Higher category theory

…topology with a focus on homotopy theory, partly funded by the Swedish Research Council project "Local to global extensions of topological quantum field theories". Related topics such as stable homotopy theory, higher category theory, homological algebra and geometric topology are also possible. Doctoral students attend seminars and conferences and may teach or take on departmental duties for up to 20% of their time. Start no later than 1 Octob

Marco Giustetto examines how synthetic higher category theory can extend the proof methods of homotopy type theory. Internal reasoning in an infinity-topos can establish classical results about spaces in a form suitable for machine verification. For the next categorical dimension, Riehl and Shulman introduced synthetic (infinity, 1)-categories: simplicial objects satisfying finitely many conditions, whose finiteness brings technical advantages. The talk considers the extension to (infinity, n)-categories, identifying which features of the n = 1 theory survive and which cannot generalize. The w