March 28, 3:30pm, Wean 8220

Bruno Benedetti, University of Miami

Polytope Graphs and Lines on Algebraic Surfaces

Bruno Benedetti, University of Miami

Polytope Graphs and Lines on Algebraic Surfaces

Abstract:

Polygons, solids, and higher dimensional polytopes, have been studied since the prehistory of mathematics. The "graph" of a polytope is just its 1-dimensional skeleton. Connectivity and diameter of polytope graphs are of relevance for linear optimization, as in the simplex method.

We'll sketch an algebraic and (if time permits) a metric approach that are producing some promising results. The algebraic approach sheds also new light to a classical problem in algebraic geometry, namely: arrangements of lines that live on some algebraic surface of P3, like the 27 lines on any smooth cubic.

This reflects joint work with M. Varbaro, M. Di Marca, B. Bolognese, and K. Adiprasito.

Before the talk, at 3:10pm, there will be tea and cookies in Wean 6220.