SMS scnews item created by Boris Lishak at Mon 19 Nov 2018 1539
Type: Seminar
Distribution: World
Calendar1: 21 Nov 2018 1200-1300
CalLoc1: Carslaw 535A
CalTitle1: Lowe -- Secondary fans of punctured Riemann surfaces

Geometry and Topology Seminar

Secondary fans of punctured Riemann surfaces

Robert Lowe (TU Berlin)

Please join us for lunch at 1 p.m.


A famous construction of Gelfand, Kapranov and Zelevinsky associates to each finite point configuration \(A \subset \mathbb{R}^d \) a polyhedral fan, which stratifies the space of weight vectors by the combinatorial types of regular subdivisions of \(A\). That fan arises as the normal fan of a convex polytope. In a completely analogous way we associate to each hyperbolic Riemann surface \(R\) with punctures a polyhedral fan. Its cones correspond to the ideal cell decompositions of \(R\) that occur as the horocyclic Delaunay decompositions which arise via the convex hull construction of Epstein and Penner. Similar to the classical case, this secondary fan of \(R\) turns out to be the normal fan of a convex polyhedron, the secondary polyhedron of \(R\). This is joint work with Michael Joswig and Boris Springborn.