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12/04/2018, 16:00 — 17:00 — Abreu Faro Amphitheatre

João Filipe Queiró, *Universidade de Coimbra*

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Sums and products of equivalence orbits

Similarity and equivalence of matrices over fields are well-understood relations, and that understanding is elementary, specially in the case of equivalence. For matrices over rings – e.g. the integers – the situation is different. Equivalence is still simple and its study leads to the concept of invariant factors of a matrix. About these, several interesting basic questions can be raised. This talk will address two of those questions: how do invariant factors behave under matrix addition and multiplication? Some things are known about these problems, and the second one – already completely solved for certain classes of rings – has deep relations with other parts of mathematics.

#### See also

Poster