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Gabriele Lobbia (Mar 03 2021 at 12:06):Dear Colleagues,
I am pleased to announce a new online seminar series: ItaCa Fest 2021.
ItaCa Fest is an online webinar aimed to gather the community of ItaCa (https://progetto-itaca.github.io/).
We will start the 14th of April at 14:30 Italian time (UTC+1) with our first speakers:
Ivo Dell'Ambrogio
Pawel Sobocinski
Further speakers will include: Walter Tholen, Amar Hadzihasanovic, Olivia Caramello and Paolo Saracco.
Please check our webpage periodically for an updated list of speakers:
https://progetto-itaca.github.io/pages/fest21.html
You can also find us on researchseminars (https://researchseminars.org/seminar/itaca) and on twitter (https://twitter.com/progetto_itaca).
With best wishes,
Gabriele
(for the organizers)
Matteo Capucci (he/him) (Sep 24 2021 at 07:22):The next installment of ItaCa Fest is happening on September 28th (next Tuesday), from 2.30pm to 4.30pm Italian time (UTC+2)
See our website for more information.
Mauro Porta
Pro and Ind-categories in Algebra and GeometryIn this talk we are going to discuss some natural instances of pro and ind categories in algebraic and geometric contexts, highlighting the importance of working with objects in Ind(Cat∞) and Pro(Cat∞) instead of their Cat∞ realizations. Towards the end we will raise some questions, with the intent of determining what is the “correct” object to consider in these contexts, so as to optimize the generalization/applicability trade-off.
Tim Van Der Linden
Algebras with representable representations(Joint work with Xabier García-Martínez, Matsvei Tsishyn and Corentin Vienne)
Just like group actions are represented by group automorphisms, Lie algebra actions are represented by derivations: up to isomorphism, a split extension of a Lie algebra B by a Lie algebra X corresponds to a Lie algebra morphism B → Der(X) from B to the Lie algebra Der(X) of derivations on X. The aim of this talk is to elaborate on the question, whether the concept of a derivation can be extended to other types of non-associative algebras over a field K, in such a way that these generalised derivations characterise the K-algebra actions. We prove that the answer is no, as soon as the field K is infinite. In fact, we prove a stronger result: already the representability of all abelian actions – which are usually called representations or Beck modules – suffices for this to be true. Thus we characterise the variety of Lie algebras over an infinite field of characteristic different from 2 as the only variety of non-associative algebras which is a non-abelian category with representable representations. This emphasises the unique role played by the Lie algebra of linear endomorphisms gl(V) as a representing object for the representations on a vector space V.
Matteo Capucci (he/him) (Sep 27 2021 at 08:28):Zoom link for tomorrow's talks
Reid Barton (Sep 27 2021 at 11:48):I think the timezone is actually UTC+2, right?
Matteo Capucci (he/him) (Sep 27 2021 at 12:35):Mmmh maybe? Definitely GMT+2
Matteo Capucci (he/him) (Sep 27 2021 at 12:36):Is GMT=UTC?
Reid Barton (Sep 27 2021 at 12:45):For practical purposes, yes
Matteo Capucci (he/him) (Sep 27 2021 at 13:33):Hence you're right, I'm gonna correct the time
Ivan Di Liberti (Sep 27 2021 at 14:35):Just to be clear, it is the italian time zone.
Daniele Palombi (Oct 21 2021 at 12:43):ItaCa fest is live on zoom! Join us at: https://progetto-itaca.github.io/
Daniele Palombi (Oct 21 2021 at 12:44):Today's talks:
Zanfa - Generalized presheaf-bundle adjunctions
Trimble - Grothendieck groups of 2-rigs as lambda rings
Morgan Rogers (he/him) (Oct 22 2021 at 10:04):Oops I missed it :crying_cat:
Daniele Palombi (Nov 16 2021 at 14:02):Dear friends of ItaCa,
This month's episode of ItaCa Fest will be this Thursday (November 18), from 14:30 to 16:30 UTC+1
See our website for more info.
This month's speakers:
Domenico Fiorenza — Sapienza, University of Rome
Categorical shadows lurking behind integral formulas for generaProfessor Friedrich: And so, if you have a complex genus taking rational values, i.e., a ring homomorphism from the complex cobordism ring to the field Q of rational numbers, you have an integral formula expressing it.
The Categorist: If a formula is true, it must be expressed by a commutative diagram.
Professor Friedrich: But my formula is true!
The Categorist: Then it must be expressed by a commutative diagram.
Professor Friedrich: Show me.
The Categorist: Let us consider the category of spectra…
Professor Friedrich: And so?
The Categorist: Well… I don’t see a commutative diagram here.
Professor Friedrich: And so?
The Categorist: And so your formula must be false.
Professor Friedrich: But my formula is true!
The Categorist: Impossible.
Sir Michael: There is something I think I know on the Spanier-Whitehead dual of a smooth manifold that may happen to be of some relevance here.
(Emil Ionesco, Triceratops)
Federico Olimpieri — University of Leeds
Categorifying Intersection TypesWe study a family of distributors-induced bicategorical models of lambda-calculus, proving that they can be syntactically presented via intersection type systems. We first introduce a class of 2-monads whose algebras are monoidal categories modelling resource management. We lift these monads to distributors and define a parametric Kleisli bicategory, giving a sufficient condition for its cartesian closure. In this framework we define a proof-relevant semantics: the interpretation of a term associates to it the set of its typing derivations in appropriate systems. We prove that our model characterize solvability, adapting reducibility techniques to our setting. We conclude by describing wo examples of our construction.
Daniele Palombi (Nov 18 2021 at 13:34):And we're live!