Research interests

Classical and higher Teichmüller theory, geometric structures, character varieties, symplectic geometry of moduli spaces, hyper-Kähler structures, harmonic maps, minimal surfaces, Higgs bundles.

Papers

  1. The complex symplectic geometry of the deformation space of complex projective structures.
    Geometry & Topology 19 (2015), no. 3, 1737–1775. Download.
  2. Minimal surfaces and symplectic structures of moduli spaces.
    Geometriae Dedicata 175 (2015), 309–322. Download.
  3. Bi-Lagrangian structures and Teichmüller theory. Joint with Andy Sanders.
    Submitted. Preprint: arXiv:1708.09145 or HAL-01579284. Download.
  4. Computing twisted harmonic maps. Joint with Jonah Gaster and Léonard Monsaingeon.
    In preparation. This upcoming paper produces a new proof of Corlette's theorem on the existence of equivariant harmonic maps, by using successive triangulations of the surface and a discretized heat flow. This proof is constructive in the sense that it provides a method to numerically compute such harmonic maps.
  5. Hyperkähler geometry of character varieties. Joint with Andy Sanders.
    In preparation. This upcoming paper studies a generalization due to A. Sanders of the Kähler structure of Teichmüller space to an open set of the character variety $\mathcal{X}(S, G)$, where $S$ is a closed surface and $G$ is a semisimple Lie group.

Notes

  1. Minimal surfaces and quasi-Fuchsian structures.
    Notes written the NSF workshop Higgs bundles and harmonic maps in Asheville, NC in Januray 2015. Download.

Ph.D.

I did my doctoral studies at Université de Toulouse III from 2008 to 2011 under the supervision of Jean-Marc Schlenker. Ph.D. thesis: The symplectic geometry of the deformation space of complex projective structures on a surface.

Download Ph.D. thesis (in English).

Mathematical software

I have been working on two computer projects in relation to my research:

Circle Packings

This software created by Benjamin Beeker and myself computes and shows circle packings and Riemann conformal mappings.

Read more in the "Software" section here.

Hitchin

This is an ongoing project with Jonah Gaster.

This software computes and shows equivariant harmonic maps from the hyperbolic plane $\mathbb{H}^2$ to hyperbolic 3-space $\mathbb{H}^3$ (or in the future, more general symmetric spaces).

Read more in the "Software" section here.

Mathematics Colloquium & Teichmüller Theory Seminar

I am organizing the Mathematics Colloquium at Rugers-Newark: see dedicated web page.

I am co-organizing the Teichmüller Theory Seminar at Rugers-Newark with Jane Gilman and John Loftin: see dedicated web page.

Workshop on Analytic Aspects of Higher Teichmüller Theory

I am co-organizing the Workshop on Analytic Aspects of Higher Teichmüller Theory in September 2016 at Rugers-Newark with Zeno Huang and John Loftin: see dedicated web page.

CV

Download my CV (in English. For French click here).

Please contact me for my Research Statement or my Teaching Statement.