student profile: Mr Dominic Tate


Thesis work

Thesis title: Triangulations, Buildings and Real Projective Structures.

Supervisors: Stephan TILLMANN , Anne THOMAS

Thesis abstract:

My aim is to develop the existing tools for understanding of the structure of moduli spaces of convex real projective structures of finite volume on a non-compact surface. To this end I plan to identify a canonical triangulation of a surface using recent work from Cooper and Adeboye [2013]. The latter’s result bounding projective invariants owing to Fock and Goncharov [2006] in their parameterisation of the moduli space may be used to define a function on the triangulations of a given convex projective surface. The investigation of such functions is a lens through which I can compare ideal triangulations on a given surface and develop techniques for identifying canonical examples. I would then like to apply similar techniques to compactifications of these moduli spaces. Recent work by Parreau [2015] and Alessandrini [2007] makes use of buildings to compactify the relevant moduli spaces and I would like to use this work to recover topological or geometric information about the moduli space. This information will then be a starting point for a generalising these techniques to higher dimensions or other moduli spaces using Lie groups other than PSL(3,R).

Note: This profile is for a student at the University of Sydney. Views presented here are not necessarily those of the University.