会议摘要（Abstract）

本次会议以“几何拓扑及相关主题”为主题，致力于促进几何拓扑领域的前沿研究与跨学科交流。几何拓扑作为数学中一个重要而活跃的研究方向，涉及多维空间的复杂结构与性质，涵盖从低维拓扑到高维拓扑的丰富内容。此次研讨会旨在为学者们提供一个高水平的交流平台，汇聚各地的顶尖研究人员与新兴学者，共同探讨几何拓扑中的最新进展，分享研究成果，并推动学术合作。

会议将重点讨论以下几个方面：

1. 泰希米勒理论与高阶泰希米勒理论：研究将聚焦于二维几何拓扑，特别是对泰希米勒理论、二次微分、映射类群、模空间、随机双曲面、高阶泰希米勒理论的研究。

2. 分类问题与理论框架：三维和四维几何拓扑将作为会议的另一重要议题，讨论这些维度中的拓扑空间分类问题及其相关的数学理论框架，探索新的分类方法与算法。

3. 几何拓扑与同伦论的联系：高维几何拓扑与同伦论之间的关系仍是一个重要的研究方向。此次会议将进一步探讨同伦论在高维拓扑中的应用，特别是动机同伦论的拓扑视角。

The conference, themed "Geometric Topology and Related Topics," aims to promote frontier research in the field of geometric topology and interdisciplinary communication in general geometry and topology. As a vibrant and significant area of mathematical research, geometric topology deals with the complex structures and properties of multi-dimensional spaces, spanning a wide range of topics from low-dimensional to high-dimensional topology. This workshop provides a platform for researchers and students to come together, discuss the latest developments in geometric topology, share research findings, and foster academic collaboration.

The conference will focus on the following key topics:

Teichmüller Theory and higher Teichmüller Theory: Research will center on two-dimensional geometric topology, particularly the study of Teichmüller theory, quadratic differentials, mapping class groups, moduli spaces, random hyperbolic surface, higher Teichmüller theory.

Classification Problems and Theoretical Frameworks: Three-dimensional and four-dimensional geometric topology will be another central theme, addressing classification problems of topological spaces in these dimensions, and the mathematical theoretical frameworks involved.

Connections Between Geometric Topology and Homotopy Theory: The relationship between high-dimensional geometric topology and homotopy theory remains a key area of research. This session will further investigate the application of homotopy theory in high-dimensional topology, with a particular focus on the topological perspectives of motivic homotopy theory.

Geometric topology is a quite active research field in modern mathematics. In the current research, the two dimensional geometric topology studies about the Riemann surfaces, Teichmüller theory, moduli spaces and their dynamic systems, the 3 and 4 dimensional geometric topology concerns the classification problems, while the higher dimensional geometric topology relates to the motivic homotopy theory. This workshop will bring together experts to talk about recent developments in these related fields, discuss further questions of mutual interest, and seek possible new cooperation. More importantly, to encourage young mathematicians to participate more in these communities, we would like to make enough rooms for young scholars, including Postdocs and PhD students, to present their recent works or even work-in-progress. We believe TSIMIF is a perfect location for this purpose.

举办意义(Description of the aim)

This conference aims to bring together leading scholars in contemporary geometric topology to provide a high-level platform for exchanging ideas and discussing the latest advancements in the field. It will gather top researchers and emerging scholars from around the world to explore new developments in geometric topology. Our main objectives include:

1. Exploring new Developments
Geometric topology has undergone significant transformations in recent years, with breakthrough methods emerging in higher-dimensional spaces. This workshop aims to provide a comprehensive discussion of these innovative methods, with a focus on:

Recent developments in Teichmüller space

Recent developments in higher Teichmüller space

Classification problems in low-dimensional topology

Motivic homotopy theory and its geometric interpretation

2.  Interdisciplinary Dialogue
We are committed to creating a powerful knowledge-sharing platform that allows researchers to:
Share recent research findings: Through presentation sessions, participants will have the opportunity to present their work in detail and receive feedback from their peers.
Identify potential collaborative research opportunities: The conference will provide spaces for informal interactions, group discussions, and networking, where attendees can explore complementary aspects of their research and uncover potential cross-disciplinary and cross-team collaborations. This will promote synergistic innovation in the field of geometric topology.
Connect different subfields of geometric topology: By structuring the academic program, we aim to create dialogue platforms for researchers working in different branches of geometric topology, such as 2-dimensional, low-dimensional, and high-dimensional geometric topology. This will encourage participants to share the latest progress in their respective areas and explore potential pathways for cross-disciplinary research.

