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### The cohomology of the affine Grassmannian and a new combinatorial formula for fusion coefficients

**Student-Run Algebraic Geometry Seminar**

Speaker: | Anne Schilling, UC Davis |

Location: | 1147 MSB |

Start time: | Thu, Jan 26 2012, 1:10PM |

It is a classical result of Schubert calculus that the intersection multiplicities of certain Schubert varieties (Grassmannians) are intimately related to the Littlewood-Richardson coefficients, which arise as structure coefficients of Schur functions. This has recently been generalized to the affine setting by Lam, Lapointe, Morse, Shimozono and others. In particular, the affine analogues of the Schur functions have structure coefficients, which include fusion coefficients. It has been a notoriously difficult problem to find a combinatorial (or positive) formula for these coefficients. Here we combine algebraic geometry, representation theory, and combinatorics to give a new combinatorial formula for the fusion coefficients in certain cases. This is based on joint work with Jennifer Morse.