Conference: Equivariant Homotopy Theory in Context Workshops

This award provides travel support for early career US-based mathematicians to attend four workshops during the semester program “Equivariant Homotopy Theory in Context” at the Isaac Newton Institute for Mathematical Sciences in Cambridge, UK in the first half of 2025.The workshop names and dates are: 1. Introductory workshop for Equivariant Homotopy Theory in Context, January 13-17, 2025 2. Operads and calculus, April 7-11, 2025 3. New horizons for equivariance in homotopy theory, May 12-16, 2025 4. Beyond the telescope conjecture, June 16-20, 2025 Priority for funding will be given to those who do not have funds from other sources . The direct impact of NSF funding will be the training and career development of up to 30 researchers, by means of the opportunity to participate in a major program in Europe and at the Newton Institute, in particular, which is a major international nexus in mathematics. A secondary impact is to further develop collaboration between emerging research groups in algebraic topology and derived algebraic geometry in the US and Europe, in particular the United Kingdom. Holding this program as well as the workshops at the Newton Institute for Mathematical Sciences makes particular sense, because this is an international field, with leaders in many countries. The last decade has seen an explosion of exciting results in homotopy theory and related areas of algebraic geometry, algebra, and the algebraic topology of manifolds. Crucial here are new equivariant techniques, the study of symmetries and group actions in algebraic topology. Historically, advances in differential topology depended on the solution of basic homotopy theoretic questions and, in the same way, the advent of equivariant homotopy theory was guided by the study of manifolds with group actions. It quickly became much more than that and the interplay between equivariant homotopy theory and its applications in algebraic K-theory, chromatic homotopy theory, functor calculus, and other fields drove a self-reinforcing narrative that is only expanding now. This semester-long program and workshops are building on this momentum and creating an environment for further exchange of ideas. Workshop websites are: https://www.newton.ac.uk/event/ehtw01/ https://www.newton.ac.uk/event/ehtw02/ https://www.newton.ac.uk/event/ehtw03/ https://www.newton.ac.uk/event/ehtw04/ 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.