Sommes de Gauss et séries thêta
Dualité de Langlands quantique
Un survol des conjectures de Drinfeld, Beilinson, Gaitsgory et al. et de résultats de Gaitsgory sur la correspondance de Langlands quantique.
Pentagramma mirificum and elliptic functions (Napier, Gauss, Poncelet, Jacobi, ...)
We give an exposition of unpublished fragments of Gauss where he discovered (using a work of Jacobi) a remarkable connection between Napier pentagons on the sphere and Poncelet pentagons on the plane. As a corollary we find a parametrization in elliptic functions of the classical dilogarithm five-term relation.
BGG resolutions via configuration spaces
We study the blow-ups of configuration spaces. These spaces have a structure of what we call an Orlik–Solomon manifold; it allows us to compute the intersection cohomology of certain flat connections with logarithmic singularities using some Aomoto type complexes of logarithmic forms. Using this construction we realize geometrically the Bernstein–Gelfand–Gelfand resolution as an Aomoto complex.
Arrangements of hyperplanes and Lie algebra homology.
Homological algebra and divergent series.
On chiral differential operators over homogeneous spaces.
Page 1