Equivariant Kähler model for Fujiki's class C

报告人：Jia Jia(贾甲), Tsinghua University

摘要：Let X be a compact complex manifold in Fujiki's class C, i.e., admitting a big (1,1)-class [\alpha]. Consider Aut(X) the group of biholomorphic automorphisms and Aut_{[\alpha]}(X) the subgroup of automorphisms preserving the class [\alpha] via pullback. We show that X admits an Aut_{[\alpha]}(X)-equivariant Kähler model. I will talk several applications. We show that Aut_{[\alpha]}(X) is a Lie group with only finitely many components, which generalises an early result of Fujiki and Lieberman on the Kähler case. We also show that every torsion subgroup of Aut(X) is almost abelian, and Aut(X) is finite if it is a torsion group. This is based on a joint work with Sheng Meng.

时间：2023-12-23 16:00-17:00

地点：Room A-110, TSIMF

Bounding anti-canonical volumes of singular Fano threefolds

报告人：Zou Yu(邹瑜), Tsinghua University

摘要：In this talk, I will present our recent work concerning the explicit upper bound for anti-canonical volumes of e-lc Fano threefolds. More generally, We provide a reasonably small explicit upper bound with a sharp order, for the anti-canonical volumes of threefolds of e-lc Fano type (0＜e＜1/3). This is a joint work with Chen Jiang.

时间：2023-12-23 14:30-15:30

地点：Room A-110, TSIMF

On tate milnor-witt motives

报告人：Nanjun Yang(杨南君), Beijing Institute of Mathematical Sciences and Applications

摘要：Smooth projective Gm-varieties with isolated rational fixed points admit Tate Milnor-Witt motives. Over Euclidean fields, we give a splitting for- mula of such motives, which reduces the computation their Chow-Witt groups to that of their Chow groups and cohomologies of Witt sheaf. This a joint work with Jean Fasel.

时间：2023-12-23 09:00-10:00

地点：Room A-110, TSIMF

Beilinson-Parshin adeles via solid algebraic geometry

报告人：Chris Brav, Moscow Institute of Physics and Technology

摘要：We give an introduction to solid algebraic geometry, in the sense of Clausen-Scholze, a refinement of classical algebraic geometry built on spectra of solid rings, a certain category of “topological” rings including classical adic-like topological algebras. We show that the additional locality afforded by working with a larger collection of test spectra leads to a new construction of adelic decompositions of quasi-coherent sheaves, in the form of Beilinson-Parshin. This is joint work Grigory Konovalov.

时间：2023-12-23 10:30-11:30

地点：Room A-110, TSIMF

Explicit bounds of singularities on Fano fibrations

报告人：Chen Bingyi (陈炳仪）, YMSC, Tsinghua University

摘要：It was conjectured by McKernan and Shokurov that given a Fano fibration from X to Z, the singularities on Z are bounded in terms of those on X. Recently this conjecture was proved by Birkar. In this talk, I will discuss explicit bounds of singularities on Z in this conjecture in relative dimension one and in the toric case.

时间：2023-12-23 13:00-14:00

地点：Room A-110, TSIMF