The UC Berkeley combinatorics seminar |
---|

DATE |
SPEAKER |
TITLE (click to show abstract) |

August 30th | Hunter Spink Stanford |
## Log-concavity of Matroid h-vectors(Joint with Andrew Berget and Dennis Tseng) For any matroid M, we compute the Tutte polynomial using mixed intersection numbers of classes in the combinatorial Chow ring of M arising from Grassmannians. Using this, we resolve and strengthen an old conjecture of Dawson (independently proved by Ardila-Denham-Huh) on the log-concavity of the h-vector of the independence complex of M. |

September 6th | Holiday - no talk | |

September 13th | Zhongyang Li University of Connecticut |
## Asymptotics of random perfect matchingsI will discuss random perfect matchings on a large class of graphs, which form Schur processes. I will then talk about the limit shape (Law of Large Numbers) and convergence of height fluctuations to Gaussian Free Field (Central Limit Theorem) for random perfect matchings on these graphs in the scaling limit. |

September 20th | Martha Precup Washington University in St. Louis |
## Hessenberg varieties and the Stanley--Stembridge conjectureHessenberg varieties are subvarieties of the flag variety with important connections to representation theory, algebraic geometry, and combinatorics. In 2015, Brosnan and Chow, and independently Guay-Paquet, proved the Shareshian--Wachs conjecture, which links the combinatorics of chromatic symmetric functions to the geometry of Hessenberg varieties via a symmetric group action on the cohomology ring of regular semisimple Hessenberg varieties. This talk will give an overview of that story and present a set of linear relations satisfied by the multiplicities of certain permutation representations in that representation. As an application of these results, we prove an inductive formula for the multiplicity coefficients corresponding to partitions with a maximal number of parts. This talk is based on joint work with M. Harada. |

September 27th | Mei Yin University of Denver | |

October 4th | Greta Panova University of Southern California | |

October 11th | Swee Hong Chan University of Califonia, Los Angeles | |

October 18th | Daoji Huang University of Minnesota | |

October 25th | Sean Griffin University of California, Davis | |

November 1st | GaYee Park University of Massachusetts, Amherst | |

November 8th | Stoyan Dimitrov University of Illinois, Chicago | |

November 15th | Luis Ferroni University of Bologna | |

November 22nd | Jessica De Silva California State University, Stanislaus |
## Erdös-Ko-Rado GraphsThe Erdös-Ko-Rado (EKR) theorem states that the maximum size of an intersecting family of r-element subsets of [n] can be attained by taking all subsets containing some fixed element. This classical result in extremal combinatorics has been rephrased in the language of graph theory as an extremal property regarding independent sets of a graph. A family of independent r-sets of a graph G is an r-star if every set in the family contains some fixed vertex v. A graph is r-EKR if the maximum size of an intersecting family of independent r-sets can be attained by an r-star. In this context, the classical EKR theorem determines the values of r for which the empty graph satisfies the r-EKR property. This talk will highlight that there is much to be discovered in the search for EKR graphs, along with motivation and early findings for classes of very well-covered graphs. |

November 29th |