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Meeting 35

20th June 2024 (University of Manchester)

Venue: Room: G.107, ground floor, Alan Turing Building, University of Manchester.

Oxford Road train station is ~10 minutes walk, Piccadilly train station is ~25 minutes walk. Manchester Victoria train station ~40 minutes walk.

Confirmed speakers:


Schedule
2:00-3:00 Simona Paoli
3:00-3:30 Break
3:30-4:30 Marcelo Fiore
4:30-5:00 Break
5:00-6:00 Sean Moss

Titles and Abstracts:

  • Simona Paoli
    • Title: A directed approach to higher categories
    • Abstract: Several models of higher categories have been described using the combinatorics of simplicial objects, based on the category simplicial delta. A prototype example is that a category can be described as a simplicial set satisfying appropriate conditions (the Segal conditions) via the nerve functor. After recalling some of these models, I will introduce the category of fat delta, due to Joachim Kock. This category carries some of the intuition of the simplicial delta, but has a richer structure and is a directed category. I will discuss some of the advantages of a directed approach to model higher categories, illustrating results in dimension 2, and indicating possible higher dimensional generalizations.
  • Marcelo Fiore
    • Title: Monoidal bicategories, differential linear logic, and analytic functors
    • Abstract: I shall consider bicategorical models of differential linear logic, introducing bicategorical counterparts of the notions of a linear exponential comonad and of a codereliction transformation, which are respectively central to the study of linear logic and of differential categories.

      As an application, I will present an extension of the differential calculus of analytic functors on sets to analytic functors between presheaf categories, analogous to the extension of calculus from one to many variables.

      This is joint work with Nicola Gambino and Martin Hyland available from arXiv 2405.05774 [arxiv.org].

  • Sean Moss
    • Title: Markov categories, ergodic theory, and random graphs
    • Abstract: I will give an introduction to categorical probability theory via Markov categories and demonstrate it with two examples taken from joint work. First, by taking a few extra axioms that hold in the standard model of probability, we can give a conceptual reframing of the proof of the classical ergodic decomposition theorem for a dynamical system. Second, by embracing non-standard theories, we can give a new perspective on random graph models, or 'graphons', which are used to model very large graphs in terms of randomly sampled finite subgraphs. I will not assume knowledge of ergodic theory or random graph models.

Meeting of YaMCATS are open to everyone. However, please register by using this link, by Thursday 13th June 2024.
Your registration will facilitate us producing the final report for our funders, and also plan the local organisation of the meeting (coffee breaks, lecture rooms, etc...).

Meeting # 35 of YaMCATS is a satellite meeting of the: 75th British Mathematical Colloquium, University of Manchester 17th June to 20th June 2024.