3. Nurturing Emerging Talent

A major highlight of this workshop is the special support for early-career mathematicians. The conference will provide focused opportunities for postdoctoral researchers and PhD students to present their latest research, including ongoing projects. This approach not only highlights emerging talent but also promotes knowledge exchange and potential future collaborations. Our plans include:

Providing speaking opportunities for postdoctoral and PhD researchers Offering opportunities for postdoctoral and PhD researchers to show their new work

本次会议旨在汇集当代几何拓扑研究最前沿的学者提供一个高水平的交流平台，汇聚各地的顶尖研究人员与新兴学者，共同探讨几何拓扑中的最新进展。我们的主要目标包括：

1. 探索前沿的新发展发展
几何拓扑近年来经历了重大变革，在多维空间中出现了突破性方法。本工作坊旨在全面讨论这些创新方法，重点关注：
- 泰希米勒理论的最新进展
- 高阶泰希米勒理论的最新进展
- 低维拓扑中的分类问题
- 动机同伦论及其几何学意义

2. 跨学科对话
我们致力于创造一个强大的知识分享交流平台，让研究者能够：
- 分享最新研究发现：通过报告环节，为参会学者提供详细阐述自身学术成果的机会。
- 识别潜在的合作研究机会：为参会者提供互动空间，使得参会者可以通过非正式交流、小组讨论等形式，发现彼此研究中的互补性，探索跨学科、跨研究团队的合作可能性，从而推动几何拓扑领域的协同创新。
- 连接几何拓扑的不同子领域：通过设计学术日程，为二维、低维、高维几何拓扑等不同分支的研究者创造对话平台，鼓励他们分享各自领域的最新进展，并探讨跨领域研究的潜在路径。

3. 培养新兴人才

本次研讨会的一大亮点是对早期职业数学家的特别支持。会议将特别关注为博士后研究人员和博士生提供展示其最新研究成果的机会，包括正在进行的研究项目。这种做法不仅突出了新兴人才，还促进了知识的交流与潜在的未来合作。我们计划：
- 为博士后、博士生研究者提供演讲机会
- 为博士后、博士生研究者提供展示新工作的机会

会议摘要（Abstract）

The stable homotopy groups of spheres have been a central and enduring topic in algebraic topology, playing a key role in our understanding of the deep structure of spaces. Over the decades, substantial progress has been made in both theoretical and computational aspects of these groups. Classical tools such as spectral sequences, especially the Adams and Adams-Novikov spectral sequences have provided a robust framework for advancing the theoretical understanding of stable homotopy groups. However, many questions remain unanswered.

This workshop will focus on the problem of computing stable homotopy groups, including both history and the recent advances in this subject. We will begin by providing an overview of the history and foundational concepts underlying the study of stable homotopy groups of spheres. We will also explore how these groups are connected to broader areas in algebraic topology and mathematics, such as cobordism theory, K-theory, and motivic homotopy theory.

The computational aspect has seen recent breakthroughs, particularly through the use of modern tools like motivic and equivariant homotopy theory, for example, the recent result by Lin, Wang and Xu. We will survey some of the latest results in these areas, highlighting the role of computational techniques, including the use of motivic tools, higher chromatic tools and spectral sequences, which have pushed the boundaries of what can be computed.

Despite these advancements, significant challenges remain in understanding the full structure of the stable homotopy groups of spheres. We will address some open problems in the field. Finally, we will outline possible future directions: where does the future of stable homotopy theory lie, and how might we move closer to a complete understanding?

举办意义(Description of the aim)

This workshop aims to gather leading experts and early-career researchers to explore the latest advances in the field of stable homotopy theory, with a particular focus on the calculation and structure of stable homotopy groups of spheres. As one of the most fundamental problems in algebraic topology, understanding these groups has led to deep insights across multiple areas of mathematics, including cobordism theory and K-theory.

Thematic Focus:

The workshop will revolve around the following thematic areas:

1. Computational Techniques and theoretical developments: Recent progress in computational methods, particularly the use of motivic and equivariant homotopy theory, has led to new insights into the stable homotopy groups of spheres. Sessions will focus on motivic homotopy theory, computation-assisted spectral sequences computation, and other advances in computational tools, offering a comprehensive overview of the current state of the art.

2. Interactions with Other Fields and Open Problems: The workshop will emphasize the intersections of stable homotopy theory with other mathematical areas. We will address some open problems in the field and outline possible future directions.

Distinguished Lectures (tentative):

The workshop will feature special lectures by Weinan Lin, Guozhen Wang and Zhouli Xu. whose pioneering work on Adams spectral sequence computation has largely extend our understanding of the stable homotopy groups.

In addition to these distinguished lectures, the workshop will include interactive problem-solving sessions, collaborative working groups, and open discussions on new computational challenges and conceptual developments. The goal is to foster collaboration, encourage the exchange of ideas, and inspire further research in stable homotopy theory and its related fields.

