The log-concavity conjecture and the tropical Laplacian

Computer Science/Discrete Mathematics Seminar II
Topic:The log-concavity conjecture and the tropical Laplacian
Speaker:June Huh
Affiliation:Princeton University; Veblen Fellow, School of Mathematics
Date:Tuesday, February 17
Time/Room:10:30am - 12:30pm/S-101
Video Link:http://video.ias.edu/csdm/2015/0217-JuneHuh

The log-concavity conjecture predicts that the coefficients of the chromatic (characteristic) polynomial of a matroid form a log-concave sequence. The known proof for realizable matroids uses algebraic 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. This talk will be followed by talk of Karim Adiprasito at March 3, who recently proved the log-concavity conjecture for a large class of non-realizable matroids.