David Ayala

David Ayala is an Associate Professor of Mathematics at Montana State University in Bozeman, Montana, specializing in quantum topology. His research uses homotopy theory and category theory to construct global invariants that abstract physical invariants of confined quantum systems in ground states.

Dr. Ayala received his PhD from Stanford University under Ralph Cohen. Prior to his position at Montana State University, he held postdoctoral positions at the Mathematical Sciences Research Institute (MSRI) at UC Berkeley, the University of Southern California, Harvard University, and the University of Copenhagen.

His research centers on factorization homology, an association of objects from locally standard entities (such as manifolds and links) with higher-algebraic data. His work demonstrates how Poincaré duality intertwines with Koszul duality through factorization homology, yielding identities within the values of these constructions. Recent publications focus on the tangle hypothesis, symmetries of cyclic nerves, and additivity for factorization algebras, showing his continued engagement with cutting-edge topics in higher category theory and algebraic topology.

Dr. Ayala has supervised five PhD students to completion: Anna Cepek (2019) on configuration categories, Daniel Perry (2019) on homotopy groups of contact 3-manifolds, Eric Berry (2021) on additivity of factorization algebras, Adam Howard (2021) on immersions of surfaces, and Benjamin Moldstad (2024) on stable circle actions. His collaborative work with John Francis, Aaron Mazel-Gee, and Nick Rozenblyum demonstrates strong interdisciplinary connections within the mathematical community.