The Research lectures and progress reports will consist of lectures given by researchers, and by master and PhD students. This will be a review of recent REDAGAAC activities. There will be also contributed external talks.
Abstract of the research lectures
BARRY Demba, University of Bamako, Mali. Cohomological invariants of quadratic forms and algebras with involution (joint work with A. Masquelein and A. Quéguiner-Mathieu).
In this talk we present some classical cohomological invariants for quadratic forms and explain why the absolute Arason invariant does not extend to algebras with involution. As for orthogonal involutions, using the Rost invariant for some torsors, we define a relative Arason invariant for unitary involutions. The last part of the talk will be devoted to the properties of this relative invariant for algebras of degree 4 and 8.
CAMARA Moustapha, University Assane Seck of Ziguinchor, Sénégal. Points algébriques sur certaines courbes planes lisses.
Étant donné C , une courbe projective irréductible et lisse définie sur Q de genre g, la célèbre conjecture de Mordell prédit que lorsque g ≥ 2, la courbe C possède un nombre fini de solutions dans un corps de nombres donné. Dans cette présentation, nous retracerons cette histoire puis nous nous intéresserons à la détermination des points algébriques de degré donné sur certaines courbes planes lisses de genre au moins deux.
DEMBÉLÉ Lassina, King’s College, London, UK. Parametrising abelian surfaces with RM by Z[sqrt(2)] using Richelot isogenies.
In this talk, we describe a parametrisation of abelian surfaces with real multiplication by Z[sqrt(2)] using Richelot isogenies, and give some arithmetic applications.
RAMAKRISHNA Ravi, Cornell University, USA (online). The Inverse Galois Problem.
Given a polynomial f(x) with rational coefficients, we can let K be its splitting field and try to compute the finite group Gal(L/Q). The Inverse Galois Problem (it’s really a Conjecture!) asserts that every finite group G is realizable as Gal(K/Q) for some finite extension K/Q. I will survey this problem, the progress to date on it, and some of its variants.
SORÉ Hermann, Nazi Boni University, Burkina Faso. On a Quillen adjunction between the categories of differential graded and symplicial coalgebras.
We prove that the normalization functor of the Dold-Kan correspondence does not induce a Quillen equivalence between Goerss’ model category of simplicial coalgebras and Getzler-Goerss’ model category of differential graded coalgebras.
