数学主题分类 Mathematics Subject Classification: 

Fourier Analysis, Quantum Information and Subfactor Theory. 算子代数、量子信息

会议摘要（Abstract）

A hundred years ago, matrix mechanics brought revolutionary progress to modern physics, leading the scientific community into deep exploration of the microscopic world. To celebrate this significant milestone, we plan to invite scholars and researchers from around the world to participate in the "100 Years of Matrix Mechanics" International Symposium in January 2025 at the Tsinghua Sanya International Mathematics Forum (TSIMF). This conference aims to gather the world's top scholars to discuss frontier research and applications based on matrix mechanics, covering multiple fields of mathematics, physics, and computer science.

The birth of matrix mechanics provided modern physics with new mathematical tools and methods, allowing us to understand the fundamental laws of nature more deeply. It not only provided new solutions to several problems in classical physics but also laid the foundation for various modern scientific research. Over the past century, the theories and methods of matrix mechanics have continuously developed, greatly advancing multiple fields such as information science, computational technology, and mathematics.

The conference topics include but are not limited to the following aspects:

•     Mathematics and Matrix Algebra: Exploring new developments in matrix theory in modern mathematics and the importance of matrix algebra in various applications. Discussing the various properties, structures of matrices, and their relationships with other algebraic systems.

•     Coding and Error Correction Theory: Researching information coding technology based on matrix methods, discussing the application of matrix methods in error correction theory, including exploring new error correction codes and optimizing existing coding schemes.

•     Computational Technology: In-depth exploration of the application of matrix computation in large-scale parallel computing, especially the development of efficient algorithms and their importance in complex system simulations.

•     Symmetry and Algebra: Discussing the application of matrix methods in symmetry research, exploring the discovery of new symmetric structures and their applications in physics.

•     Tensor Categories and Topological Structures: Studying the broad applications of matrices and tensor categories in different scientific fields, including modeling of complex systems and topological structures in many-body models.

This symposium is not only a review of history but also a prospect for future development. We will arrange a series of special reports, academic discussions, and workshops to provide participants with a platform for in-depth exchange and cooperation. We look forward to the participation of scholars from around the world to share the latest research results and frontier ideas, promoting the further development of matrix mechanics in science and technology.

一百年前，矩阵力学为现代物理学带来了革命性进展，带领科学界进入了微观世界的深层探索。为庆祝这一重要里程碑，我们计划在2025年1月于清华三亚国际数学论坛（TSIMF）诚邀全球的学者和研究人员参加“矩阵力学100年”国际研讨会。本次会议旨在汇聚全球顶尖学者，共同探讨以矩阵力学为基础的前沿研究和应用，涵盖数学、物理和计算机科学的多个领域。

矩阵力学的诞生为现代物理学提供了新的数学工具和方法，使我们能够更加深入地理解自然界的基本规律。它不仅为经典物理学的若干问题提供了全新的解决方案，还奠定了若干现代科学研究的基础。在过去的一个世纪中，矩阵力学的理论和方法不断发展，极大地推动了信息科学、计算技术和数学等多个领域的进步。

会议主题包括但不限于以下几个方面：

数学与矩阵代数：探讨矩阵理论在现代数学中的新发展，以及矩阵代数在各种应用中的重要性。讨论矩阵的各种性质、结构以及与其他代数系统的关系。

编码和纠错理论：研究基于矩阵方法的信息编码技术，讨论矩阵方法在纠错理论中的应用，包括探讨新型纠错码和优化现有编码方案。

计算技术：深入探讨矩阵计算在大规模并行计算中的应用，特别是高效算法的开发及其在复杂系统模拟中的重要性。

对称性与代数：探讨矩阵方法在对称性研究中的应用，探索新型对称结构的发现和在物理学中的应用。

张量范畴与拓扑结构：研究矩阵和张量范畴等在不同科学领域中的广泛应用。包括复杂系统的建模和多体模型中的拓扑结构。

此次研讨会不仅是对历史的回顾，更是对未来发展的展望。我们将安排一系列专题报告、学术讨论和工作坊，为参会者提供一个深入交流和合作的平台。期待来自世界各地的学者们共同参与，分享最新的研究成果和前沿思想，推动矩阵力学在科学和技术中的进一步发展。

举办意义(Description of the aim)

Objectives

The "100 Years of Matrix Mechanics" International Symposium aims to review and celebrate the outstanding achievements of matrix mechanics over the past century, while also exploring its potential applications in future science and technology. By bringing together top scholars and researchers from around the world, this conference hopes to achieve breakthroughs in the following areas: First, to delve into the latest research advances in matrix mechanics in information processing and computational technology; second, to share innovative methods and outcomes of applying matrix mechanics in various disciplines; and third, to promote interdisciplinary exchange and collaboration, inspiring new research ideas and cooperative projects.

Impact

This symposium will have a profound impact on both the academic and industrial sectors. Firstly, it will facilitate academic exchanges in fields related to matrix mechanics, promoting the dissemination and application of new theories and methods. Secondly, by showcasing the latest research results and practical application cases, the conference will bring new insights and development directions to fields such as information processing, computational technology, and physical models. Additionally, the conference will provide a platform for young researchers to present their achievements, encouraging innovation and exploration in the field of matrix mechanics.

会议目标：“矩阵力学100年”国际研讨会旨在回顾和庆祝矩阵力学一百年来的卓越成就，同时展望其在未来科学和技术中的应用潜力。通过汇集全球顶尖学者和研究人员，本次会议希望在以下几个方面取得突破：一是深入探讨矩阵力学在信息处理和计算技术中的最新研究进展；二是分享在不同学科中应用矩阵力学的创新方法和成果；三是推动跨学科的交流与合作，激发新的研究思路和合作项目。

会议影响：本次研讨会将对学术界和工业界产生深远影响。首先，会议将促进矩阵力学相关领域的学术交流，推动新理论和新方法的传播和应用。其次，通过展示最新的研究成果和实际应用案例，会议将为信息处理、计算技术、物理模型等领域带来新的启示和发展方向。此外，会议还将为年轻研究人员提供一个展示自己成果的平台，激励他们在矩阵力学领域的创新和探索。