分野別セミナー

14:00 -- 14:45
Nuiok Dicaire (University of Edinburgh)
The theory of localisable monads


Abstract:
Monads have many useful applications both in mathematics and in computer science. Notably they provide a convenient way to describe computational side-effects. An important question is how to handle several instances of such side-effects or a graded collection of them. The usual approach consists in defining many “small” monads and combining them together using distributive laws. In this talk, we take a different approach and look for a pre-existing internal structure to a monoidal category that allows us to develop a fine-graining of monads. This uses techniques from tensor topology and provides an intrinsic theory of local computational effects without needing to know how the constituent effects interact beforehand. We call the monads obtained "localisable" and show how they are equivalent to monads in a specific 2-category. To motivate the talk, we will briefly consider applications in concurrency and quantum theory.


15:00 --15:45
Jean-Simon Pacaud Lemay (Kyoto University/RIMS)
An introduction to the world of Differential Categories


Abstract:
Differential categories provide the foundation of differentiation using category theory. Differential categories have been used in mathematics for differential geometry, commutative algebra, algebraic geometry, etc. and also in computer science for machine learning, differential linear logic, differential lambda calculus, etc. In this talk, I will provide an introduction and an overview of the theory of differential categories.


16:00 -- 17:00 Free Discussions