Conference: Algebraic Structures in Topology 2024

Purdue University, West Lafayette IN

Investigators

Abstract

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.