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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 | The Base Change Of Fundamental Group Schemes |
| 李灵光 | |
| Let \(k\) be a field, \(K/k\) a field extension, \(X\) a connected scheme proper over \(k\), \(x_K\in X_K(K)\) lying over \(x\in X(k)\), \(\mathcal{C}_X\) and \(\mathcal{C}_{X_K}\) the Tannakian categories whose objects consist of vector bundles on \(X\) and \(X_K\) respectively, \(\pi(\mathcal{C}_X,x)\) and \(\pi(\mathcal{C}_{X_K},x_K)\) the corresponding Tannaka group schemes respectively. We give a unified criterion for base change isomorphism of Tannakian fundamental group schemes \(\pi(\mathcal{C}_{X_K},x_K)\xrightarrow{\cong} \pi(\mathcal{C}_X,x)_K.\) As an application, we generalize the base change isomorphism of certain fundamental group schemes under separable extension and extension of algebraically closed fields, such as S, Nori, EN, F, Étale, Loc, ELoc and Unipotent fundamental group schemes. |
| 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 | TBA |
| 陈炳仪 | |
| 中午 | 午餐 |
| 14:30–17:00 | 自由讨论 |