We consider certain representations of a surface group into PGL(4,R) called convex cocompact coaffine representations. These representations act geometrically on a 3-dimensional convex body in projective space, and are part of a broader (and more difficult) landscape of such geometric actions. From classical cases, we would anticipate an analytic object called a transverse measured lamination to capture the geometry of these representations, however paradoxical examples reveal that a generalization is necessary. We will discuss a nice resolution to these difficulties, and describe a space of affine measured laminations which parametrize the space of convex cocompact coaffine representations. Along the way we make an interesting connection to the dynamics of affine interval exchange transformations. Joint work with James Farre.
Fanny Kassel
