I am a Lecturer in Pure Mathematics at the University of Glasgow. Before that, I was a Coxeter Assistant Professor at the University of Toronto, where my unofficial mentor was Kasra Rafi. I received my PhD from the Graduate Center of the City University of New York, under supervision of Jeremy Kahn.
I am interested in moduli spaces of geometric structures (hyperbolic surfaces, metric graphs, flat tori) and extremal problems on them (maximizing invariants such as the systolic ratio or kissing number).
Contact
Email: Maxime dot Fortier dash Bourque at glasgow dot ac dot uk
Autumn 2020: 3H Analysis of Differentiation and Integration & 3H Writing and Presenting Mathematics
Spring 2020: 4H Further Complex Analysis
Autumn 2019: 3H Analysis of Differentiation and Integration
Spring 2019: 4H Further Complex Analysis
Papers
A divergent horocycle in the horofunction compactification of the Teichmüller metric, submitted. [ pdf | arxiv ]
with Bram Petri, Kissing numbers of regular graphs, submitted. [ pdf | arxiv ]
with Bram Petri, Kissing numbers of closed hyperbolic manifolds, submitted. [ pdf | arxiv ]
Hyperbolic surfaces with sublinearly many systoles that fill, Comment. Math. Helv.95 (2020), 515-534 [ pdf | arxiv | journal ]
with Kasra Rafi, Local maxima of the systole function, accepted to the Journal of the European Mathematical Society. [ pdf | arxiv ]
with Y. Chen, R. Chernov, M. Flores, S. Lee, and B. Yang, Toy Teichmüller spaces of real dimension 2: the pentagon and the punctured triangle, Geom. Dedicata197 (2018), 193-227
[ pdf | arxiv | journal ]
with Kasra Rafi, Non-convex balls in the Teichmüller metric, J. Differential Geom.110 (2018), 379-412
[ pdf | arxiv | journal ]
The holomorphic couch theorem, Invent. Math.212 (2018), 319-406
[ pdf | arxiv | journal ]
The converse of the Schwarz Lemma is false, Ann. Acad. Sci. Fenn. Math.41 (2016), 235-241
[ pdf | arxiv | journal ]
Conformal grafting and convergence of Fenchel-Nielsen twist coordinates, Conform. Geom. Dyn.19 (2015), 1-18
[ pdf | arxiv | journal ]