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| 8:50–9:00 | 会议注册 |
| 9:00–10:00 | Moduli spaces of threefolds on the Noether line |
| 张通 | |
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In this talk, I will discuss some recent results on classifying threefolds of general type with \(p_g \ge 5\) and with smallest possible canonical volume. This is a joint work with S. Coughlan, Y. Hu, and R. Pignatelli. |
| 10:00–10:20 | 茶歇 |
| 10:20–11:20 | Some Progress on the Fundamental Group Schemes |
| 李灵光 | |
| In this talk, I will present some progress on the fundamental group schemes concerning base change, Künneth formula, Lefschetz-type theorem, and birational invariance. This is a joint work with Niantao Tian and Hao Wang. |
| 11:20–11:30 | 茶歇 |
| 11:30–12:30 | F-bundles and Mirror Symmetry of Flag Varieties |
| 张驰 | |
| In this talk, I will give an introduction to F-bundle and its application to the mirror symmetry of flag varieties. F-bundle is a formal/non-archimedean version of variation of nc-Hodge structures which plays a crucial role in the theory of atoms as birational invariants from Gromov-Witten theory, recently developed by Ludmil Katzarkov, Maxim Kontsevich, Tony Pantev, Tony Yue Yu. The theory of F-bundle also provides a useful framework for proving the equivariant big mirror symmetry theorem for partial flag varieties. |
| 中午 | 午餐 |
| 14:30–15:30 | \(p\)-Jordan constants of Cremona group of rank 2 in odd characteristic |
| 陈亦飞 | |
| A classical theorem of C. Jordan asserts that finite subgroups in a general linear group over a field of characteristic zero contains normal abelian subgroups of bounded index. In general, a group G has Jordan property, if any finite subgroup of G contains a normal abelian subgroup of index at most J, where J is a constant only depending on G. J.P. Serre proves Cremona group of rank 2 has Jordan property, and he conjectures Cremona group of any rank has Jordan property. The conjecture is proved by Prokhorov-Shramov and Birkar. In this talk, we give explicit bounds for Cremona group of rank 2 in odd characteristic. This is a joint work with C. Shramov. |
| 15:30–16:00 | 茶歇 |
| 16:00–17:00 | Asymptotic Betti bounds for hypersurfaces in a singular variety |
| 张鼎新 | |
| I will explain how to use Chern-Schwartz-MacPherson classes and perverse sheaves to establish sharp upper bounds for the sum of Betti numbers of very ample hypersurfaces embedded in a projective variety, regardless of the singularity of the ambient variety. These bounds are asymptotically optimal as the degree of the hypersurface tends to infinity. This is joint work with Xuanyu Pan and Xiping Zhang. |
| 18:00 | 晚宴 |
| 09:00–10:00 | Inequalities for volume polynomials |
| 肖建 | |
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We give an overview on some different notions of volume polynomials in geometry and present a new family of inequalities for them. If time is permitted, we also discuss some applications to combinatorics. Joint work with June Huh, Mateusz Michalek and Botong Wang. |
| 10:00–10:20 | 合影、茶歇 |
| 10:20–11:20 | Toric orbits on cominuscule Grassmannians and modular compactifications |
| 方汉隆 | |
| The study of tame compactifications for quotients of cominuscule Grassmannians by diagonal torus actions has significant implications for modular problems in algebraic and arithmetic geometry. This talk will present recent joint works on this topic: first, with Songhao Zhu,with Xian Wu, and with Alex Massarenti and Xian Wu on the one-dimensional torus action case; second, with Mingyi Zhang on higher-dimensional torus action cases of rank 2; and finally, with Luca Schaffler, and Xian Wu on higher-dimensional cases of higher ranks. The discussion will conclude with several compelling open questions. |
| 11:20–11:30 | 茶歇 |
| 11:30–12:30 | Boundedness of singularities on Fano fibrations |
| 陈炳仪 | |
| Given a fibration, a natural and important question in birational geometry is to relate the singularities of the base space and those of the total space. Birkar in 2023 proved that for a Fano fibration, the singularities of the base space is bounded in terms of the singularities of the total space, which confirmed a conjecture of McKernan and Shokurov. In this talk, I will discuss some recent development on this conjecture, including effective bounds for this conjecture in some special cases and a generalization of this conjecture. Part of my talk is based on joint work with Caucher Birkar. |
| 中午 | 午餐 |
| 14:30–17:00 | 自由讨论 |