ZOOM

Meeting ID: 832 8778 9283

Passcode: TSIMF

会议摘要（Abstract）

Data analysis has a wide range of applications in science and engineering. Topological computational analysis has become an important analytical tool. As an emerging branch of algebraic topology, persistent homology integrates certain geometric features into topological invariants, thereby bridging the gap between traditional topology and geometry. Computational topology, particularly topological deep learning, holds the promise of providing potentially revolutionary approaches to scientific research. For example, persistent homology has achieved significant success in the extraction, simplification, and drug discovery of complex macromolecular structures. The topological descriptions serve as an excellent foundation for machine learning applied to large-scale complex datasets and images. In computational science, algebraic topology is also applied in concurrent computing, distributed computing, sequential computation, and networks. In summary, computational topology has found many valuable applications in fields such as physics, chemistry, biology, materials science, fluid dynamics, computer graphics, control theory, geometric design, shape analysis, and computational science. This success has greatly advanced the development of related mathematical fields, including computational geometry, differential geometry, spectral geometry, geometric topology, geometric algebra, combinatorial mathematics, partial differential equations, optimization theory, inverse problems, and statistics.

The upcoming seminar on Data Analytics and Topology will bring together researchers from mathematics, physics, chemistry, biology, and computational science to explore new methods for connecting different disciplines and to promote the application of topology in both mathematics and various applied fields.

The primary goals of the proposed seminar are as follows:

● To promote the development of mathematical analysis and topological tools that can effectively utilize current computational capabilities to advance our understanding of the complexities of chemical, biological, and computational systems.

● To inspire a flow of information from "experiment to mathematics," similar to how quantum physics in the last century contributed to the establishment of heuristic new mathematics.

● To foster new connections, interactions, and collaborations between mathematicians and data scientists.

● To provide a platform for exchanging ideas and sharing topological results related to data science and computational science research.

● To introduce graduate students, postdoctoral researchers, and junior faculty members to this field and related disciplines, helping to train the next generation of researchers in computational topology.

● To enhance the participation of women, underrepresented minorities, and individuals with disabilities in research related to computational topology and its applications.

举办意义(Description of the aim)

Currently, a significant obstacle for mathematicians in the fields of computational topology and its applications is the lack of knowledge in data science and/or computational science. Conversely, for data scientists and computer scientists, the primary barrier is the absence of knowledge in the newly developed mathematical tools and topological techniques. The upcoming seminar aims to help bridge the gap between scientists and mathematicians and to foster collaboration between these two communities.

Quantum algebra has become an important direction in mathematical research in recent years. It is a natural combination and extension of theories such as representation theory, Hopf algebra theory, tensor category theory, and Lie theory. It has also gained widespread attention due to its profound connections with low-dimensional topology, rational conformal field theory, and topological field theory. In recent years, the field of quantum algebra has developed rapidly, with a series of outstanding works and progress emerging.

To enhance communication and discussions among experts in quantum algebra, showcase cutting-edge work from various directions within the field, and promote cross-disciplinary collaborations, we organize the Advances in Quantum Algebra conference in February 2025. The conference focuses on several core directions of quantum algebra, including tensor categories, Hopf algebras, vertex operator algebras, subfactor theory, topological order, topological quantum field theory, and low-dimensional topology, among others.

The conference aims to gather experts’ views and suggestions on core issues in the field, providing valuable references for young scholars in this area. Through the display of cutting-edge work across various directions of quantum algebra, this conference seeks to stimulate intellectual exchange among the experts, providing an excellent platform for cross-disciplinary and cross-field collaboration, while further advancing the development of quantum algebra.

We are delighted to annouce the “The Lotus and the Swampland” School and conference, to be held in TSIMF, Tanya, China, from Feb. 10 to Feb. 13, 2025, hosted by the BIMSA (Beijing Institute of Mathematical Sciences and Applications). This event is proposed by Prof. Cumrun Vafa, who will also be attending it.

This unique event will consist of a two-day School, followed by a two-day conference. It brings together experts in the Swampland program and its application to the universe. Each distinguished speaker is expected to deliver a lecture during the School and present a talk in the conference, providing participants with a comprehensive learning experience.
Event Details:
• Location: TSIMF, Sanya, China (http://www.tsimf.cn/)
• School: [Feb. 10-11, 2025] (two days)
• Workshop: [Feb. 12-13, 2025] (two days)
The School aims to summarize lessons we have learned from string theory about quantum gravity with a focus on the Swampland program equipping attendees with new insights and practical tools.

Date

2025-02-10 ~ 2025-02-13

Location

Organizers

• Babak Haghighat ( YMSC & BIMSA )

• Fengjun Xu ( 徐锋军, BIMSA )

• Shing-Tung Yau ( Tsinghua University&BIMSA )

• Cumrun Vafa ( Harvard University )

Special Guest

• Cumrun Vafa ( Harvard University )

Speakers

• Alek Bedroya ( Princeton University )

• Hector Parra de Freitas ( Harvard University )

• Severin Luest ( U. Montpellier )

• Jacob McNamara ( Caltech )

• Georges Obied ( Oxford )

• Gary Shiu ( University of Wisconsin-Madison )

• Houri Tarazi ( Chicago University )

• Tim Wrase ( Lehigh University )

• Kai Xu ( Harvard )