会议日程

会议报告摘要

例外多项式和例外扩张

熊玮 湖南大学

介绍局部域的例外扩张的概念，并用来研究有限域上的例外多项式，得到 Carlitz-Wan猜想的一个推广（与丁治国和张起帆老师合作）。

Distributions of integral points and Zeta values

蔡立 首都师范大学

We study the distribution of integral matrices with a fixed characteristic polynomial. We determine the leading term of the distribution in terms of zeta functions of orders. The proof is based on an equi-distribution property of orbits, a reformulation of the distribution into orbital integrals via the strong approximation with Brauer-Manin obstruction and the Tate-Nakayama duality, endoscopic fundamental lemma, and a critical input that links orbital integrals to residues of zeta functions of orders. This is a joint work with Taiwang Deng.

On the Eisenstein part of the arithmetic of J_1(N)

任远 电子科技大学

In this talk, we first recall the notion of Eisenstein primes. Then, we will see that abelian torsion groups and component groups of J_1(N) are Eisenstein. We will also briefly discuss some related further questions.

Class groups of Q(N^{1/p})

李加宁 山东大学

Let K=Q(N^{1/p}), where p and N are two primes such that p|N+1. Iimura proved in 1980s that p divides the class number of K using genus theory. In 2021, Lang-Wake gave a new proof by constructing a special newform of level N^2 which cuts out a unramified cyclic of degree p extension of K. If p^r divides N+1 exactly, Lang-Wake further in 2025 shows that there exists exactly r such newforms. We show that these r newforms cut out the same unramified cyclic degree p-extension of K, under the assumption that p is a regular prime.

MDS Codes and Zero-Sum Problems

韩冬春 做爱直播

Maximum distance separable (MDS) codes are central topics in finite geometry and coding theory. In this talk, by connecting these codes to zero-sum problems over finite abelian groups, we determine the maximal lengths of certain MDS codes.

Height filtration on flag varieties

范洋宇 北京理工大学

In this talk, we will discuss the height filtration on flag varieties over functional fields from a representation-theoretic viewpoint.

Motivic Chern Classes of Schubert Cells in Grassmannians

范久瑜 四川大学

We will first recall the background on motivic Chern classes and then prove a Pieri formula for motivic Chern classes of Schubert cells in the equivariant K-theory of Grassmannians, which is described in terms of ribbon operators on partitions.

Rubin's conjecture on local units in the anticyclotomic tower at inert primes

朱秀武 北京雁栖湖应用数学研究院

In this talk, we will prove Rubin's conjecture on the structure of local units in the anticyclotomic Zp-extension of an unramified quadratic extension of Qp in p=3 case by extending Burungale-Kobayashi-Ota's work.

Composition series for GKZ-systems

方江学 首都师范大学

The hypergeometric functions were introduced by Euler as a power series in one variable. Gauss studied hypergeometric functions as solutions of the hypergeometric differential equationon the complex plane. Riemann give a complete description of the monodromy group for Gauss hypergeometric function. The monodromy group of a linear differential equation in the complex plane characterizes the behavior of the analytic continuation of its solutions. After them, people had introduced many generalizations of Gauss hypergeometric functions by increasing the number of parameters or the number of variables or both. In 1980s, Gelfand, Kapranov and Zelevinsky generalized the hypergeometric function in a unified way. They associated to any matrix A with integer entries a system of partial differential equations whose solutions are hypergeometric functions, which are now called the GKZ-systems or A-hypergeometric D-modules. In this talk, I will review some basic results of the Gauss hypergeometric functions and the GKZ-systems. Especially, I will construct a filtration on the GKZ-system with semisimple subquotients.

Frobenius nonclassical hypersurfaces

段炼 上海科技大学

In this talk, we will study Frobenius nonclassical hypersurfaces defined over finite fields. A smooth hypersurface X in projective space over Fq is called Frobenius nonclassical if the image of every geometric point under the q-th Frobenius endomorphism lies in the tangent hyperplane at that point. This concept generalizes the notion introduced for curves by Stöhr and Voloch.