Oxford Office short talks
José: Given a base logic with predicates on states, there are two tasks one might want to accomplish simultaneously: add in a notion of dynamics to the states (which is done comonadically), and enhance the logic used (which is achieved by a determining a monad on posets). I’ll sketch how specifying a lax morphism of monads with a hyperdoctrine as its underlying functor provides a base semantics for enhanced (e.g., temporal) formulae on behaviours of systems, which then induce a new hyperdoctrine whose contexts are the systems themselves.
Q: Linear error-correcting codes form the mathematical backbone of modern digital communication and storage systems, but identifying champion linear codes (linear codes achieving or exceeding the best known minimum Hamming distance) remains challenging. By training a transformer to predict the minimum Hamming distance of a class of linear codes and pairing it with a genetic algorithm over the search space, we develop a novel method for discovering champion codes. This model effectively reduces the search space of linear codes needed to achieve a best minimum Hamming distance. Our results present the use of this method in the study and construction of error-correcting codes, applicable to codes such as generalised toric, Reed–Muller, Bose–Chaudhuri–Hocquenghem, Algebraic–Geometry, and potentially quantum codes.
Khyathi: Fusion categories capture finite particle-like excitations and their fusion rules. I will briefly recall their motivation and then sketch some plausible “double fusion” constructions - via delooping, quintet and Grothendieck approaches - briefly highlighting how these encode lattice-like structures, domain walls, and junctions between phases.