mini-workshop2017

Mini-Workshop: A CATEGORICAL DAY IN TURIN

May 11th, 2017

Department of Mathematics "G. Peano", University of Turin.

Aims: This Mini-Workshop consists of four introductory lectures at the level of students of the Master program in Mathematics. The main aim is to present some techniques in Category Theory which are of interest in different areas of Mathematics. This edition is related to Algebra, Algebraic Geometry, Computer Science and Logic.

Math-Lab: Gli studenti della Laurea Magistrale del Dipartimento di Matematica "G. Peano" sono invitati e, partecipando ad almeno due delle quattro lezioni, potranno avere una firma per Math-Lab. E' richiesta l'iscrizione, vedere link qui sotto.

Registration: Although there is no registration fee, we ask the participants to fill out the following form where one can also subscribe to the social dinner to be held on the day of the conference.

(Registration form)

PROGRAM:

• 9:00 - 11:00 Gabriele Vezzosi, Univ. Firenze. (aula C)

Title: A quick introduction to derived algebraic geometry

Abstract. We will motivate the introduction of higher categorical tools in algebraic geometry, leading to derived algebraic geometry. We will then give some applications of derived algebraic geometry to obstruction theory for moduli spaces and to symplectic and Poisson geometry.

Slides.

• Coffee Break
• 11:30 - 12:20 Laiachi El Kaoutit, Univ. Granada. (aula C)

Title: Basic Theory of Abstract Groupoid

Abstract. In this introductory talk, we present the elementary theoretical aspects of abstract groupoids and their groupoids-sets. Specially, we will focus on examples (some of them will not be of mathematical nature) that lead to a clearer difference when studding the symmetries from the classical group theory point of view, and that show what really lies behind the oid-world.

Slides.

• Lunch break
• 14:00 - 15:50 Fabio Gadducci, Univ. Pisa. (aula C)

Title: Petri nets and monoidal categories: a survey (and some new results)

Abstract. A seminal result in concurrency theory shows that an algebraic interpretation of Petri nets in terms of commutative monoids can be used to provide an elegant characterisation of the deterministic computations of a net via monoidal categories, accounting for their sequential and parallel composition. In turn, this characterisation leads to the interpretation of such computations as sequents of a multiplicative fragment of linear logic, thus as an instance of the classical Curry-Howard isomorphism. The talk presents a survey of the topic, including some recent results concerning non-deterministic computations, and their characterisation in terms of bimonoidal categories.

• Break
• 16:00 - 16:50 Fosco Loregian, Univ. Masaryk, Brno, Czech Republic. (aula C)

Title: Homotopical Algebra

Abstract. Homotopical Algebra is built on the idea that the ultimate nature of the objects studied in algebraic topology has nothing to do with geometry. Shapes and invariants could be attributed to many other algebraic and combinatorial structures having no geometrical nature whatsoever.

Moving its early steps from this basic intuition, reinforced by a sheer amount of examples, this language grew up to provide a solid foundation of algebraic topology and it has, today, countless application to algebraic geometry, logic, category theory...

We give a survey of the basic definitions and some of these applications.

Slides.

Organizers: Alessandro Ardizzoni, Cristiana Bertolin, Felice Cardone, Paolo Saracco