Maxime Fortier Bourque

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

Office: 421 Maths building

CV

Teaching

• 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

1. A divergent horocycle in the horofunction compactification of the Teichmüller metric, submitted. [ pdf | arxiv ]
2. with Bram Petri, Kissing numbers of regular graphs, submitted. [ pdf | arxiv ]
3. with Bram Petri, Kissing numbers of closed hyperbolic manifolds, submitted. [ pdf | arxiv ]
4. Hyperbolic surfaces with sublinearly many systoles that fill, Comment. Math. Helv. 95 (2020), 515-534 [ pdf | arxiv | journal ]
5. with Kasra Rafi, Local maxima of the systole function, accepted to the Journal of the European Mathematical Society. [ pdf | arxiv ]
6. 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. Dedicata 197 (2018), 193-227 [ pdf | arxiv | journal ]
7. with Kasra Rafi, Non-convex balls in the Teichmüller metric, J. Differential Geom. 110 (2018), 379-412 [ pdf | arxiv | journal ]
8. The holomorphic couch theorem, Invent. Math. 212 (2018), 319-406 [ pdf | arxiv | journal ]
9. The converse of the Schwarz Lemma is false, Ann. Acad. Sci. Fenn. Math. 41 (2016), 235-241 [ pdf | arxiv | journal ]
10. Conformal grafting and convergence of Fenchel-Nielsen twist coordinates, Conform. Geom. Dyn. 19 (2015), 1-18 [ pdf | arxiv | journal ]
11. with Malik Younsi, Rational Ahlfors functions, Constr. Approx. 41 (2015), 157-183 [ pdf | arxiv | journal ]
12. with Thomas Ransford, Super-identical pseudospectra, J. London Math. Soc. 88 (2009), 511-528 [ journal ]

Theses

• The holomorphic couch theorem, PhD thesis, Graduate Center, CUNY, 2015.
• Applications quasiconformes et soudure conforme, masters thesis, Université Laval, 2010.
• Fonctions automorphes dans le plan complexe, undergraduate thesis, Université Laval, 2009.

Slides from talks

• Flatland, Sphereland and Beyond, Maths Taster Talk, Open Day, University of Glasgow, September 2019.
• Searching for convex sets in Teichmüller space, AMS Sectional Meeting, Indiana University, April 2017.
• Non-convex balls in the Teichmüller metric, 14th annual Graduate Student Topology and Geometry Conference, Indiana University, April 2016.
• Moving one Riemann surface inside another, Geometry Seminar, Indiana University, February 2015.
• Fonctions d'Ahlfors rationnelles, Séminaire d'Analyse, Université Laval, January 2014.

Video

• Local maxima of the systole function, Workshop on Geometry of Teichmüller Space, Fields Institute, August 2018.

Links

• Geometry and Topology seminar
• Core Structures @ Glasgow

Online profiles

• ORCID
• arXiv
• Google Scholar
• MathSciNet

PhD students

• Aitor Azemar (co-supervised with Vaibhav Gadre)