Conference: Algebraic Structures in Topology 2024

会议：拓扑中的代数结构 2024

• 批准号: 2348092
• 负责人: Manuel Rivera
• 金额: $ 4.67万
• 依托单位: Purdue University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2024
• 资助国家: 美国
• 起止时间: 2024-03-01 至 2025-02-28
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2348092&HistoricalAwards=false
• 关键词: Conference; Algebraic; Structures; Topology; 2024

This award provides support for US based participants in the conference "Algebraic structures in topology 2024” that will take place from June 5th to June 14th, 2024 in San Juan, Puerto Rico. Algebraic topology is a field of theoretical mathematics whose main goal is to study different notions of “shape” that belong to the realm of “continuous” mathematics, using tools from algebra that belong to the “discrete” realm. Algebraic topology has been applied successfully to other fields of mathematics, and, more recently, to science including quantum physics, solid state physics, string theory, data science, and computer science. This conference will focus on recent developments in algebraic topology and its applications. The conference will feature a series of events accessible to audiences at different levels. These include: 1) a three-day school with mini-courses accessible to graduate students and mathematicians from fields outside algebraic topology, 2) a public event with talks and discussions accessible to a general audience, 3) a week-long research conference featuring invited speakers and contributed talks in algebraic topology. Furthermore, the conference aims to engage with groups that are historically underrepresented in academic research in mathematics, particularly with mathematicians of Hispanic and Latin American origin, in a deep and direct manner. Geographically, culturally, as well as politically, the strategically selected location, Puerto Rico, sits between the mathematical communities based in United States, Canada, Europe, and Latin America. Along with a strong engagement with the local community, the event will feature works by a significant number of Hispanic mathematicians. The overarching theme of the conference is the use of algebra to give structure to geometric contexts. The mini-courses will be on the topics of algebraic K-theory, configuration spaces, and string topology and aim to bring participants to the state-of-the-art in these subjects. The research talks will highlight recent breakthroughs in different sub-fields of algebraic topology including stable and chromatic homotopy theory, K-theory, higher category theory, higher algebra, derived geometry, operads, homological stability, configuration spaces, string topology, and topological data analysis and will be given by leading experts in these fields. By bringing together a diverse cohort of mathematicians working on different sub-fields, the organizers aim to foster new ideas and perspectives. The public lectures will discuss research in theoretical mathematics, and its relevance to society, science, and technology, with examples coming from topology.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

该奖项为参加“2024 年拓扑中的代数结构”会议的美国参与者提供支持，该会议将于 2024 年 6 月 5 日至 14 日在波多黎各圣胡安举行。代数拓扑是理论数学的一个领域，其主要目标是使用属于“代数”拓扑的代数工具来研究属于“连续”数学领域的不同“形状”概念。已成功应用于其他数学领域，最近还应用于科学领域，包括量子物理学、固体物理学、弦理论、数据科学和计算机科学。本次会议将重点讨论代数拓扑及其应用的最新发展。包括一系列面向不同级别观众的活动，包括：1）为期三天的学校，为研究生和代数拓扑以外领域的数学家提供迷你课程，2）面向公众的演讲和讨论。广大观众， 3) 为期一周的研究会议，邀请代数拓扑方面的演讲嘉宾和贡献演讲。此外，会议旨在与历史上在数学学术研究中代表性不足的群体，特别是西班牙裔和拉丁美洲裔数学家进行深入的交流。从地理、文化和政治角度来看，战略性选择的地点波多黎各位于美国、加拿大、欧洲和拉丁美洲的数学社区之间，并且与当地社区有着密切的联系。活动将特色会议的首要主题是使用代数为几何背景提供结构。迷你课程的主题包括代数 K 理论、配置空间、弦拓扑和目标。研究报告将重点介绍代数拓扑不同子领域的最新突破，包括稳定同伦理论和色同伦理论、K 理论、高等数学。范畴论、高等代数、派生几何、运算、同调稳定性、构型空间、弦拓扑和拓扑数据分析，将由这些领域的顶尖专家汇聚在一起，组织者旨在培养新的想法和观点，公开讲座将讨论理论数学研究及其与社会、科学和技术的相关性，并以拓扑学为例。该奖项反映了 NSF 的法定使命，并被认为值得支持。通过评估利用基金会的智力优势和更广泛的影响审查标准。