As we wrap up the last of our tutorials, let's gather for a stress-free night out to several college bars! We'll start at 8 PM this Saturday 25th May at New College.
We are also ready to unveil the next edition of our mathematical magazine, known simply as “The Invariant”. We're hosting a release party at a G&Ds sometime next week, stay tuned!
As always, please follow our social media for the latest updates.
PhD position in Mathematics focusing on geometric deep learning
Deadline: 10 June 2024
Start date: 1 January 2025 (or by agreement)
More info and application here.
15:30
Non-semisimple link and manifold invariants: on algebraically strong invariants
Abstract
I will talk about link and three-manifold invariants defined in terms of a non-semisimple finite ribbon category C together with a choice of tensor ideal and a trace on it. If the ideal is all of C, these invariants agree with those defined by Lyubashenko in the 90’s, and as we show, they only depend on the Grothendieck class of the objects labelling the link. These invariants are therefore not able to determine non-split extensions, or they are algebraically weak. However, we observed an interesting phenomenon: if one chooses an intermediate proper ideal between C and the minimal ideal of projective objects, the invariants become algebraically much stronger because they do distinguish non-trivial extensions. This is demonstrated in the case of C being the super-modular category of an exterior algebra. That is why these invariants deserve to be called “non-semisimple”. This is a joint work with J. Berger and I. Runkel.