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
Auth: borisl@dora.maths.usyd.edu.au

# Secondary fans of punctured Riemann surfaces

### Robert Lowe (TU Berlin)

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.