Members' Seminar | |

Topic: | Hard Lefschetz theorem and Hodge-Riemann relations for combinatorial geometries |

Speaker: | June Huh |

Affiliation: | Princeton University; Veblen Fellow, School of Mathematics |

Date: | Monday, November 9 |

Time/Room: | 2:00pm - 3:00pm/S-101 |

Video Link: | https://video.ias.edu/membsem/2015/1109-Huh |

A conjecture of Read predicts that the coefficients of the chromatic polynomial of a graph form a log-concave sequence for any graph. A related conjecture of Welsh predicts that the number of linearly independent subsets of varying sizes form a log-concave sequence for any configuration of vectors in a vector space. In this talk, I will argue that two main results of Hodge theory, the Hard Lefschetz theorem and the Hodge-Riemann relations, continue to hold in a realm that goes beyond that of Kahler geometry. This implies the above mentioned conjectures and their generalization to arbitrary matroids. Joint work with Karim Adiprasito and Eric Katz.