Schedule:
January 8 Tom Rodewald (Georgia Tech)
December 25 Jun Zhang (USTC)
December 18 Siyang Liu (University of Southern California)
Title :Symplectic Aspects of Representation Theory of Hypertoric Varieties
Abstract: In this talk we will discuss a symplectic model for T-equivariant hypertoric category \mathscr{O} as constructed by Braden-Licata-Proudfoot-Webster, which is the Fukaya-Seidel category of complexified complement of hyperplane arrangements associated to the corresponding hypertoric variety. This would provide a categorification of K-theoretic stable envelopes for hypertoric varieties. This is partly based on the recent work collaborated with S. Lee, Y. Li, and C. Y. Mak and the work in preparation with S. Ganatra, W. Li, and P. Zhou.
December 11 Bohan Fang (PKU)
December 4 Yilin Wu (USTC)
November 27 Junxiao Wang (PKU)
Nov-20
Chris Brav (SIMIS)
Title: The cyclic Deligne conjecture and Calabi-Yau structures
Abstract:
The Deligne conjecture, many times a theorem, states that for a dg category C, the dg endomorphisms End(Id_C) of the identity functor-- that is, the Hochschild cochains-- carries a natural structure of 2-algebra. When C is endowed with a Calabi-Yau structure, then Hochschild cochains and Hochschild chains are identified up to a shift, and we may transport the circle action from Hochschild chains onto Hochschild cochains. The cyclic Deligne conjecture states that the 2-algebra structure and the circle action together give a framed 2-algebra structure on Hochschild cochains. We establish the cyclic Deligne conjecture, as well as a variation that works for relative Calabi-Yau structures on dg functors D --> C, more generally for functors between stable infinity categories. We discuss examples coming from oriented manifolds with boundary, Fano varieties with anticanonical divisor, and doubled quivers with preprojective relation. This is joint work with Nick Rozenblyum.
Oct 16 Ben Zhou (Tsinghua)
Title: Higher genus Gromov-Witten correspondences for log Calabi-Yau surfaces
Abstract: Strominger, Yau, and Zaslow (SYZ) phrased mirror symmetry as a duality between special Lagrangian fibrations over an affine manifold base. The Gross-Siebert program seeks to translate the SYZ conjecture into the language of algebraic geometry using toric degenerations and tropical geometry. From a toric log Calabi-Yau surface X with a smooth anticanonical divisor, one can construct a scattering diagram (which locally one associates a Poisson algebra) and its quantization using the Gross-Siebert program. One can then infer from the scattering diagram various kinds of Gromov-Witten invariants. I will explain the above terms, and how higher-genus correspondences between certain open, closed, and logarithmic Gromov-Witten invariants associated to the log Calabi-Yau surface X can be derived. Part of this is joint work with Tim Gr\"afnitz, Helge Ruddat, and Eric Zaslow.
Oct 9 Kenji Fukaya (Tsinghua)
Title: Categorification of Atiyah-Floer conjecture
Abstract: Atiyah-Floer conjecture relates two versions of Floer homologies one in gauge theory the other in symplectic geometry. I will explain how we “upgrade”it to a functorial equivalence of 2-A-infinity categories. Also I will explain its 2-3 dimensional topological Field theory and Lagrangian correspondences.
