Conference: Algebraic Structures in Topology 2024

该奖项为美国参与者提供支持，会议“拓扑学中的代数结构2024”将于2024年6月5日至6月14日在波多黎各的圣胡安举行。代数拓扑学是理论数学的一个领域，其主要目标是研究属于“连续”数学领域的不同“形状”概念，使用属于“离散”领域的代数工具。代数拓扑学已经成功地应用于数学的其他领域，最近还应用于包括量子物理、固态物理、弦理论、数据科学和计算机科学在内的科学。这次会议将集中在代数拓扑学及其应用的最新发展。会议将举办一系列面向不同层次受众的活动。其中包括：1）为期三天的学校与迷你课程访问研究生和数学家从代数拓扑以外的领域，2）公开活动与会谈和讨论访问一般观众，3）为期一周的研究会议，邀请演讲者和贡献会谈代数拓扑。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的数学家，以深入和直接的方式进行接触。地理上，文化上，以及政治上，战略选择的位置，波多黎各，坐落在美国，加拿大，欧洲和拉丁美洲的数学社区之间。沿着与当地社区的密切合作，该活动将展出大量西班牙裔数学家的作品。会议的首要主题是使用代数给结构的几何背景。迷你课程将讨论代数K理论，配置空间和弦拓扑的主题，旨在使参与者了解这些主题的最新技术。研究会谈将突出最近在代数拓扑的不同子领域的突破，包括稳定和色同伦理论，K理论，高级范畴理论，高等代数，导出几何，运算，同调稳定性，配置空间，弦拓扑和拓扑数据分析，并将由这些领域的领先专家给出。通过汇集不同子领域的数学家，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的研究，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，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。

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.