Gleb Nenashev: Triangulations of Root Polytopes
Time: Wed 2018-05-16 10.15 - 11.15
Lecturer: Gleb Nenashev, SU
Location: Room 3418, Lindstedtsvägen 25. Department of Mathematics, KTH
Triangulations of a product of two simplices and, more generally, of root polytopes are closely related to Gelfand-Kapranov-Zelevinsky's theory of discriminants, to tropical geometry, tropical oriented matroids, and to generalized permutohedra. We introduce a new approach to these objects, identifying a triangulation of a root polytope with a certain bijection between lattice points of two generalized permutohedra. In order to study such bijections, we define trianguloids as edge-colored graphs satisfying simple local axioms. Our trianguloids are in bijection with triangulations of root polytopes.