Fall 2025
Seminar time and location:
Thursday 15:00-16:00, Jingchunyuan 77201
Information can also be found on Professor Qizheng Yin's webpage or the official webpage.
September 11th
Speaker: 邵维力(Weili Shao) (Xiamen University)
Title: On local accumulation complexity of the set of log canonical volumes in dimension ≥ 2
Abstract: For a projective log canonical pair (X,B) of log general type, the set of volumes vol(X,K_X+B) satisfies the Descending Chain Condition (DCC) when the coefficients of the boundary divisor lie in a given DCC set. A natural further direction is to investigate the fine distribution of these volumes, particularly the structure of their (iterated) accumulation points.
In this talk, I will survey known results on the accumulation behavior of volumes and present recent progress on their iterated accumulation structure. Through explicit geometric constructions, we prove that even in the simplest case where the coefficient set is {0}, the local accumulation complexity of the volume set can be infinite. Our approach builds upon earlier work by Blache and Alexeev–W. Liu.
October 9th
Speaker: 许世坦(Shitan Xu) (Peking University)
Title: Rationality of Brauer-Severi Surface Bundles over Rational 3-folds.
Abstract: Rationality problems for conic bundles have been well studied over surfaces. In this talk, we generalize an etale cohomology diagram from the case of conic bundles to Brauer-Severi surface bundles over rational 3-folds . We use this generalization to prove a sufficient condition for a Brauer-Severi surface bundle to be not stably Rational. We also give an example satisfying these sufficient conditions.
October 16th
Speaker: 鈴木文顕(Fumiaki Suzuki) (Peking University)
Title: On direct summands of products of Jacobians over arbitrary fields
Abstract: We show that a principally polarized abelian variety over a field k is, as an abelian variety, a direct summand of a product of Jacobians of curves which contain a k-point if and only if the polarization and the minimal class are both algebraic over k. This extends results of Beckmann-de Gaay Fortman and Voisin over the complex numbers to arbitrary fields, and refines an obstruction to the direct summand property over the rational numbers due to Petrov-Skorobogatov. We then give applications to the integral Tate conjecture for 1-cycles on abelian varieties over finite fields, including the case ell=p. This is joint work with Federico Scavia.
October 23rd
Speaker: Giovanni Inchiostro (University of Washington)
Title: Stable maps to quotient stacks and KSBA-compactifications of surfaces fibered in log Calabi-Yau pairs
Abstract: I will present a compactification of the moduli space of maps from families of curves, to certain moduli spaces M, via the example of M being the GIT moduli space of binary forms of degree 2n. One application of our results is the construction of certain moduli of surfaces and threefolds fibered log Calabi-Yau pairs. I will then explain how to use these moduli spaces to study the boundary of certain KSBA-moduli spaces of surfaces fibered in log Calabi-Yau pairs. This is based on a joint work with Andrea Di Lorenzo, and a joint work with Roberto Svaldi and Junyan Zhao.
October 30th
Speaker: 吴磊(Lei Wu) (Zhejiang University)
Title: Generalized nearby cycles via logarithmic and relative D-modules
Abstract: Nearby cycles for D-modules along a hypersurface was introduced by Kashiwara and Malgrange by using the so called V-filtrations and by Beilinson-Bernstein by using b-functions in 1980s, which provide a powerful tool in algebraic geometry and representation theory.
In this talk, I will construct (generalized) nearby cycles for regular holonomic D-modules along F, a finite union of hypersurfaces motivated by the method of Beilinson-Bernstein. Then I will give a logarithmic interpretation of Bernstein-Sato ideals of F by using the log structures induced from the graph embedding of F. Finally, I will explain that the relative support of the (generalized) nearby cycles along log stratas are determined by the zeroes of the Bernstein-Sato ideals along the same strata, which generalizes a classic result of Kashiwara and Malgrange.
