of C^3, when the Donaldson-Thomas (DT) invariant of length d sheaves is p(d), the number of plane partitions of d.  The DT invariants have several refinements, for example a cohomological one, where instead of a DT invariant, one studies … Read More

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Abstract: Donaldson-Thomas theory associates integers (which are virtual counts of sheaves) to a Calabi-Yau threefold X. The simplest example is that of C^3, when the Donaldson-Thomas (DT) invariant of length d sheaves is p(d), the number of plane partitions of d.  The DT invariants have several refinements, for example a cohomological one, where instead of a DT invariant, one studies … Read More

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I will give an update on the dictionary between the representations of quantum toroidal algebras and branes of Type IIB string theory. I will argue that brane crossings correspond to R-matrices, of which the “degenerate resolved conifold” is one example. A more interesting example is given by the “Hanany-Witten R-matrix”, for which the brane creation effect and Hanany-Witten rules become … Read More

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In a few cases, for a quasiprojective suface S it is known that there are vertex algebras which provide formulas for enumerative invariants of moduli spaces of sheaves on S. I will explain a number of examples where this is known or expected to hold and focus on extending this structure to the case of elliptic surfaces. I will describe … Read More

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Abstract: Given a polarized hyperplane arrangement, Braden-Licata-Proudfoot-Webster defined two convolution algebras: A &  B. We show that both of them can be realized as Fukaya categories of hypertoric varieties. This proves a conjecture of Braden-Licata-Phan-Proudfoot-Webster in 2009 and gives a geometric interpretation of the Koszul duality between A & B. The proof relies on the construction of non-commutative vector fields … Read More

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Abstract: In 2013, Beem-Lemos-Liendo-Peelaers-Rastelli-van Rees constructed a correspondence between four dimensional N=2 SCFTs, a certain kind of supersymmetric quantum field theory, and vertex algebras. When applied to the theories of class S, one obtains a rich family of vertex algebras which furnish novel representations of critical level, affine Kac-Moody algebras. Moreover, these vertex algebras satisfy an intricate set of gluing … Read More

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Abstract: By now it is known that many interesting phenomena in geometry and representation theory can be understood as aspects of mirror symmetry of 3d N=4 SUSY QFTs. Such a QFT is associated to a hyper-Kähler manifold X equipped with a hyper-Hamiltonian action of a compact Lie group G and admits two topological twists. The first twist, which is known as … Read More