召集人：

付保华，中国科学院数学与系统科学研究院，研究员；

胡文传，四川大学，数学学院，教授；

曹晋，北京科技大学，数理学院，副教授

时间：2026.09.27—2026.10.03

Conference Information

Ⅰ. Seminar Theme, Content, and Significance：

Since Grothendieck laid its foundations, the theory of motives has been deeply integrated into the core architecture of algebraic geometry, arithmetic algebraic geometry, and algebraic topology, becoming a unifying cornerstone of modern algebraic geometry. Algebraic K-theory, through milestone works such as the Grothendieck–Riemann–Roch theorem, Quillen’s construction of higher K-groups, and Voevodsky’s construction of the triangulated category of motives, has formed a profound intrinsic unity with the theory of motives. At the end of the last century, Voevodsky constructed the triangulated category of motives and used it to successfully solve the Milnor conjecture, revealing the universal utility of the theory of motives. Later, Brown used the theory of motives to solve the motivic version of Zagier’s conjecture. In recent years, Guozhen Wang and Zhouli Xu used motivic homotopy theory to settle the final case of the generalized Poincaré conjecture. Thus, the theory of motives has developed into a cross-disciplinary research network connecting number theory, geometry, and topology, and continues to catalyze integration and innovation across frontier branches.

This workshop has invited domestic scholars working in the theory of motives, algebraic K-theory, and related fields to engage in in-depth exchanges on the following frontier topics: the characterization of motivic fundamental groups on algebraic curves and their periods; the structure and classification of Chow–Witt motives; applications of the theory of motives to certain arithmetic problems for elliptic curves; and motivic homotopy theory and the geometric properties of Chow varieties, among others.

At present, relevant scholars in China are scattered and their research directions are relatively independent. This conference aims to build a collaborative platform and help scholars break through research barriers: on the one hand, by promoting mutual learning among research topics and cross-disciplinary cooperation; on the other hand, by consolidating research strength to jointly advance the domestic development of the theory of motives and K-theory.

Ⅱ、Program Schedule：

Check-in: Sep. 27, 2026

Talks: Sep. 28 – Oct. 2, 2026

Departure: Oct. 3, 2026

Venue: Tianyuan Mathematics Research Center (Chishitan Reservoir, Yiliang County, Kunming, Yunnan Province)

Ⅲ、Practical Information：

1. This seminar is financially supported by the TYMRC. Accommodation and meals for participants will be covered by the Center. All other expenses (including round-trip transportation) shall be borne by the participants themselves.

2. The Center will arrange shuttle services to/from the following locations: Kunming High-Speed Railway Station, Kunming Changshui International Airport, and downtown Kunming. Participants are kindly requested to log in to the project management system (http://tianyuanpm.amss.ac.cn/) in a timely manner to register their travel information.

3. As the Center is located at a considerable distance from the nearest hospital, participants are advised to bring an adequate supply of essential personal medications.

4. Conference Contact:

Name (Affiliation): Jin Cao (USTB)         Phone Number: 15810102976

Name (Affiliation): Wenchuan Hu (SCU) Phone Number: 13980640692

会议日程一（Schedule Ⅰ）

会议日程二（Schedule Ⅱ）

会议日程三（Schedule Ⅲ）

会议日程四（Schedule Ⅳ）

会议日程五（Schedule Ⅴ）

报告摘要（Report Abstracts）

报告题目 Title: Arithmetic purity of strong approximation for toric varieties with constant global sections

Speaker: 徐飞 (首都师范大学)

报告摘要 Abstract:

Based on various geometric phenomena, it is conjectured that the strong approximation property should be invariant up to a closed subset of codimension greater than 1. This conjecture has been verified for many cases, particularly for certain complete toric varieties by S. Chen. In this talk, we will extend Chen's result to all complete toric varieties and explain the recent work of Santers on Manin's conjecture for integral points on toric varieties. This is joint work with Dasheng Wei and Yi Zhu.

报告题目 Title: The cohomology ring of compactified Jacobians: an update

Speaker: 訚琪峥 (北京大学)

报告摘要 Abstract:

The cohomological study of compactified Jacobians is crucial for understanding curve singularities. For any integral curve with planar singularities, conjectures of Maulik-Yun, Rennemo, Shende, and Oblomkov-Rasmussen-Shende predict a natural multiplicative bigrading on the cohomology ring of the compactified Jacobian. I will discuss the challenges we are facing, past attempts, and a new approach towards the construction of such a multiplicative bigrading. Based on joint work in progress with Davesh Maulik and Junliang Shen.

