TSSC 2025

Shenzhen, China, January 5-12

• English
• 注册报到
• 日程安排
• 组织协调
• 前沿报告
• 专题课程
• 基础课程
• 主页

专题课程

（T1）课程题目：计算几何与智能制造

申立勇  中国科学院大学
袁春明  中国科学院数学与系统科学研究院
课程简介： 计算几何是针对处理几何对象的算法及数据结构的系统化研究，可用于解决智能制造领域中所遇到的诸多问题，包括曲线曲面的表示、曲线曲面的隐式化和参数化、曲线曲面求交等，以及针对高速、高精、高可信数控系统的最优插补、空间刀补、误差补偿、轨迹规划与干涉分析等。本课程将介绍如何以计算代数几何与符号计算为工具来求解这些问题，并讨论该方向的最新进展。
主讲人简介： 申立勇，中国科学院大学数学科学学院教授，密码学院副院长，研究兴趣为计算几何、计算机辅助设计，数字化设计与数控技术等。在ACM Trans. Graphic.、IEEE Trans. Vis. Comput. Graphic.、Comput. Aided Geom. Design等期刊及国际会议上发表论文100余篇。曾获国际几何设计与处理大会最佳论文奖、首届吴文俊计算机数学青年学者奖。
主讲人简介：袁春明，中国科学院数学与系统科学研究院研究员，研究兴趣为数学机械化、数字化设计与智能制造中的数学方法。 成果主要发表在 Found. Comput. Math.、Trans. Amer. Math. Soc.、 J. Symb. Comput.等国际期刊上。曾获 ACM-SIGSAM 颁发的 ISSAC 杰出论文奖、 卢嘉锡青年人才奖。

（T2）课程题目：计算机定理证明系统Lean简介

潘锦钊  同济大学
课程简介： Lean是一个交互式定理证明器，提供了一套严格的逻辑和数学框架，使得推理可以被精确地形式化描述。本课程计划从使用者的角度出发，介绍Lean的逻辑基础，与通常的逻辑的关系，以及一些基本的使用方法及例子。最后介绍Lean在基础数学前沿领域的影响，及今后可能的研究方向。
主讲人简介： 潘锦钊，同济大学博士后，研究方向为椭圆曲线的算术。同时也是Lean较早的使用者，参与了Lean数学库的维护工作。

（T3）课程题目：Machine Learning and Symbolic Computation

Matthew England  Coventry University, UK
课程简介： The course will be split into four parts: an introduction, two case studies, and a consideration of where future potential lies.
1. Introduction: We will briefly revise the fields of Machine Learning and Symbolic Computation separately and consider different ways in which they may interact, and the potentials and challenges of this interaction.
2. ML to Optimise CAD/QE: We will introduce the symbolic computation algorithm Cylindrical Algebraic Decomposition (CAD) and its application Quantifier Elimination (QE), before outlining work applying ML to optimise CAD.
3. ML to Optimise Symbolic Integration: We will revise symbolic integration and recent work to replace or optimise this with machine learning.
4. Explainable AI and Symbolic Computation: We will finish by outlining the field of Explainable AI and the speaker's hypothesis that this may give the most fruitful interactions between Machine Learning and Symbolic Computation, following some preliminary results.
主讲人简介： Dr Matthew England is an Associate Professor in Computer Science at Coventry University in the UK. He currently serves as the co-Director of the university's Research Centre of Computational Science and Mathematical Modelling. He is the elected Treasurer for the ACM Special Interest Group in Symbolic and Algebraic Manipulation (SIGSAM) and on the editorial board for Springer Mathematics in Computer Science and Maple Transactions. His research has focussed on algorithms for symbolic computation, particularly for real polynomial systems: derivation of new algorithms, their analysis, their implementation in computer algebra systems, and their application in fields as diverse as biology and economics. His recent work has focused on the integration of computer algebra with other areas of computer science: SAT/SMT solvers and machine learning (EPSRC Projects EP/T015748/1 and EP/R019622/1).

（T4）课程题目：Algebraic Geometry and Data Science

Manolis C. Tsakiris  中国科学院数学与系统科学研究院
课程简介： This mini-course will consist of two sessions of 80 minutes each. The aim of the mini-course is to give an introduction to a few problems in data science and machine learning, whose mathematical analysis and algorithm design can benefit from techniques of algebraic geometry. In particular, we will discuss low-rank matrix completion, subspace clustering, phase retrieval and linear regression without correspondences. We will focus on the algebraic geometric formulation of these problems, in which dimension theory, Groebner bases, Hilbert Functions and even local cohomology will make an appearence. Basic knowledge of polynomial ring theory will be assumed.
主讲人简介： Manolis C. Tsakiris holds a PhD degree in Mathematics from the University of Genova advised by Aldo Conca, and a PhD in Electrical Engineering from Johns Hopkins University advised by Rene Vidal. His research interests concern Applied Algebraic Geometry and Commutative Algebra. He is currently Associate Professor at the Academy of Mathematics and Systems Science of the Chinese Academy of Sciences.