Research publications and preprints

1. Holomorphic curves in the 6-pseudosphere and cyclic surfaces with Jérémy Toulisse. Accepted for publication in Transactions of the AMS. arXiv

2. A general Cayley correspondence and higher Teichmüller spaces with Steve Bradlow, Oscar Garcia-Prada, Peter Gothen and André Oliveira, to appear in Annals of Mathematics Nov. 2024 vol 200 #3. arXiv

3. Arakelov-Milnor inequalities and maximal variations of Hodge structure with Olivier Biquard, Oscar Garcia-Prada and Domingo Toledo.  Compositio Mathematica, 159(5) May 2023, 1005-1041. arXiv

4. (G,P)-opers and global Slodowy slices with Andrew Sanders,  Advances in Mathematics, Volume 377, 22 January 2021. arXiv

5. Conformal limits and the Białynicki-Birula stratification of the space of λ-connections  with Richard Wentworth. Advances in Mathematics, Volume 350, 9 July 2019, Pages 1193-1225. arXiv

6. Studying Deformations of Fuchsian Representations with Higgs Bundles, SIGMA 15 (2019), 010, 32 pages (Special Issue on Geometry and Physics of Hitchin Systems). Survey article roughly based on Summer 2018 mini-course given at UIC. arXiv

7. SO(p,q)-Higgs bundles and higher Teichmüller components with  Marta Aparicio-Arroyo, Steve Bradlow, Oscar Garcia-Prada, Peter Gothen and André Oliveira. Inventiones Mathematicae 218 (2019) 197–299. arXiv

8. Exotic components of SO(p,q) surface group representations, and their Higgs bundle avatars with  Marta Aparicio-Arroyo, Steve Bradlow, Oscar Garcia-Prada, Peter Gothen and André Oliveira. Comptes Rendus Mathematique Volume 356, Issue 6, June 2018, Pages 666-673. arXiv

9. SO(n,n+1)-surface group representations and their Higgs bundles. Annales scientifiques de l'ENS volume 53, issue 6 (2020)  1561-1616. arXiv

10. The geometry of maximal components of the PSp(4,R) character variety with Daniele Alessandrini. Geometry & Topology 23 (2019) 1251–1337. arXiv

11. Various generalizations and deformations of PSL(2,R) surface group representations and their Higgs bundles.  Geometry and Physics: a Festschrift in honour of Nigel Hitchin, Oxford Press October 25, 2018.

12.  The geometry of maximal representations of surface groups into SO(2,n) with Nicolas Tholozan and Jérémy Toulisse. Duke Math Journal, Volume 168, Number 15 (2019), 2873-2949. arXiv

13. Finite order automorphism of Higgs bundles: theory and application  (Ph.D. thesis)

14. Parallel transport on principal bundles over stacks with Eugene Lerman and Seth Wolbert. Journal of Geometry and Physics Volume 107, September 2016, pp 187-213. arXiv

15. Maximal Sp(4,R) surface group representations, minimal surfaces and cyclic surfaces. Geometriae Dedicata 180 (2015), no. 1, 241–285. arXiv

16. Asymptotics of Higgs bundles in the Hitchin component with Qiongling Li. Advances in Mathematics, Volume 307, 5 February 2017, Pages 488–558. arXiv

17. A Symplectic Proof of a Theorem of Franks with Ely Kerman, Ben Reiniger, Bolor Turmunkh and Andrew Zimmer, Compositio Mathematica, Volume 148, Issue 06, November 2012, pp 1069–1084. arXiv