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We survey a new approach towards Lusztig's conjecture on the irreducible characters of a reductive algebraic group over a field of positive characteristic. The main result that we review is that Lusztig's conjecture is implied by a multiplicity conjecture on the stalks of certain sheaves on a...
In a recent paper ‘A variant of the Hales–Jewett theorem’, M. Beiglböck provides a version of the classic coloring result in which an instance of the variable in a word giving rise to a monochromatic combinatorial line can be moved around in a finite structure of specified type (for example, an...
For some small values of f , we prove that if G is a group having a complex (real) representation with fixity f , then it acts freely and smoothly on a product of f +1 spheres with trivial action on homology.
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