Pairs of orthogonal countable ordinals

We characterize pairs of orthogonal countable ordinals. Two ordinals $\alpha$ and $\beta$ are orthogonal if there are two linear orders $A$ and $B$ on the same set $V$ with order types $\alpha$ and $\beta$ respectively such that the only maps preserving both orders are the constant maps and the identity map. We prove that if $\alpha$ and $\beta$ are two countable ordinals, with $\alpha \leq \beta$, then $\alpha$ and $\beta$ are orthogonal if and only if either $\omega + 1\leq \alpha$ or $\alpha =\omega$ and $\beta < \omega \beta$

Categorical aspects are useful for topology—after 30 years

AbstractThis is a survey paper presenting selected results on Embeddings of categories, Homeomorphisms of products and coproducts of spaces and Clones

The Mathematics of Ivo Rosenberg

International audienceThis paper is dedicated to the memory of the distinguished scholar and friend Professor I.G .Rosenberg. We survey some of his most well known and not so known results, as well as present some new ones related to the study of maximal partial clones and their intersections

Singular moduli spaces on K3 surfaces and derived categories

Il nucleo attorno a cui questa tesi si sviluppa è il teorema di Torelli derivato per superficie K3; si tratta di un criterio coomologico che stabilisce quando due superficie K3 proiettive hanno categorie derivate (di fasci coerenti) equivalenti. Vengono presentati gli strumenti che intervengono nella dimostrazione di questo teorema: trasformate di Fourier-Mukai da un lato; dall'altro, spazi di moduli di fasci su superficie K3 proiettive (teoria di Mukai). Per una classe di spazi di moduli singolari, vengono infine presentati alcuni risultati dovuti a Kaledin, Sorger e M. Lehn