报告题目 Title: 曲线的整K2群的自由秩

Speaker: 唐国平 (中国科学院大学)

报告摘要 Abstract:

我们将介绍一些数域上亏格为g的特殊曲线族的整K2群中g个Z-线性无关元，这里亏格g不超过7。

报告题目 Title: Hermitian K-theory of quadric hypersurfaces

Speaker: 谢恒 (中山大学)

报告摘要 Abstract:

In this talk, we show that Hermitian K-theory of quadric hypersurfaces fit into fibration sequences relating them to the base ring and to Clifford algebras. As an application, we prove that the signature map from the Witt groups of real spheres to their KO-theory is an isomorphism. This result recovers Bott's 8-periodicity from the viewpoint of Witt theory.

报告题目 Title: The Milnor Group, the Shafarevich–Tate Group, and the Congruent Number Problem

Speaker: 秦厚荣 (南京大学)

报告摘要 Abstract:

We develop a new Shimura lift for weight 3/2 modular forms in the study of congruent numbers, allowing us to derive a new criterion for them and, furthermore, to establish a close connection between Milnor K-groups and Shafarevich–Tate groups, thereby linking the Birch–Swinnerton-Dyer conjecture and the Birch–Tate conjecture. Whether there exist infinitely many primes congruent to 1 modulo 8 that are congruent numbers is a well-known open problem; we will discuss this famous problem.

报告题目 Title: Cohomological invariants of hermitian forms with applications to Galois cohomology

Speaker: 胡勇 (南方科技大学)

报告摘要 Abstract:

For decades, it has been a well developed method to use cohomological invariants to study quadratic forms. Based on classical algebraic constructions, some low degree cohomological invariants for hermitian forms are also known. In this talk, we introduce a uniform way to define cohomological invariants for hermitian forms in all degrees and in arbitrary characteristic, and we show that they can detect hyperbolicity completely. We will also discuss applications of these invariants in Galois cohomology.

报告题目 Title: Hodge-theoretic mirror symmetry for elliptic curves

Speaker: 周杰 (清华大学)

报告摘要 Abstract:

Mirror symmetry has inspired significant developments in modern geometry, culminating in the philosophy that Gromov–Witten invariants are period integrals.  At genus zero, this is established by Givental and  Lian–Liu–Yau for appropriate mirror pairs, and is, more conceputally, formulated in terms of variations of polarized Hodge structures.  The higher-genus case remains largely open in general. In this talk, I will explain Hodge-theoretic higher-genus mirror symmetry for elliptic curves, building on the works of Bloch–Okounkov and Okounkov–Pandharipande.

报告题目 Title: Weight structures and applications

Speaker: 金方舟 (同济大学)

报告摘要 Abstract:

Weight structures are a dual notion of t-structures, which are introduced by Bondarko as a counterpart of Deligne's theory of weights in motivic categories. I will discuss constructions of weight structures and applications.

报告题目 Title: Computing the Tame Kernel of Q(sqrt(-491)) by Generators and Relations

Speaker: 张龙 (青岛大学)

报告摘要 Abstract:

Let F = Q(sqrt(-491)), the first unresolved case in the Belabas--Gangl computation of tame kernels of imaginary quadratic fields with |Delta| < 1000. Starting from their direct computation, we reproduce the descent and terminal relation calculation and use Lim's later exact sequence to reduce the difficult cyclotomic class-group problem to the determination of the inverse-cyclotomic p-primary eigenspace of the S-class group of F(zeta_p), together with the corresponding local splitting term; for p = 13 this closes the computation and gives K_2(O_F) = <{2, 4 - omega}_12> ~= Z/13Z, omega = (1 + sqrt(-491))/2. This complements the earlier work of Burns, de Jeu, Gangl, Rahm and Yasaki, who determined the order by K_3- and regulator-based methods, whereas here the original direct K_2 computation is completed and an explicit generator is recovered.

报告题目 Title: Fauzan's proof of the irrationality of zeta(5)

Speaker: 赖力 (厦门大学)

报告摘要 Abstract:

Fauzan recently made a breakthrough, proving that zeta(5) is irrational. In this talk, we discuss some of our understanding of Fauzan's work.

报告题目 Title: The weak Chinburg conjecture on Mahler measures

Speaker: 郭学军 (南京大学)

报告摘要 Abstract:

For every negative fundamental discriminant -f and every k >= 1, we construct a rational function R_{f,2k} and a constant r_{f,2k} such that m(R_{f,2k}) = r_{f,2k} L(chi_{-f}, 1-2k), where m denotes the logarithmic Mahler measure and chi_{-f} is the quadratic Dirichlet character associated with -f. This proves the weak Chinburg conjecture.

