关于举行代数拓扑与几何系列学术研讨会II的通知

报告人

报告主题及摘要

报告时间

Hana Jia Kong (Institute for Advanced Study)

报告题目: Calculations in the motivic stable homotopy category

报告摘要: Calculations in the motivic category are interesting and have close connections to number theory as well as classical stable homotopy theory. One example of motivic applications in the classical theory is the Adams spectral sequence computations by Isaksen—Wang—Xu. They base their approach on a theoretical result by Gheorghe—Wang—Xu about a t-structure on the p-complete cellular C-motivic category. I will first talk about a generalization of this result, joint with Tom Bachmann, Guozhen Wang, and Zhouli Xu. The generalization leads to computational applications in the classical and motivic Adams spectral sequences. Another important computational tool in the classical theory is the Adams–Novikov spectral sequence. I will talk about its motivic analog, the motivic slice spectral sequence, and how it computes the motivic ’image-of-j’ spectrum defined by Bachmann–Hopkins. The slice computation is joint with Eva Belmont and Dan Isaksen. The comparison between the motivic slice spectral sequence and the motivic Adams spectral sequence parallels the classical Adams and Adams–Novikov spectral sequences.

9:10-10:10

Guozhen Wang (Fudan University)

报告题目: Topological cyclic homology of local fields

报告摘要: We introduce a new method for computing topological cyclic homology of locally complete intersections over p-adic intergers, by using relative hochschild homology and resolving the base ring spectrum with an Adams reslolution. Using the Nygaard filtration on the E1-term, we can construct algebraic Tate and algebraic homotopy fixed points spectral sequences, which are algebraic and catpture lots of informations in the Tate and homotopy fixed points spectral sequences computing T P and T C−1 . Using this method, we can give a uniform way of computing topological cyclic homology of local fields of mixed characteristic.

10:30-11:30

Xiaowen Hu (Sun Yat-Sen University)

报告题目: Mirror symmetry of quadric hypersurfaces

报告摘要: We show mirror symmetry of quadric hypersurfaces, in terms of identification of the associated Frobenius manifolds. We will explain several key points: compactification and desingularization of Givental’s mirror Landau-Ginzburg models, and the computation of the so-called broad periods, which mirror the quantum cohomology of quadric hypersurfaces involving the primitive cohomology class. We will also present some related unsolved problems.

14:00-15:00

Chunyi Li (University of Warwick)

报告题目: Bridgeland stability conditions on the Hilbert scheme of K3 surfaces

报告摘要: The bounded derived category of coherent sheaves on varieties has been an active subject in algebraic geometry for decades. In the past few years, Bridgeland stability conditions have become one of the most powerful tools in studying problems in derived categories. We will talk about some aspects of stability conditions, including the background, motivational questions, and applications. 1 2 We finish the talk with one of our recent results in which we construct a family of stability conditions on the Hilbert scheme of K3 surfaces.

15:30-16:30