*********************************** * Princeton Discrete Math Seminar * * joint with Algebraic Geometry * *********************************** June Huh is a new hire in math, visiting this week, and giving two related talks. They are both joint with the algebraic geometry seminar. The first talk is amazing, and I do recommend discrete math people to go to it if they can. NOTE THE DATE on the first talk! Date: Tuesday 4th March, 4:30 in Fine Hall 322. Speaker: June Hu, Michigan U. Title: Rota's conjecture and positivity of algebraic cycles in toric varieties Rota's conjecture predicts that the coefficients of the characteristic polynomial of a matroid form a log-concave sequence. I will outline a proof for representable matroids using the Bergman fan. The same approach to the conjecture in the general case (for possibly non-realizable matroids) leads to several intriguing questions on higher codimension algebraic cycles in the toric variety associated with the permutohedron. ----------- Date: Thursday 6th March, 4:30 in Fine Hall 224. Speaker: June Hu, Michigan U. Title: The tropical Laplacian The tropical Laplacian is a symmetric square matrix associated with a balanced graph on a sphere, defined in a similar way to the Laplacian of an abstract graph. We will see by examples how the tropical Laplacian appears in the study of polytopes, matroids, and graphs. The speaker will pose many elementary questions on tropical Laplacians. A related but independent talk explaining the geometric origin of the questions will be given in the Tuesday (March 4) Algebraic Geometry Seminar. ----------- Next week: Wesley Pegden Anyone wishing to be added to or removed from this mailing list should contact Paul Seymour (pds@math.princeton.edu)