Conference: "SINGULAR LANDSCAPES"

Session

Afternoon session

Jun 22, 2015, 2:00 PM

Centre Paul-Langevin AUSSOIS

16. Milnor numbers of projective hypersurfaces and the chromatic polynomial of graphs

Mr June Huh (Princeton)

6/22/15, 2:00 PM

I will give an overview of a proof of a conjecture of Read that the coefficients of the chromatic polynomial of any graph form a unimodal sequence. There are two main ingredients in the proof, both coming from works of Bernard Teissier: The first is the idealistic Bertini for sectional Milnor numbers, and the second is the isoperimetric inequality for mixed multiplicities of ideals.

12. Algebraic geometry, theory of singularities, and convex geometry

Mr Askold Khovanskii (University of Toronto)

6/22/15, 3:15 PM

I will review some results which relate these areas of mathematics. Newton polyhedra connect algebraic geometry and the theory of singularities to the geometry of convex polyhedra. This connection is useful in both direc- tions. On the one hand, explicit answers are given to problems of algebra and the theory of singularities in terms of the geometry of polyhedra. On the other hand, algebraic...