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### LLT Polynomials and Schur Positivity in Rational Shuffle Conjecture

**Algebra & Discrete Mathematics**

Speaker: | Mikhail Mazin, KSU |

Related Webpage: | https://www.math.ksu.edu/~mmazin |

Location: | 1147 MSB |

Start time: | Fri, Sep 11 2015, 2:10PM |

Rational Shuffle conjecture provides a combinatorial formula in terms of rational parking functions for certain symmetric polynomials, naturally appearing in the theory of Macdonald polynomials and K-theory of Hilbert schemes. These polynomials are believed to be Schur positive. In this talk I will discuss our recent result, showing that the combinatorial side of the rational Shuffle conjecture is indeed Schur positive. The proof is based on comparing the contributions of parking functions with a fixed underlying Dyck path with LLT polynomials, which are known to be Schur positive.

The talk is based on a joint work with Eugene Gorsky.