Algèbre et géométrie

We continue the discussion of piecewise interpretable Hilbert spaces from the Monday seminar. We will prove the main structure theorem of `Piecewise Interpretable Hilbert Spaces' (C., Hrushovski) which analyses a scattered piecewise interpretable Hilbert space into asymptotically free subspaces. We will clarify the model theoretic content of this theorem, highlighting the roles of one-basedness and strong minimality. We will also study its representation theoretic content, establishing a connection with induced represetnations. We will see that this theorem generalises a theorem of Tsankov about unitary representations of oligomorphic groups. This is […]

Dans cet exposé, nous présenterons une généralisation des groupes de Frobenius : les quasi-groupes de Frobenius. On dit qu'une paire de groupes C < G est un quasi-groupe de Frobenius si C est d'indice fini dans son normalisateur (dans G) et s'il satisfait la propriété TI, i.e, deux conjugués distincts de C s'intersectent trivialement. Du point de vue de la théorie des modèles, nous travaillerons dans un contexte où l'existence d'une bonne notion de dimension (finie) sur les ensembles définissables est assurée (ce qui englobe les univers rangés et les […]

By work of Itaï Ben Yaacov complete valued fields with value groups embedded in the real numbers can be viewed as metric structures in continuous logic. For technical reasons one has to consider the projective line over such a field rather than the field itself. In this talk we introduce the above setting and give a classification of the complete theories of metric valued fields in equicharacteristic 0 in terms of their residue field and value group. This can also be seen as an approximate Ax-Kochen-Ershov principle. If time permits, […]