报告题目 Title: Singular automorphic products and BKM algebras

Speaker: 王好武 (武汉大学)

报告摘要 Abstract:

After proving the moonshine conjecture, Borcherds asked in 1995 whether there exist only finitely many holomorphic automorphic products of singular weight. We show that, up to conjugation, there are exactly 27 such products on lattices of the form $2U\oplus L$. The classification proceeds by identifying each product at a standard $1$-dimensional cusp with the superdenominator of a BKM superalgebra that carries a graded module structure over an affine Lie superalgebra $\hat{\mathfrak{g}}$. The auxiliary algebras $\hat{\mathfrak{g}}$ are shown to satisfy strong conditions that reduce the possibilities to an initial list of 1372 candidates. An elimination argument leaves exactly 85 algebras $\hat{\mathfrak{g}}$ that correspond to the 27 products. This classification is closely connected with certain distinguished families of vertex operator superalgebras. Our results provide a systematic framework for extending affine Lie superalgebras to hyperbolic ones with modularity, generalizing the work of Feingold and Frenkel (1983). This talk is based on our recent work arXiv: 2609.15658, joint with Kaiwen Sun and Brandon Williams.

报告题目 Title: K2 of Families of Non-Hyperelliptic Curves of Arbitrary Genus

Speaker: 刘杭 (深圳大学)

报告摘要 Abstract:

We give an integrality criterion for a tame Steinberg symbol {f,g} on a curve over a number field using tempered polynomials. As an application, for the triangle and rectangle symbols on the families of curves studied by the speaker and de Jeu, we obtain an exact integrality criterion in terms of the parameter. We show non-hyperellipticity for smooth affine members of the families, and present numerical tests of Beilinson's conjecture in genus three, four and five.

报告题目 Title: Locally unramified cohomology and Kottwitz exact sequence beyond number field

Speaker: 曹阳 (山东大学)

报告摘要 Abstract:

(joint work with Ting-Yu Lee) The classical Kottwitz exact sequence studies the local-global principle for Galois cohomology with coefficients in connected linear algebraic groups over number fields. In this talk, we consider this local-global problem over general global fields, including Laurent function fields and p-adic function fields. We will show that a new phenomenon occurs, and introduce a new cohomological obstruction given by locally unramified cohomology.

报告题目 Title: The equivariant Milnor-Witt motive of moduli space of curves

Speaker: 杨南君 (北京雁栖湖应用数学研究院)

报告摘要 Abstract:

Grothendieck's Chow motives make every Weil cohomology factor through them. Extending to smooth nonprojective varieties gives Voevodsky's mixed motives. Around 2020, Milnor-Witt motives refined this, encoding quadratic field data and approaching the motivic stable homotopy category. In this talk, we decompose the equivariant Milnor-Witt motive of the moduli space of elliptic curves with two marked points. Combining this with Lorenzo-Mantovani, we determine its Chow-Witt ring.

报告题目 Title: Nonrational varieties with unirational parametrizations of coprime degrees

Speaker: 余讯 (天津大学)

报告摘要 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.

报告题目 Title: Lawson homology groups of Chow varieties

Speaker: 陈友明 (重庆理工大学)

报告摘要 Abstract:

Let C_{p,d}(P^n) denote the Chow variety of effective p-cycles of degree d in the complex projective space P^n. In this talk, the rational Lawson homology groups L_qH_k(C_{p,d}(P^n))_Q for 0 <= q <= k <= 2d will be computed. Furthermore, the stability of Lawson homology groups of Chow varieties under natural embeddings and algebraic suspension maps within a specified range will be established. This is joint work with Prof. Wenchuan Hu.

报告题目 Title: Geometric Shafarevich boundedness conjecture for families of polarized varieties

Speaker: 申屠均超 (中国科学技术大学)

报告摘要 Abstract:

Faltings proved the Mordell conjecture: curves of genus >= 2 over a number field have finitely many rational points, via the Shafarevich conjecture. Its higher-dimensional analogue asks whether polarized families over a complex base have finitely many deformation types. I will present recent progress on Shafarevich boundedness for moduli of stable minimal models, including KSB stable pairs, yielding a uniform Mordell conjecture for open curves over function fields.

报告题目 Title: Algebraic K-theory, geometric connectedness and Chow groups

Speaker: 杨森 (滁州学院)

报告摘要 Abstract:

Bloch et al applied algebraic K-theory to study the structures of Chow groups. When the ground field is a number field, Bloch established the pro-representability of the second Chow group. We use K-theory and geometric connectedness to extend Bloch's result to arbitrary fields of characteristic zero. This proves the pro-representability of the second Chow group in generality, without any additional assumption on the ground field.