Conference: Algebraic structures in topology, San Juan, Puerto Rico, 2026

The third Algebraic Structures in Topology conference will be held July 10-17, 2026, in San Juan, Puerto Rico. This conference brings together mathematicians working in algebraic topology, a field that uses algebraic tools to study qualitative and quantitative properties of geometric spaces. A central theme of this iteration is the interactions between algebraic topology and fields of national priority, including quantum physics, quantum computing, and data science. The meeting will feature a mini-course session designed to introduce graduate students to cutting-edge research areas, followed by a research conference with talks given by leading researchers and short contributed talks offering early-career mathematicians the opportunity to present their work. By gathering researchers from both theoretical and applied backgrounds, the conference aims to spark new collaborations and open new research directions at the intersection of pure mathematics and real-world applications. Supporting the training and professional development of junior mathematicians, including graduate students and postdoctoral researchers, is a primary goal of the meeting. By exposing participants to the mathematical aspects of high-priority national research areas such as quantum information science, data science, and advanced computational methods, this conference aligns with NSF’s emphasis on strengthening the US STEM workforce and sustaining American leadership in emerging technologies.

The conference will highlight recent advances in algebraic topology and its applications, with an emphasis on the use of higher algebra to illuminate problems in topology and geometry arising from physical systems. Featured research topics include homotopy theory, algebraic K-theory, moduli spaces and homological stability, knot theory, topological field theories, fusion categories, topological aspects of quantum computing, and topological data analysis. By bringing together researchers from across these areas, the conference seeks to foster the cross-pollination of ideas, support the development of the next generation of mathematicians, and leverage United States strength in algebraic topology to advance progress in applied fields. The conference webpage is: algtoppr.github.io

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.

Award Number: 2553410
Principal Investigator: Manuel Rivera
Funds Obligated: $30,000
State: IN