Alexander Berglund, Associate Professor, SU
My research revolves around interactions between algebraic topology and commutative algebra. In my PhD thesis, I used ideas from homotopy theory to solve problems in commutative algebra concerning the cohomology of Stanley-Reisner algebras and the classification of Golod rings. More recently, I have become interested in reversing the flow of ideas, using algebraic models to study homotopy theory. In particular, L-infinity algebra models for Q-local homotopy types and E-infinity algebra models for p-complete homotopy types. When working with the algebraic models, tools from homological algebra such as Koszul duality for operads, minimal models, and various notions of formality become available. I am developing such tools to study algebraic models for constructions such as mapping spaces, loop spaces and polyhedral products, with applications to string topology and toric topology. I am currently studying the cohomology of classifying spaces of homotopy automorphism groups or, equivalently, characteristic classes for fibrations with a specified fiber.