Orateur: Emanuele Delucchi (Fribourg):
Titre: An invitation to combinatorial algebraic topology: the cohomology algebra of toric arrangements.
Résumé:  The term "Combinatorial algebraic topology" designates a sprawling field with important applications, from shape recognition to distributed computing. Hallmarks of this field are the construction of discrete models for spaces and methods for studying their homotopy type, e.g. Discrete Morse theory.
In this talk I will give an introduction to combinatorial algebraic topology with, as a case study, an application to the problem of understand the topology of the complement of divisors in varieties. This is a classical topic which is still little understood outside the case of arrangements of hyperplanes in complex vector spaces (where the seminal work of, e.g., Arnol'd, Brieskorn and Deligne has led to a nowadaway established research area).
I will explani how the use of combinatorial models allows us to go beyond hyperplane arrangements, focussing on the case of arrangements in the complex torus, for which interest has been renewed by recent work of De Concini and Procesi. In particular, we can give a full description of the integer cohomology algebra of a toric arrangements's complement (thus establishing the counterpart of a celebrated result of Orlik and Soloment for hyperplane arrangements).
The results I'll discuss are joint work with Giacomo d'Antonio and Filippo Callegaro.