Adrian Albert Lectures in Algebra

Yves André (ENS Paris)



Lattices and Stability

Friday October 16, at 5:15pm in Ryerson 251

Crystallography, number theory and coding theory give strong motivations for the study of (euclidean) lattices. A modern version of reduction theory introduces the notion of semistable lattice, and explains that any lattice is canonically an extension of semistable ones. We shall explain the relationship with the notion of semistability for vector bundles (and for filtered vector spaces), evoke a common framework, and discuss the following delicate (open) question: is the tensor product of two semistable lattices semistable?


Slope filtrations I, II

Monday, October 19, at 4pm in E202 and Tuesday October 20, at 4:30 in E 206

Slope filtrations occur in algebraic and analytic geometry (coherent sheaves, motives...), in asymptotic analysis, in ramification theory, in geometry of numbers, in several p-adic theories... These functorial filtrations, which are indexed by rational (or sometimes real) numbers, have a lot of common properties. We shall outline a unified treatment of slope filtrations, with the aim of freeing the ``yoga of stability" from any ad hoc property of the underlying category. We shall describe a number of examples and survey how new ties between different domains have been woven by dint of deep correspondences between different concrete slope filtrations.