Dear all, Today we have a joint meeting with the LIPN seminar: [Intervenant]     Zeinab Galal, University of Manchester [Localisation]     Salle B107, bâtiment B, Université de Villetaneuse [Date]     25/11/2022 10:30 - 12:00 Résumé :  Fixpoint operators are tools to reason on recursive programs and infinite data types obtained by induction (e.g. lists, trees) or coinduction (e.g. streams). They were given a categorical treatment with the notion of categories with fixpoints. An important result by Plotkin and Simpson in this area states that provided some conditions on bifree algebras are satisfied, we obtain the existence of a unique uniform fixpoint operator. This theorem allows to recover the well-known examples of the category Cppo (complete pointed partial orders and continuous functions) in domain theory and the relational model in linear logic. In this talk, I will present a categorification of this result where the 2-dimensional framework allows to study the coherences associated to the reductions of ?-calculi with fixpoints i.e. the equations satisfied by the program computations steps. *The BBB link is different for this week: *https://bbb.lipn.univ-paris13.fr/b/sei-eer-t24* *code: 757416 Details of next week and beyond will be sent at the start of next week. See you there, Morgan On 17/11/2022 14:31, Morgan Rogers wrote:

Dear all,

Damiano is unwell, so we are back to having Will Troiani presenting *tomorrow morning **at 10:30am* in *B107* of the Institut Galilée (at Villetaneuse), and on BBB, https://bbb.lipn.univ-paris13.fr/b/rog-vao-uwm-s2j

    Title: Elimination and cut elimination in multiplicative linear logic.     Abstract: we give a fresh perspective to Girard's Geometry of Interaction program which seeks to find a model of linear logic where cut-equivalent terms are not interpreted identically, but     instead are related inside the model via some domestic transformation. Our model interprets proofs as coordinate rings, where the quotient ideals describe the patterns of equality     previously mentioned. The ideals of two different proofs which are related via cut-reduction are then related by the (pre-existing) Buchberger Algorithm, which is used to compute Gröbner     bases from generating sets for ideals.

I would also like to take this opportunity to announce that Eric Hoffbeck has kindly volunteered to present for the group on 02/12 or 09/12 or both. Details of that will be announced next week.

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Damiano est malade, donc nous allons accueillir Will Troiani *demain à 10h30 dans B107*, et sur BBB.

Je prends cette opportunité d'annoncer que Eric Hoffbeck fera un exposé chez nous ou le 2, ou le 9 Décembre (ou les deux). Les détails seront annoncé la semaine prochaine.

Amicalement, Morgan

On 07/11/2022 14:03, Morgan Rogers wrote:

...

Hello again!

Here is the corrected schedule for the upcoming events in the working group, bearing in mind that /11/11 is a national holiday/... Everything will take place as usual on *Fridays **at 10:30am* in *B107* of the Institut Galilée (at Villetaneuse), and on BBB, https://bbb.lipn.univ-paris13.fr/b/rog-vao-uwm-s2j

18/11: *Damiano Mazza* will continue the reading group on dualities between algebra and geometry, following Axel's technical talk two weeks ago. I expect we shall be exploring Anel and Joyal's /Topo-logie/.

25/11:*Zeinab Galal *will talk about /Two-dimensional fixpoint operators/. This talk was organised for the LoVe seminar, so there is likely to be a bigger attendance than usual.

02/12: *William Troiani* will present his recent preprint on cut elimination and Buchberger's algorithm. This is more algebra than category theory, but we'll see what category theory can be thrown at it anyway!

If you have something categorical that you want to talk about before the end of the semester, or you are particularly interested in one of the topics that were suggested at the start of the semester, let me know.

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Voici le programme corrigé des prochains événements du groupe de travail, sachant que le /11/11 est un jour férié/... Tout se déroulera comme d'habitude les *vendredi à 10h30 *dans*B107* de l'Institut Galilée (à Villetaneuse), et sur BBB, https://bbb.lipn.univ-paris13. fr/b/rog-vao-uwm-s2j

18/11 : *Damiano Mazza* continuera le groupe de lecture sur les dualités entre algèbre et géométrie, suite à l'exposé technique d'Axel il y a deux semaines. Je m'attends à ce que nous explorions l'article /Topo-logie/ d'Anel et Joyal.

25/11: *Zeinab Galal* parlera des opérateurs de points fixes 2-dimensionnels. Cet exposé a été organisée pour le séminaire LoVe, il est donc probable qu'il y ait une plus grande participation que d'habitude.

02/12 : *William Troiani* présentera sa récente prépublication sur l'élimination des coupures et l'algorithme de Buchberger. C'est plus de l'algèbre que de la théorie des catégories, mais nous verrons ensemble comment la théorie des catégories peut y entrer dedans !

Si vous avez quelque chose de catégorique dont vous voulez parler avant la fin du semestre, ou si vous êtes particulièrement intéressé par l'un des sujets qui ont été proposés au début du semestre, faites-le moi savoir.

Bonne semaine, Morgan