I'm mainly interested in low dimensional manifolds and their moduli. A lot of my research revolves around the study of surfaces and curves on surfaces. This involves the study of (curvature free) systolic type inequalities, the geometry and spectra of hyperbolic surfaces, high genus random surfaces, mapping class groups, the geometry of Teichmüller and moduli spaces, infinite type surfaces, and a general interest in combinatorial geometry and geometric group theory.

Members of the research group in Luxembourg:

PhD students: David Fisac (co-tutelle with Florent Balacheff)
Post-docs: Pallavi Panda, Mélanie Theillière, Kate (Katie) Vokes, Mingkun Liu

Former members of the research group in Luxembourg:

Post-docs: Funda Gültepe, Yan Mary He, Wai Yeung Lam, Alan McLeay, Binbin Xu
PhD students; Nhat Minh Doan (PhD completed in January 2022), Thi Hanh Vo (PhD completed in May 2022)
Visiting PhD students (long term): Pallavi Panda (Lille), Cayo Rodrigo (IMPA, Rio)

We are also part of the "Research cluster in low dimensional geometry and topology".

Former members of the research group in Fribourg:

PhD students: Federica Fanoni and Bram Petri. Both Federica and Bram successfully completed their PhD in June 2015.
Post-docs: Ariadna Fossas Tenas (February 2016 - July 2016), Viveka Erlandsson (October 2015 - March 2016), Valentina Disarlo (June 2014 - August 2014), Matthieu Gendulphe (January 2012 - August 2012).

Co-authors:

Jim Anderson, Javier Aramayona, Florent Balacheff, Ara Basmajian, Peter Buser, Will Cavendish, Antonio Costa, Vincent Despré, Olivier Devillers, Arnaud de Mesmay, Valentina Disarlo, Nhat Minh Doan, Emily Dryden, Mattijs Ebbens, Viveka Erlandsson, Federica Fanoni, Ariadna Fossas, Niloufar Fuladi, Thomas Gauglhofer, Funda Gültepe, Larry Guth, Milagros Izquierdo, Ghislain Jaudon, Chris Judge, Steve Karam, Benedikt Kolbe, Cyril Lecuire, Marissa Loving, Eran Makover, Daniel Massart, Gérard Maze, Alan McLeay, Greg McShane, Camille Petit, Bram Petri, Alexandra Pettet, Lionel Pournin, Stéphane Sabourau, Dragomir Šarić, Jean-Marc Schlenker, Ken Shackleton, Juan Souto, Craig Sutton, Ser Peow Tan, Monique Teillaud, Paul Turner, Gert Vegter, Nicholas Vlamis, Thi Hanh Vo, Yunhui Wu, Yuhao Xue, Robert Young, Ashley Weber, Samuel Zappa.