Codimension-1 Flats in Convex Projective Geometry- Martin Bobb (Michigan)
Abstract: Convex projective manifolds generalize hyperbolic manifolds while allowing for some similarities to non-positively curved spaces, and some interesting deformation theory. In this lecture we will discuss the structure of codimension-1 flats in compact convex projective manifolds.
Rank one phenomena in convex projective geometry- Mitul Islam (Michigan)
Abstract: The goal of this talk is to develop analogies between rank one non-positive curvature/ CAT(0) and convex projective geometry. We will introduce the notion of rank one automorphisms of properly convex domains and characterize them as contracting group elements. We will prove that a discrete rank one automorphism group is either virtually cyclic or acylindrically hyperbolic. This leads to some applications like computation of space of quasimorphisms, counting of closed geodesics, and genericity results.
Moduli space of unmarked convex projective surfaces- Zhe Sun (Luxembourg)
Abstract: Mirzakhani found a beautiful recursive formula to compute the volume of the moduli space of Riemann surfaces. We discuss the possible similar recursive formula where the Riemann surfaces are replaced by the convex projective surfaces. We investigate the boundedness of projective invariants, area, and many other notions that are uniformly related to each other and we show one of these bounded subsets has polynomially bounded Goldman symplectic volume.