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Meeting 40 - Sheffield

Thursday, 16 April 2026, Sheffield.

Hosted by the School of Mathematics and Statistics of the University of Sheffield.
Supported by LMS.
If you will arrive by train, you can either walk from the station or take the tram.  Here are some directions.
It takes around 40mnts to walk from the train station to the University of Sheffield. Google-maps, or equivalent, is advisable.

If you would like to attend this meeting, please register by using this link, by 12:00noon (UK time) on Monday 13th April 2026. This will help us with organising the coffee breaks, and will also facilitate us producing the final report, as required by LMS.

All talks will happen in  Lecture Theatre 06 (aka LT6). Coffee breaks will be served in the Common Room I15.

Confirmed speakers:

Schedule

  • 13:00--14:00: Paula Verdugo: Double categorical equivalences.
  • 14:00--14:30: coffee break.
  • 14:30--15:30: Muriel Livernet: A nested family of homotopy theories arising from spectral sequences.
  • 15:30--16:00: coffee break.
  • 16:00 --17:00 Peter Huston: A gentle introduction to fusion 2-categories.
  • 17:00 -- Onwards. Informal discussions / pub / dinner.

Abstracts

  • Paula Verdugo:
    • Title: Double categorical equivalences.
    • Abstract: In this talk we will discuss the difficulties that arise when trying to decide on a canonical notion of “equivalence” for double categories. We will use model categorical techniques to support Campbell’s gregarious equivalences as the candidates to consider. In doing this, we will see how to construct many model structures on the category of double categories, including recovering existing ones.
      This talk is based on joint work with Lyne Moser and Maru Sarazola.
  • Muriel Livernet,
    • Title: A nested family of homotopy theories arising from spectral sequences.
    • Abstract: The aim of this presentation is to provide an overview of the results obtained with Sarah Whitehouse (and other collaborators, including J. Cirici, X. Fu, A. Guan, D.E. Santander, E. Roff and S. Ziegenhagen) and also to share my enthousiasm for multicomplexes (also known as twisted complexes) A functor $F$ from a category $C$ to the category of spectral sequences gives rise to a family $Er$ of morphisms in $C$ defined as the morphisms that are sent by $F$ to isomorphisms at the $r+1$-page of the spectral sequence. What can we say about the localization of $C$ with respect to this family? Can we compare the different localization when $r$ varies? These questions will be (partially answered) for $C$ the categories of filtered complexes, (truncated)-multicomplexes and directed graphs.
  • Peter Huston.
    • Title: A gentle introduction to fusion 2-categories.
    • Abstract: Fusion 2-categories are a generalization of fusion 1-categories, corresponding under the cobordism hypothesis to fully extended (3+1)D TQFTs. In this talk, I will motivate the definition of fusion 2-category, explore the classification of fusion 2-categories given in arxiv:2411.05907, and sketch some applications of fusion 2-categories related to (2+1)D symmetry-enriched topological order.