ERATO蓮尾プロジェクトの勝股です。もう一つの講演のご案内をいたします。

Dear all,

On Tuesday 10 May, Nuiok Dicaire and Jean-Simon Pacaud Lemay will give talks for our project colloquium during 16:00-18:00. Further details can be found below.

If you would like to attend, please register through the following Google form: https://forms.gle/6PoGNEfJVHLYDAdKA We later send you a zoom link by an email (using BCC).

For the latest information about ERATO colloquium / seminar, please see the webpage https://docs.google.com/document/d/1Qrg4c8XDkbO3tmns6tQwxn5lGHOrBON5LtHXXTpX... .

Shin-ya Katsumata (ERATO MMSD Colloquium Organizer) Email: [email protected] ------- Tuesday 10 May 2022, 16:00-17:00

Nuiok Dicaire, the University of Edinburgh Title: A new approach to localising 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. We will conclude the talk by looking at how the theory of localisable monads can be combined with graded-monads and category-graded monads.

Tuesday 10 May 2022, 17:00 - 18:00

Jean-Simon Pacaud Lemay (JSPS postdoctoral fellow) Title: A tour around the world of differential categories

Abstract: The theory of differential categories uses category theory to provide the abstract foundations of differential calculus in both mathematics and computer science. Differential categories have recently gained lots of interest and popularity. In mathematics, differential categories have found applications in commutative algebra, differential geometry, algebraic geometry, and synthetic differential geometry. In computer science, differential categories have found applications in differential linear logic, differential lambda calculus, differentiable programming, automatic differentiation, and machine learning.

In this talk, I will provide a tour on the world of the differential categories. We will visit the four chapters of differential categories:

1. Differential categories, which axiomatize the algebraic foundations of differentiation. 2. Cartesian differential categories, which axiomatize differential calculus over Euclidean spaces. 3. Differential restriction categories, which axiomatize differential calculus over open spaces. 4. Tangent categories, which axiomatize differential calculus over smooth manifolds.

We will talk about the famous "map of differential categories", and also the history and applications of differential categories.