Dr. Miguel Moreira (MIT)
Wall-crossing for K-theoretic invariants via non-abelian localization abstract
Abstract:
An important question with many practical applications in enumerative geometry is to understand how enumerative invariants attached to moduli spaces of sheaves/complexes/quiver representations change when we vary the stability condition. Wall-crossing for motivic invariants has been a central tool in Donaldson-Thomas theory of CY 3-folds. In a non-CY setting, more recently, Joyce developed a wall-crossing framework for cohomological invariants and Liu adapted his ideas to K-theoretic invariants. In this talk, I will explain a new approach to such wall-crossing formulas and an alternative way to define enumerative invariants in the presence of strictly semistable objects. This new framework extends the range of wall-crossing formulas we can prove, allowing us to deal for example with objects in the derived category of sheaves. This is joint work with Ivan Karpov.
13:00 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 43
Prof. Dr. Junliang Shen (Yale)
Cohomology of compactified Jacobians: Fourier transform and perverse filtration I abstract
Abstract:
The Fourier transform has played a crucial role in the cohomological study of Jacobians over the decades. Recently, in efforts to understand the P=W conjecture for the Hitchin system, a theory of Fourier transform was developed for (possibly singular) compactified Jacobians, where the perverse filtration comes into play naturally. The purpose of these lectures is to explain some applications of this circle of ideas in the study of cohomology of the more classical compactified Jacobians associated with stable curves. The (in)dependence of the cohomology ring on the degree and the stability condition will be discussed. Based on joint work in progress with Younghan Bae and Davesh Maulik.
14:15 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 43
Prof. Dr. Qizheng Yin (Peking University)
Cohomology of compactified Jacobians: Fourier transform and perverse filtration II abstract
Abstract:
The Fourier transform has played a crucial role in the cohomological study of Jacobians over the decades. Recently, in efforts to understand the P=W conjecture for the Hitchin system, a theory of Fourier transform was developed for (possibly singular) compactified Jacobians, where the perverse filtration comes into play naturally. The purpose of these lectures is to explain some applications of this circle of ideas in the study of cohomology of the more classical compactified Jacobians associated with stable curves. The (in)dependence of the cohomology ring on the degree and the stability condition will be discussed. Based on joint work in progress with Younghan Bae and Davesh Maulik.
15:45 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 43
Zhiyu Liu (Zhejiang Univeristy and ETH-ITS)
Brill-Noether, Bogomolov-Gieseker, Bayer-Macri-Toda
17:00 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 43