Equidistribution and freeness on Grassmannians

Notes on Equidistribution

Perverse Sheaves on Grassmannians

We give a complete quiver description of the category of perverse sheaves on Hermitian symmetric spaces in types A and D, constructible with respect to the Schubert stratification. The calculation is microlocal, and uses the action of the Borel group to study the geometry of the conormal variety Λ.

Equidistribution on the Sphere

A concept of generalized discrepancy, which involves pseudodiierential operators to give a criterion of equidistributed pointsets, is developed on the sphere. A simply structured formula in terms of elementary functions is established for the computation of the generalized discrepancy. With the help of this formula ve kinds of point systems on the sphere, namely lattices in polar coordinates, t...

On Cloning Context-Freeness

A first-order language is called monadic if its non-logical vocabulary lacks both function symbols and relation symbols of arity greater than one. Formulas of this kind of language can be mechanically tested for validity but its expressive power seems to be too restricted to be of any interest for linguistics. Monadic second-order languages on the other hand extend the language of (full) first-...

Root games on Grassmannians

We recall the root game, introduced in [P], which gives a fairly powerful sufficient condition for non-vanishing of Schubert calculus on a generalised flag manifold G/B. We show that it gives a necessary and sufficient rule for nonvanishing of Schubert calculus on Grassmannians. In particular, a LittlewoodRichardson number is non-zero if and only if it is possible to win the corresponding root ...