Title: Log-concavity Conjectures and the Tropical Laplacian
Speaker: June Huh, Princeton
Date: Monday, April 27, 2015 11:00 am
Location: CoRE Bldg, Room 431, Rutgers University, Busch Campus, Piscataway, NJ
A conjecture of Rota predicts that the coefficients of the chromatic polynomial of a matroid form a log-concave sequence. A related conjecture of Welsh predicts that the number of independent subsets of given size form a log-concave sequence for any matroid. The known proofs for realizable matroids uses algebric geometry in an essential way, and the conjecture is open in its full generality. I will give a survey of known results, and introduce a stronger conjecture that a certain Laplacian matrix associated to a matroid has exactly one negative eigenvalue.