Geodesics and minimal surfaces
Abstract: There are several properties of closed geodesics which are proven using its Hamiltonian formulation, which has no analogue for minimal surfaces. I will talk about some recent progress in proving […]
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Donaldson-Thomas invariants and hyperkahler manifolds: the example of theories of class S[A1]
Abstract: I will report on a project which aims to encode the DT invariants of a CY3 triangulated category in a geometric structure on its stability space. I will focus on […]
Tropical Lagrangian multi-sections and locally free sheaves
Abstract: The SYZ proposal suggests that mirror symmetry is T-duality. It is a folklore that locally free sheaves are mirror to a Lagrangian multi-section of the SYZ fibration. In this talk, I will introduce the notion […]
Birkhoff’s conjecture on integrable billiards and Kac’s problem “hearing the shape of a drum”
Abstract: Billiards on an elliptical billiard table are completely integrable: phase space is foliated by invariant submanifolds for the billiard flow. Birkhoff conjectured that ellipses are the only plane domains with […]
Elliptic chiral homology and chiral index
Abstract: We present an effective quantization theory for chiral deformation of two-dimensional conformal field theories. We explain a connection between the quantum master equation and the chiral homology for vertex operator […]
Gopakumar-Vafa type invariants of holomorphic symplectic 4-folds
Abstract: Gromov-Witten invariants of holomorphic symplectic 4-folds vanish and one can consider the corresponding reduced theory. In this talk, we will explain a definition of Gopakumar-Vafa type invariants for such a reduced […]