会议时间：2026年5月8日-10日
会议地点：科大东区物质科研楼C1124
报告人
郝峰（山东大学 ）
胡飞（南京大学）
江智（复旦大学/上海数学中心）
刘杰（中国科学院数学与系统科学研究院）
余成龙（上海数学与交叉学科研究院）
袁瑶（首都师范大学）
张通（华东师范大学）
朱智贤（首都师范大学）
组委会：刘永强（中国科学技术大学）
张磊（中国科学技术大学）
主办单位：中国科学技术大学
会议日程：TBA
题目&摘要
郝峰（山东大学）
Title: Diffeomorphism types of simply connected 3-dimensional Mori fibre spaces
Abstract: Isikovski, Mori, and Mukai showed that Fano threefolds admit finitely many (105) diffeomorphism types. In this talk, I will discuss the diffeomorphism types of three dimension Mori fibre spaces. For three dimensional simply connected Mori fibre spaces with torsion free cohomologies, we introduce finitely many numerical invariants classifying the their diffeomorphism types. This is a joint work with Yang Su and Jianqiang Yang.
胡飞（南京大学）
Title: A gap principle for polynomial volume growth of zero-entropy automorphisms
Abstract: Let X be a normal projective variety of dimension d and f an automorphism of X with zero entropy. We prove that if the degree growth of f is maximal, i.e., deg_1(f^n) \asymp n^{2d-2}, then the polynomial volume growth satisfies plov(f) = d^2. As a consequence, we establish a gap principle: the polynomial volume growth plov(f) cannot take any value in the open interval (d(d-1), d^2). This reveals a new rigidity phenomenon for the polynomial volume growth of zero entropy automorphisms. This is joint work with Chen Jiang.
江智（复旦大学）
Title: The Barja-Pardini-Stoppino inequalities and classifications of irregular surfaces of general type
Abstract: Barja, Pardini, and Stoppino introduced some new Severi-type inequalities for surfaces of general type about 10 years ago. We will show when equalities hold for these surfaces. As an application, we have some new results on fine classification of irregular surfaces. This is a joint work with Songsong Huang.
刘杰（中国科学院数学与系统科学研究院）
Title: Symplectic singularities via cotangent bundles
Abstract: I will provide a brief introduction to the notion of symplectic singularities, as introduced by Beauville. I will then present a novel construction of symplectic singularities using the cotangent bundle of smooth varieties, and discuss its applications to the Ginzburg–Kazhdan conjecture and the Kaledin–Lehn–Sorger conjecture. This is based on joint work with Bohua Fu.
余成龙（上海数学交叉中心）
Title: Rigidity Criterion for Certain Calabi-Yau families
Abstract: Based on joint work with Ruiran Sun and Kang Zuo, this talk presents a new rigidity criterion for families of polarized Calabi-Yau manifolds over quasi-projective curves. Motivated by the observation that non-rigid examples typically degenerate along higher-dimensional singular loci, we conjecture that a family is rigid if it admits a smooth compactification whose singular fiber has only isolated singularities. We verify this conjecture for a broad class of singularities with concentrated mixed Hodge spectrum—including ordinary double points and cusps. We also discuss the relationship of our results to C.-L. Wang’s work on the Weil–Petersson metric near certain degenerations.
袁瑶（首都师范大学）
Title: Lefschetz filtration and Perverse filtration on the compactified Jacobian.
Abstract: Let $C$ be a complex integral curve with plannar singularities. Let $J$ be the compactified Jacobian of $C$. There are two filtrations on the cohomology group $H^*(J)$. One is obtained by the nilpotent morphism defined by cupping a certain ample divisor on $J$, which we call the Lefschetz filtration. To obtain the other filtration, we put $C$ into a family of curves $\mathcal{C}\rightarrow B$ so that $J$ can be embedded into a family $f:\mathcal{J}\rightarrow B$, and we let $B, \mathcal{C},\mathcal{J}$ be smooth. Then $Rf_*(\mathbb{Q}_{\mathcal{J}})$ decomposes into a direct sum of its (shifted) perverse cohomologies. Restricting this decomposition to fibers, we get a filtration on $H^*(J)$ called the perverse filtration. We show that these two filtrations are opposite to each other as conjectured by Maulik-Yun.
朱智贤（首都师范大学）
Title: On a conjecture of Kazhdan-Polishchuk
Abstract: At the 2022 ICM, David Kazhdan proposed a conjecture concerning a Brill–Noether-type variety naturally associated to any stable vector bundle of rank 2 and degree 2g-1 on a smooth projective curve of genus g. This is now known as the Kazhdan–Polishchuk conjecture. In this talk, we introduce a jet scheme approach to the conjecture. This is a joint work in progress with Zhiyu Tian.
张通（华东师范大学）
Title: Moduli spaces of threefolds on the Noether line
Abstract: 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.
