学术科研

Hans Jockers：Remarks on Modularity in Quantum KTheory
Abstract: In this talk we present some observations about the modular properties of 3d BPS halfindices of particular N=2 3d gauge theories. These indices connect to quantum Ktheory via the 3d gauge theory quantum Ktheory correspondence. They are solutions to certain qdifference equations, which — for particular classes of N=2 3d gauge theories — relate to the theory of bilateral qseries ...
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Nawaz Sultani：GromovWitten invariants of some nonconvex complete intersections
Abstract: For convex complete intersections, the GromovWitten (GW) invariants are often computed using the Quantum Lefshetz Hyperplane theorem, which relates the invariants to those of the ambient space. However, even in the genus 0 theory, the convexity condition often fails when the target is an orbifold, and so Quantum Lefshetz is no longer guaranteed. In this talk, I will showcase a method to...
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Zijun Zhou: Virtual Coulomb branch and quantum Ktheory
Abstract: In this talk, I will introduce a virtual variant of the quantized Coulomb branch by BravermanFinkelbergNakajima, where the convolution product is modified by a virtual intersection. The resulting virtual Coulomb branch acts on the moduli space of quasimaps into the holomorphic symplectic quotient T^*N///G. When G is abelian, over the torus fixed points, this representation is a Verma m...
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Yang Zhou：Quasimap wallcrossing and applications
Abstract: The theory of GromovWitten invariants is a curve counting theory defined by integration on the moduli of stable maps. Varying the stability condition gives alternative compactifications of the moduli space and defines similar invariants. One example is epsilonstable quasimaps, defined for a large class of GIT quotients. When epsilon tends to infinity, one recovers GromovWitten in...
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Jie Zhou: Twisted Sectors in QuasiHomogeneous Polynomial Singularities and Automorphic Forms
Abstract: We study oneparameter deformations of CalabiYau type Fermat polynomial singularities along degreeone directions. We show that twisted sectors in the vanishing cohomology are automorphic forms for certain triangular groups. We prove consequentially that genus zero GromovWitten generating series of the corresponding Fermat CalabiYau varieties are components of automorphic forms. The...
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Cheng Shu：Mixed Hodge polynomial of character variety
Abstract: Hausel, Letellier and RodriguezVillegas computed the Epolynomial of character varieties with generic semisimple conjugacy classes. Their computation led to a conjectural formula for the mixed Hodge polynomial of character varieties. We will recall their results and introduce a new family of character varieties that are unitary in the global sense. The same method gives a conjectural f...
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Mark Shoemaker：Towards a mirror theorem for GLSMs
Abstract: A gauged linear sigma model (GLSM) consists roughly of a complex vector space V, a group G acting on V, a character \theta of G, and a Ginvariant function w on V. This data defines a GIT quotient Y = [V //_\theta G] and a function on that quotient. GLSMs arise naturally in a number of contexts, for instance as the mirrors to Fano manifolds and as examples of noncommutative c...
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Yingchun Zhang：Local Seiberg Duality to flag variety and tautological bundles over flag variety
Abstract: Seiberg Duality conjecture is proposed by Yongbin Ruan and relates GLSM of two different quivers related via quiver mutation. In this talk, I will introduce the result of the conjecture applied to $A_n$ type quiver and we prove that small I functions of flag variety (before duality) and a complete intersection in another quiver (after mutation) are equal under variable change.&...
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Xiaohan Yan: Quantum Ktheory of flag varieties via nonabelian localization
Abstract: Quantum Ktheory studies the Ktheoretic analogue of GromovWitten invariants defined as holomorphic Euler characteristics of sheaves on the moduli space of stable maps. Generating functions of such invariants, which are called the (Ktheoretic) big Jfunctions, play a crucial role in the theory. In this talk, we provide a reconstruction theorem of the permutationinvariant big Jfunctio...
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