U. Haifa Topology & Geometry seminar: Wednesday, March 11, 2026, 13:00. Speaker: William Balderrama (Bonn). Title: “Realization spaces and categorified square-zero deformation theory”.
A fundamental class of problems in algebraic topology are the realization problems: when is a given algebraic object realizable as an algebraic invariant of a space? For example, one might ask when a module over the Steenrod algebra arises as the mod p cohomology of a space. Insight from work of Dwyer-Kan, Blanc-Dwyer-Goerss, and others tells us that these problems can be fruitfully studied by constructing a moduli space of all possible realizations, then considering the various ways that this moduli space decomposes into simpler pieces. I will describe joint work with Piotr Pstr¸agowski on a new higher categorical perspective which extends these decomposition theorems.
