9:00 胡创强（中山大学）

报告题目：函数域上的代数几何导引

我们介绍代数几何的基础知识，有限域上的曲线的相关理论，构造Shtuka，4次方域最优曲线。

10:05 黄瑞芝（中国科学院数学与系统科学研究院）

报告题目：An almost flat spinc manifold bounds

We prove that every almost flat spinc manifold bounds a compact orientable manifold, thereby settling, in the spinc case, a long-standing conjecture of Farrell-Zdravkovska and S. T. Yau. This is a joint work with Fei Han and Weiping Zhang.

11:10 自云鹏（山东大学）

报告题目：Algebra of Path Integrals on the Digraphs

Iterated integral is a classical geometric structure on the smooth manifolds. It introduced an interesting hopf algebra which depends on the homotopy type of the manifold and annihilated by some ideal of the group algebra of \pi_1. In this research we introduced the iterated integral on the digraphs based on the GLMY theory of G,L,M and Yau. We proved the computation properties of this structure and induced some interesting algebraic structures to the digraphs.

15:00 王宇（北京雁栖湖应用数学研究院）

报告题目：基于高效后处理的量子阴影层析实现量子优势

在量子科学与人工智能等领域，计算形如 $tr(AB)$ 的内积（其中 $A$ 为任意密度矩阵，$B$ 为任意有界范数可观测量，即 Hermitian 且满足 $tr(B^2) \le O(poly(\log d))$）是一个基础且普遍的问题。传统的经典计算方法在时间与存储上均需 $O(d^2)$ 资源，难以扩展至指数维系统。

本报告介绍一种基于稠密对偶基随机投影的量子阴影层析方案，可在平均意义下将总体复杂度从 $O(d^2)$ 指数降低至 $O(poly(\log d))$，并在最坏情况下保持近根号级加速 $O(d~poly(\log d))$。该方法在保证单次实验常数时间$O(1)$后处理代价的同时，显著降低了量子态 A 的经典存储需求（由 $O(d^2)$ 减少至 $O(m \log d)$，其中 m 为测量样本数）。相较于随机Clifford测量在2的幂次和素数幂次的限制，其适用于任意维度的量子体系，可高效估计有界范数可观测量的期望值。特别地，对于 n-qubit 稳定子态，其与任意有界可观测量的期望值可在多项式资源内高效估计。该工作展示了一种兼具普适性与高效性的量子阴影层析方案，为高维量子数据处理提供了可验证的量子优势途径 [Phys. Rev. Lett. 135, 200601 (2025)]。

16:05 杨南君（北京雁栖湖应用数学研究院）

报告题目：Witt group of nondyadic curves
Witt group of a scheme is the Grothendieck group of orthogonal bundles modulo those with a Lagrangian. Its building blocks are 2-torsion line bundles, corresponding to Theta characteristics (if exists) of the variety.  For real algebraic varieties, its free rank is the number of Euclidean connected components of real points, being studied since Knebusch in 1970s. For curves over a number field, it admits a filtration whose graded quotients are unramified cohomologies by works of Parimala, but few results were known for the explicit group structure.

In this talk, we compute the Witt group of smooth proper curves over nondyadic local fields with $char\neq2$ by reduction, with a general study of the existence of Theta characteristics.

胡创强，2025年4月加入中山大学数学院，长期致力于编码理论、函数域及数论、奇点理论的前沿研究，在量子码的构造与解码算法、代数几何码的优化设计、Drinfeld模的算术性质、椭圆奇点精细分类及丘-李代数结构分析等方向取得丰硕成果。其论文发表于IEEE IT, Finite Fields, DCC等国际权威期刊。

黄瑞芝，中国科学院数学与系统科学研究院副研究员，博士生导师。研究方向为代数拓扑及其在流形拓扑、微分几何与数学物理中的应用。著有专著1部，相关工作发表在J. Top., Adv. Math., Tran. AMS等数学期刊。

自云鹏，博士毕业于清华大学。师从Eduard Looijenga，后于北京雁栖湖应用数学研究院任博士后研究员。现任山东大学（济南）数学学院助理研究员。研究兴趣为有向图上的拓扑与几何理论。

王宇，北京雁栖湖数学科学与应用研究院（BIMSA）助理研究员。2019 年于中国科学院数学与系统科学研究院获计算机软件与理论专业博士学位。曾在深圳鹏城实验室量子计算中心任助理研究员。目前主要研究兴趣为量子信息与量子计算，重点关注量子态学习，通过优化测量与计算资源，实现对未知量子态信息的高效读取与性质预测。

Nanjun Yang got his doctor and master degree in University of Grenoble-Alpes, advised by Jean Fasel, and bachelor degree in Beihang University. Then he became a postdoc in YMSC. Currently he is anS assistant professor in BIMSA. His research interest is the Chow-Witt group of algebraic varieties, with publications on journals such as Camb. J. Math and Ann. K-Theory.