Research

Category theory

I am interested in all topics relating to category theory. My specialism is in topos theory, and more specifically in toposes whose objects are actions of monoids. Since arriving at LIPN as a post-doc in 2022 I have been researching various applications of category theory in computer science, including:

  • Models of λ-calculus with Thomas Seiller and Will Troiani,
  • An algebraic-geometry-style approach to descriptive complexity theory with Damiano Mazza and
  • A reformulation of categorical models of differential linear logic with Marie Kerjean and Valentin Maestracci.
I organise the Category Theory working group between LIPN and the neighbouring mathematics lab, LAGA. I am also a moderator and active member on the Category Theory Zulip channel; send me a message if you would like an invite link!

Complexity theory

Monoid actions appear in computability and complexity theory at a very abstract level: we can define a generic model of computation to consist of a space (of configurations), which might carry a topological or measure structure, equipped with a monoid action expressing the effect of the operations which the model is capable of performing. Programs, possibly subject to some constraints, form structures over these actions, and so complexity classes emerge as invariants. My current research program, which is developing in the cracks between collaborations, is to try to use toposes of monoid actions as a context for computing and comparing these actions alongside other monoid actions.

Publications

Toposes of topological monoid actions

Morgan Rogers (2023)
Compositionality, volume 5.

On Supercompactly and Compactly Generated Toposes

Morgan Rogers (2023)
Theory and Applications of Categories, volume 37.

Monoid Properties as Invariants of Toposes of Monoid Actions

Jens Hemelaer, Morgan Rogers (2021)
Applied Categorical Structures , volume 29.

more

Teaching

IUT de Villetaneuse

BUT Réseaux et Télécoms (Moodle). Responsable du cours/TDs de première année :
  • R1.01 - Initiation aux réseaux informatiques
  • R1.02 - Principes et architecture des réseaux
  • R1.07 - Fondamentaux de la programmation
    • Cours: 1,
    • TPs: 1, 2, 3
  • R1.08 - Base des systèmes d'exploitation
  • R2.08 - Analyse et traitement de données structurées
Masters research projects (stages)
I am interested in supervising masters projects in maths and computer science. Below is a project I am proposing for this year.
De Morgan toposes. English description; French description.