The purpose of these notes is to present an algebro-geometric point of view on several
interrelated topics, all involving integrable systems in symplectic-algebro-geometric settings …

Dans cet article, nous proposons une démonstration pour des conjectures de Langlands,
Shelstad et Waldspurger plus connues sous le nom de lemme fondamental pour les …

Compactifications of Picard schemes have been studied by many authors using different
methods. In [CJ], we announced a treatment modeled on Grothendieck's construction of the …

The theory of algebraically completely integrable hamiltonian systems demonstrates a
fruitful interaction between dynamical systems and the geometry of vector bundles over …

The article summarizes progress by many persons; it is accessible to nonexperts. My goal is
to point to what is available, and give some feeling for the subject. When X is a nonsingular …

For G= GL 2, PGL 2, SL 2 we prove that the perverse filtration associated with the Hitchin
map on the rational cohomology of the moduli space of twisted G-Higgs bundles on a …

We conjecture an expression for the dimensions of the Khovanov–Rozansky HOMFLY
homology groups of the link of a plane curve singularity in terms of the weight polynomials of …

We construct natural relative compactifications for the relative Jacobian over a family $ X/S $
of reduced curves. In contrast with all the available compactifications so far, ours admit a …

We compare several constructions of compactified jacobians—using semistable sheaves,
semistable projective curves, degenerations of abelian varieties, and combinatorics of cell …

Recently while considering the possible special linear systems which can exist on a
nonsingular plane curve, we rediscovered an old result of Max Noether. The problem is to …