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2 événements

  • Algèbre Géométrie

    Mardi 16 mai 2017 11:30-12:30 - Liviu Mare - University of Regina (Canada)

    Liviu Mare — An affine quantum cohomology ring for flag manifolds and the periodic Toda lattice

    Résumé : The full flag (complex projective) variety G/B is canonically determined by an irreducible root system, thus by a Dynkin diagram. In a similar way, to the extended Dynkin diagram one attaches an affine root system along with the affine flag variety. Although infinite dimensional, the latter is a close relative of G/B and resembles therefore to it. However, its peculiarities deprives it (so far) of a rigorously defined quantum cohomology ring. A natural attempt is to remedy this by using "curve neighborhoods" of Schubert varieties, an effective tool already employed by Buch, Chaput, Mihalcea and Perrin in a series of recent papers. I will explain how this approach is indeed successful again, although only partially : the resulting Gromov-Witten invariants on the affine flag variety combine nicely with a natural projection map from the latter space onto G/B and give rise to a certain quantum-like product on H*(G/B). This so-called "affine quantum cohomology" ring of G/B admits canonical generators, the relations satisfied by them being just the integrals of motion of the periodic Toda lattice. The complete integrability of this integrable system will also be briefly discussed. The talk is based on joint work with Leonardo Mihalcea.

    Lieu : Fermat - Salle 2205

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  • Algèbre Géométrie

    Mardi 16 mai 2017 11:30-12:30 - Nicolas Perrin - UVSQ

    GT groupes algébriques : centralisateur d’un tore

    Lieu : Fermat 2205

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