Itaca Fest 2024
ItaCa Fest is an online webinar aimed to gather the community of ItaCa.
The seminar will be live on Zoom at this link. The time is: 3pm Italian time.
Here the list of seminars
April 10, 2024
Time | Speaker | Affiliation | Talk | Material |
---|---|---|---|---|
15:00 | P.-A. Jacqmin | Royal Military Academy | Surjection-like classes of morphisms | ▶ |
15:30 | Questions Time | |||
15:40 | M. Mancini | Università di Palermo | On the representability of actions of non-associative algebras | ▶ |
16:10 | Questions Time | |||
16:20 | A. Cigoli | Università degli Studi di Torino | From Yoneda's additive regular spans to fibred cartesian monoidal opfibrations | ▶ |
16:50 | Questions Time | |||
17:00 | Free Chat |
Pierre-Alain Jacqmin
Surjection-like classes of morphisms
Many classes of epimorphisms are considered in the literature with the aim of generalizing surjective functions from the category Set of sets to an arbitrary category. However, some of them fail to have specific desirable properties. In this talk, we are interested in classes of morphisms which interact with finite limits as surjections do in Set. More precisely, we study classes of morphisms in finitely complete categories which admit a "good" embedding in a presheaf category. By good embedding, we mean a functor which preserves and reflects finite limits and the classes of morphisms involved. We will examine both the conservative faithful and the fully faithful cases. Our main result is a complete characterization of those classes of morphisms via simple and well-known properties.
Manuel Mancini
On the representability of actions of non-associative algebras
It is well known that in the semi-abelian category Grp of groups, internal actions are represented by automorphisms. This means that the category Grp is action representable and the actor of a group X is the group Aut(X). The notion of action representable category has proven to be quite restrictive: for instance, if a non-abelian variety of non-associative algebras, over an infinite field of characteristic different from two, is action representable, then it is the category of Lie algebras. More recently G. Janelidze introduced the notion of weakly action representable category, which includes a wider class of categories.
In this talk we show that for an algebraically coherent variety of algebras and an object X of it, it is always possible to construct a partial algebra E(X), called external weak actor of X, which allows us to describe internal actions on X. Moreover, we show that the existence of a weak representation is connected to the amalgamation property and we give an application of the construction of the external weak actor in the context of varieties of unitary algebras.
Alan Cigoli
From Yoneda's additive regular spans to fibred cartesian monoidal opfibrations
It is well known that group cohomology can be interpreted in terms of equivalence classes of crossed extensions, the abelian group structure being given by the so-called Baer sums. By analogy, an intrinsic definition of cohomology in strongly semi-abelian categories, or more generally in exact Mal'tsev categories (Bourn-Rodelo), is given. In this talk, I will explain how Baer sums can be formally derived from the fibred/cofibred nature of the category of all crossed extensions of a given length. This point of view turns out to be very close to Yoneda's theory of Ext groups. We will see how his notion of additive regular span is actually an instance of fibred cartesian monoidal opfibration. Time permitting, I will give some hint on how this formal point of view can be carried on to a 2-dimensional level, thus giving a notion of cohomology 2-group.
(based on joint works with S. Mantovani, G. Metere and E.M. Vitale
May 7, 2024
Time | Speaker | Affiliation | Talk | Material |
---|---|---|---|---|
15:00 | S. Wolf | Universität Regensburg | Higher Category Theory Internal to an Infinity Topos | |
15:30 | Questions Time | |||
15:40 | F. Rota | University of Glasgow | Exceptional collections and pseudolattices in mirror symmetry | |
16:10 | Questions Time | |||
16:20 | V. Ozornova | Max Planck Institute for Mathematics | Equivalences in higher categories | |
16:50 | Questions Time | |||
17:00 | Free Chat |
Sebastian Wolf
Higher Category Theory Internal to an Infinity Topos
The goal of this talk will be to give a brief introduction to the theory of higher categories internal to an infinity-topos, developed in joint work with Louis Martini. I will also indicate why such a theory is useful to get a better understanding of the geometry of infinity topoi. If time permits, I will conclude by explaining how one can use this language to give a characterization of proper morphism of infinity topoi in the sense of Lurie.
Franco Rota
Exceptional collections and pseudolattices in mirror symmetry
In the 1990s, theoretical physicists correctly predicted curve counts in an algebraic variety (a quintic threefold X) inferring them from a “mirror variety” Y. This was the start of mirror symmetry - a field of algebraic geometry that investigates how to construct mirrors and how to make the duality precise. A modern incarnation of the theory is the homological mirror symmery (HMS) conjecture by Kontsevich, which states that the duality first observed geometrically reflects an equivalence between a category built from X and one obtained from Y.
Describing and motivating some of the structures carried by these categories, I’ll briefly mention how to interpret the HMS equivalence as a quasi-isomorphism of Ainfty-algebras, and then elaborate on necessary conditions for the equivalence, which rephrase the question into multilinear algebra.
Viktoriya Ozornova
Equivalences in higher categories
There are different notions of ‘sameness’ arising in mathematics. The first one we usually encounter is equality of elements in a set. In our ‘daily life’, we are used to identify isomorphic objects, and we are secretly doing so in our favorite category. For categories themselves, we look for equivalences between those. But when should we consider two 2-categories to be ‘the same’? And how does the pattern continue? This talk is based upon joint work with Amar Hadzihasanovich, Félix Loubaton and Martina Rovelli.
June 5, 2024
Time | Speaker | Affiliation | Talk | Material |
---|---|---|---|---|
17:00 | L. Santocanale | Aix-Marseille University | TBA | |
17:30 | Questions Time | |||
17:40 | J. Weinberger | Johns Hopkins University | TBA | |
18:10 | Questions Time | |||
18:20 | TBA | TBA | ||
18:50 | Questions Time | |||
19:00 | Free Chat |
Luigi Santocanale
TBA
TBA
Jonathan Weinberger
TBA
TBA
TBA
TBA
TBA
September 25, 2024
Time | Speaker | Affiliation | Talk | Material |
---|---|---|---|---|
15:00 | D. Stein | Radboud University Nijmegen | TBA | |
15:30 | Questions Time | |||
15:40 | D. Ahman | University of Tartu | TBA | |
16:10 | Questions Time | |||
16:20 | M. Di Meglio | University of Edinburgh | TBA | |
16:50 | Questions Time | |||
17:00 | Free Chat |
Dario Stein
TBA
TBA
Danel Ahman
TBA
TBA
Matthew Di Meglio
TBA
TBA
October 22, 2024
Time | Speaker | Affiliation | Talk | Material |
---|---|---|---|---|
15:00 | J. Bourke | Masaryk University | TBA | |
15:30 | Questions Time | |||
15:40 | G. Tendas | University of Manchester | TBA | |
16:10 | Questions Time | |||
16:20 | L. Mesiti | University of Leeds | TBA | |
16:50 | Questions Time | |||
17:00 | Free Chat |
John Bourke
TBA
TBA
Giacomo Tendas
TBA
TBA
Luca Mesiti
TBA
TBA
November 20, 2024
Time | Speaker | Affiliation | Talk | Material |
---|---|---|---|---|
15:00 | N. Carissimi | Université de Lille | TBA | |
15:30 | Questions Time | |||
15:40 | TBA | TBA | ||
16:10 | Questions Time | |||
16:20 | TBA | TBA | ||
16:50 | Questions Time | |||
17:00 | Free Chat |
Nicola Carissimi
TBA
TBA
TBA
TBA
TBA
TBA
TBA
TBA