Location: 507 Mathematics Building
Time: Friday 1:30pm-3:00pm
Organiser: Yoonjoo Kim, Tianqing Zhu
Seminar schedule:
Jan 30
Speaker: Tianqing Zhu
Title: Higher dimensional Hitchin fibrations
Abstract: I will give a brief introductory talk on Chen-Ngô's paper (1905.04741) pioneering work on the higher dimensional analog for the Hitchin fibration. We will also talk about some recent progress on this direction if time is allowed.
Feb 6 Yoonjoo Kim ( 1:00pm-2:30pm Note for the special time! )
Title: Tate-Shafarevich twist of abelian fibrations and sections
Abstract: I will talk about Kollár's preprint (arXiv:2504.21705) on degenerations of abelian torsors, their twists, and sections. A degeneration of abelian torsors may or may not have a (rational) section. When it doesn't have a section, one tries to "twist it" in the hope of building up a section. The paper gives a necessary and almost sufficient condition to achieve this.
Feb 13 James Hotchkiss
Title: The semiregularity theorem
Abstract: Suppose we are given a family of smooth projective varieties, and a coherent sheaf on a special fiber. The semiregularity theorem (due in increasing generality to Bloch, Buchweitz and Flenner, and Pridham) is a simple and beautiful criterion for when the sheaf may be deformed to nearby fibers. I will give a modern formulation (and maybe proof) of the result, and explain how it fits into Markman's preprint on the proof of the Hodge conjecture for abelian fourfolds.
Feb 20 Hanlin Cai
Title: Cartier duality for (gerbes of) vector bundles
Abstract: I will discuss Rodrigues Camargo’s recent preprint (arXiv:2512.24967) regarding Cartier duality for gerbes of vector bundles. I will begin by reviewing classical manifestations of Cartier duality, such as the Fourier transform and the duality of finite flat commutative group schemes. Building on this foundation, I will describe how these concepts are interpreted within the framework of vector bundles. Finally, I will explain the 'twisted' generalization: Cartier duality for gerbes of vector bundles.
Feb 27 Anh Ðúc Võ
Mar 6 Yifan Wu
Mar 13 Che Shen
Mar 27 Gyujin Oh
Apr 3 Shijie Dai
Apr 10 Jiahe Shen
Apr 17 Andrés Ibáñez Núñez
Apr 24 Matthew Hase-Liu
May 1 Tommaso Maria Botta