July 6, Monday 9:00 - 10:00 am
A topological quantum field theory (TQFT) in dimension d is a symmetric monoidal functor from a cobordism category Cob_{d,d-1}, with closed (d-1)-manifolds as objects and diffeomorphism classes of d-manifolds with boundary as morphisms, into the category of vector spaces. TQFTs define d-manifold invariants and have applications in mathematical physics, topological quantum computing and condensed matter physics.
A recent development are TQFTs with defects that include lower-dimensional submanifolds labeled with higher categorical data. They define invariants of stratified manifolds and describe excitations and domain walls in models from condensed matter physics and topological quantum computing.
The construction of defect TQFTs is not easy and often relies on diagrammatic calculi and additional choices such as fixed triangulations. We show in the example of 3d Dijkgraaf-Witten TQFT how defect TQFTs can be constructed in a more categorical way and discuss applications.
This is based on joint work with Joao Faria Martins.
July 8, Wednesday 9:00 - 10:00 am
Concurrent monads, due to Rivas and Jaskelioff, are a specialization of monads, an ordered-category-theoretic relaxation of lax monoidal monads (commutative monads). For the application in categorical programming semantics, they are an abstraction of notions of effectful computation that are composable not only sequentially but also in parallel; the sequential and parallel compositions are interrelated by inequational middle-four interchange. Concurrent monads categorify concurrent monoids from algebraic semantics.
I will motivate and introduce the concept, present some theory and show some examples from programming semantics and concurrency theory.
July 10, Friday 9:00 - 10:00 am
Over the last 11 years I have gone from being an “ordinary” maths professor to building a hybrid career as a professor and public communicator, with 9 books for general audiences, a monthly column in the Wall Street Journal, numerous mathematical art commissions, regular TV and radio appearances, and an international public speaking freelance career, In this talk I will share some things I have learnt along the way, about how to approach maths communication, how to balance it with research, and some examples I have found effective for opening up category theory to audiences who were previously excluded. My aim is to motivate and encourage more mathematicians to do more public communication, and to do it well.
Website based on a bootstrap design by Hartmut Eilers and Eric Koskinen.