November 6th
Speaker: 戸田幸伸 Yukinobu Toda (IPMU)
Title: The Dolbeault geometric Langlands conjecture via limit categories
Abstract: In this talk, I will give more mathematical details of my talk on Nov 4. I will introduce the notion of limit categories for cotangent stacks of smooth stacks as an effective version of classical limits of the categories of D-modules on them. Using the notion of limit categories, I will propose a precise formulation of the Dolbeault geometric Langlands conjecture, proposed by Donagi-Pantev as the classical limit of the geometric Langlands correspondence. I will show the existence of a semiorthogonal decomposition of the limit category into quasi-BPS categories, which (when G=GL_r) categorify BPS invariants on a non-compact Calabi–Yau 3-fold playing an important role in Donaldson-Thomas theory. This semiorthogonal decomposition is interpreted as a Langlands dual to the semiorthogonal decomposition for moduli stacks of semistable Higgs bundles, obtained in our earlier work as a categorical analogue of PBW theorem in cohomological DT theory. It in particular yields a conjectural equivalence between quasi-BPS categories, which gives a categorical version of Hausel-Thaddeus mirror symmetry for Higgs bundles (for any reductive group G). This is a joint work with Tudor Pădurariu (arXiv:2508.19624).
November 13th
Speaker: 邹瑜(Yu Zou) (Chongqing University)
Title: An optimal upper bound for anti-canonical volumes of canonical Fano threefolds
Abstract: In this talk, I will present a joint work with Chen Jiang and Tianqi Zhang on the upper bound for anti-canonical volumes of canonical Fano 3-folds. We confirm Prokhorov's conjecture that the optimal upper bound for anti-canonical volumes of canonical Fano 3-folds should be 72. We also characterize the equality case.
November 21st 10:00 a.m. (Note the special time)
Speaker: 胡飞(Fei Hu) (Nanjing University)
Title: Parity and symmetry of polarized endomorphisms on cohomology
Abstract: We show that the eigenvalues of any polarized endomorphism acting on the \ell-adic étale cohomology of a smooth projective variety satisfy certain parity and symmetry properties, as predicted by the standard conjectures.
These properties were previously known for Frobenius endomorphisms.
Besides the hard Lefschetz theorem, a key new ingredient is a recent Weil's Riemann hypothesis-type result due to J. Xie. We also prove a "Newton over Hodge" type property for abelian varieties and Grassmannians.
November 27th
Speaker: 余讯(Xun Yu) (Tianjin University)
Title: Nonrational Varieties with Unirational Parametrizations of Coprime Degrees
Abstract: We show that there exists a 2-dimensional family of smooth cubic threefolds admitting unirational parametrizations of coprime degrees. This together with Clemens--Griffiths' work solves the long standing open problem whether there exists a nonrational variety with unirational parametrizations of coprime degrees. Our proof uses a new approach, called the Noether--Cremona method, for determining the rationality of quotients of hypersurfaces. This is a joint work with Song Yang and Zigang Zhu.
December 4th
Speaker: 呼子笛太郎(Yobuko Fuetaro) (Tokyo University of Science)
Title: Quasi-F-splitting and the Achinger–Zdanowicz Construction
Abstract: Abstract: Quasi-F-splitting is a property of schemes in positive characteristic p, generalizing F-splitting. A remarkable property of quasi-F-split schemes is that they can be lifted modulo p^2. In fact, Achinger and Zdanowicz constructed such a lifting from the data of the splitting. In the case of F-split(=ordinary) abelian varieties or K3 surfaces, the resulting lifting agrees with the canonical lifting arising from Serre–Tate theory. In this talk, I will present a deformation-theoretic viewpoint on the Achinger–Zdanowicz construction.
December 11th
Speaker: 陈亦飞(Yifei Chen) (Chinese Academy of Sciences)
Title: Jordan constants of Cremona group of rank 2 in odd characteristic
Abstract: 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.
December 18th
Speaker: 權業善範(Yoshinori Gongyo) (Tokyo University)
Title: TBD
Abstract: TBD
December 25th
Speaker: 周琳(Lin Zhou) (Leibniz University Hannover)
Title: TBD
Abstract: TBD