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, computational geometry.

Papers

1. The complex symplectic geometry of the deformation space of complex projective structures.
2. Minimal surfaces and symplectic structures of moduli spaces.
3. Bi-Lagrangian structures and Teichmüller theory. Joint with Andy Sanders.
4. Computing discrete equivariant harmonic maps. Joint with Jonah Gaster and Léonard Monsaingeon.
Submitted. Preprint:
5. Computing equivariant harmonic maps. Joint with Jonah Gaster and Léonard Monsaingeon.
In preparation.
6. Weighted graphs on Riemannian manifolds. Joint with Jonah Gaster and Léonard Monsaingeon.
In preparation.
7. Hyperkähler geometry of character varieties. Joint with Andy Sanders.
In preparation.

"Ad" : I invite you to consider submitting your most beautiful mathematics papers to the free and open journal Annales Henri Lebesgue. (I have no ties to this journal!)

Notes

1. Higgs bundles and Hitchin components
Handwritten notes written for the workshop Higher Teichmüller-Thurston spaces in Paris XI, France in 2012. Download.
2. Minimal surfaces and quasi-Fuchsian structures
Notes written for the NSF workshop Higgs bundles and harmonic maps in Asheville, NC in Januray 2015. Download.
3. Hyperbolic geometry
Lecture notes written for a graduate course taught at Rutgers University in 2017. In preparation.
4. Riemann surfaces
Lecture notes written for a graduate course taught at TU Darmstadt in 2018-2019. In preparation.

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.

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.

Harmony

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.

CV