Dear all, next Monday we will have a seminar by Vanni Noferini; starting from the following week, we will try to go back to the original schedule of having seminars on Thursday afternoon.

You are all welcome!

Best wishes, -- Leonardo.

Speaker: Vanni Noferini Affiliation: University of Essex / Aalto University Time: Monday, 25 March 2019, h. 10:00 Place: Sala Seminari, Dipartimento di Matematica

Title: Matrices in companion rings and their Smith forms, with applications to group theory and algebraic topology

In group theory, various properties of the abelianization of a cyclically presented group can be deduced by the Smith normal form of an integer circulant matrix. Motivated by this fact, we present a number of results on the Smith form of matrices that are polynomials in the companion matrix of a polynomial with coefficients in a generic elementary divisor domain. Our tools are of purely matrix theoretical nature and I will present them from the point of view of a matrix theorist. However, they enable significant advances in pure algebra. In particular, I plan to discuss how our results provide a tool to study the homology of 3-dimensional Brieskorn manifolds, which are objects of (apparently) interest for topologists. If time permits, I will mention other possible applications to group theory.