2022 Miniworkshop on interaction between geometric topology and mathematical physics
Place: Online. The tencent meeting id is 467771970(No password).
Time: 9am (Beijing time), 26 May, 2022
Speaker: Dr. Peng Zhao (ITP)
Title: Remarks on 2d unframed quiver gauge theories
Abstract: 2d quiver gauge theories provide Kahler quotient construction of quiver varieties. By studying Seiberg-like dualities, we found a cluster algebra structure on the kahler moduli space.Mathematically, this translates to the equivalence of Gromov-Witten theories of quiver varieties related by cluster transformations, known as the Mutation conjecture. I will discuss examples of unframed quivers such as the kronecker quiver and the Markov quiver. They provide an infinite class of equivariant GIT quotients. Our physical analysis suggests a correspondence between the abelian necklace quiver and the nonabelian 2d SQCD.
Time: 10:30am (Beijing time), 26 May, 2022
Speaker: Dr. Yuhang Chen (OSU)
Title: Equivariant Moduli theories on K3 Surfaces
Abstract: We study the Hirzebruch-Riemann-Roch (HRR) theorem for proper smooth quotient Deligne-Mumford stacks, explore its relation with representation theory of finite groups, and derive a new orbifold HRR formula via an orbifold Mukai pairing. As a first application, we use this formula to compute the dimensions of G-equivariant moduli spaces of stable sheaves on a K3 surface X under the action of a finite subgroup G of its symplectic automorphism group. We then apply the orbifold HRR formula to reproduce the number of fixed points on X when G is cyclic without using the Lefschetz fixed point formula. We prove that under some mild conditions, equivariant moduli spaces of stable sheaves on X are irreducible symplectic manifolds deformation equivalent to Hilbert schemes of points on X via a connection between Gieseker and Bridgeland moduli spaces, as well as the derived McKay correspondence.As a corollary, these moduli spaces are also deformation equivalent to G-equivaraint Hilbert schemes of points on X.11:30am-12:30pm Lunch time
Time: 12:30pm (Beijing time), 26 May, 2022
Speaker: Fenglong You (Oslo)
Title: Relative quantum cohomology under birational transformations
Abstract: I will talk about how relative quantum cohomology, defined by Tseng-You and Fan-Wu-You, varies under birational transformations. Relation with FJRW theory and extremal transitions of absolute Gromov--Witten theory will also be discussed.
Time: 2 pm(Beijing time), 26 May, 2022
Speaker: Jeongseok Oh ( Imperial College London)
Title: Virtual cycles on projective completions
Abstract: For a compact quasi-smooth derived scheme M with (-1)-shifted cotangent bundle N,there are at least two ways to localise the virtual cycle of N to M via torus and cosection localisations, introduced by Jiang-Thomas. We produce virtual cycles on both the projective completion and projectivisation of N and show the ones on the former push down to Jiang-Thomas cycles and the one on the latter computes the difference. Using the idea we study the difference between quintic and twisted quintic Gromov-Witten invariants.
