Singularities of Schubert varieties

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The study of symmetries arises in almost all areas of mathematics, and in particular in geometry. In the mathematical language, symmetries usually are described by means of a group acting on an object. As an elementary example one could consider the group of Euclidean motions on the plane, generated by rotations and translations. One can generalize this picture to study the action of Lie groups or (as in the case of this proposal) algebraic groups on vector spaces (like the plane) or more complicated geometric objects. Symmetry groups arise in numerous natural sciences, be it physics (e.g. quantum or classical mechanics), or chemistry (e.g. the symmetries of crystals), or biology (e.g. the symmetries of protein structures).