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