Séance Séminaire

Séminaire Algèbre Géométrie Algébrique Topologie Algébrique

Renormalization of TFTs and the homotopy time-slice axiom of AQFTs: two examples of inversion of operations in Mathematical Physics

The process of inverting operations has made appearances in a broad range of mathematical subjects. From basic commutative algebra, where we are exposed to inverting elements of rings, to chromatic homotopy theory, where we fracture homotopical information with respect to several homology theories by inverting homology equivalences. From a modern point of view, we could say that one of the main reasons why localization, a fancy name for "inverting operations", is so important is because it connects the classical world of mathematics (embodied by ordinary categories and the mathematics within them) with higher mathematics (higher categories and the possibilities that they offer).   In this talk, we will revisit how localization creates spatial information, building the above connection, and then study two applications in Mathematical Physics. The first one, renormalization of TFTs (j/ Damien Calaque) addresses the triviality of renormalization procedures in the topological setting. The second one, the homotopy time-slice axiom of AQFTs (j/ Marco Benini-Alexander Schenkel) studies when such axiom can or cannot be strictified depending on the underlying geometry.