The Algebraic Structures in Topology is a conference series that meets every two years in San Juan, Puerto Rico and this year is partially supported by the National Science Foundation , Purdue University , the Institute of the Mathematical Sciences of the Americas at the University of Miami and the K-Theory Foundation . The conferences will feature a variety of events focusing on recent developments in algebraic topology and their applications to geometry, physics, and data science. This iteration is an official satellite event of the International Congress of Mathematicians 2026 (July 23-30, 2026).

This year’s iteration of the series will occur on July 10 – July 17, 2026. From July 10th to July 12th it will feature three introductory mini-courses on the topics of topological quantum computation, stable homotopy theory, and the cohomology of the Torelli group accessible to graduate students and researchers in related fields outside algebraic topology. The main research conference will take place from July 13th to July 17th and will feature talks by invited speakers as well as contributed talks. Everything will take place in (possibly different venues) in San Juan, Puerto Rico (TBD). More information on the mini courses and the schedule will be available soon.

Speakers

Mini-courses (July 10-12)

• Shawn Cui (Purdue University): An introduction to topological quantum computation
• Ishan Levy (Institute of Advanced Study): The chromatic view of stable homotopy theory
• Andrew Putman (University of Notre Dame): The cohomology of the Torelli group

Conference (July 13-17)

• Shawn Cui (Purdue University)
• Nir Gadish (University of Pennsylvania)
• Ishan Levy (Institute of Advanced Study)
• Mikhail Khovanov (Johns Hopkins University)
• Natalia Pacheco-Tallaj (MIT)
• Julia Plavnik (Indiana University)
• Andrew Putman (University of Notre Dame)
• Piotr Pstragowski (University of Washington)
• Józef Przytycki (George Washington University)
• Zhenghan Wang (UC Santa Barbara)
• Kirsten Wickelgren (Duke Uniersity)
• Jennifer Wilson (University of Michigan)
• Zhouli Xu (UCLA)

Organizers

This conference series is organized by Manuel Rivera (Purdue University), Ralph Kaufmann (Purdue University), Mona Merling (UPenn), and Jeremy Miller (Purdue University). The local organizers are Gabriel Montoya Vega (University of Puerto Rico, Río Piedras) and Iván Cardona (University of Puerto Rico, Río Piedras).
If you have any questions you may contact the organizers at algtoppr at gmail dot com.