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.
I received my PhD from the Graduate Center of the City University of New York, under supervision of Jeremy Kahn.
My research interests are in Teichmüller theory, complex analysis, and hyperbolic geometry.

Contact

Email: Maxime dot Fortier dash Bourque at glasgow dot ac dot uk

Office: 421 Maths building

CV

Teaching

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, accepted to Commentarii Mathematici Helvetici. [ pdf | arxiv ]
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. Dedicata 197 (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 ]
with Malik Younsi, Rational Ahlfors functions, Constr. Approx. 41 (2015), 157-183 [ pdf | arxiv | journal ]
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.

Upcoming and recent travel

Séminaire Géométrie et Topologie, Institut de Mathématiques de Jussieu-Paris Rive Gauche, April 2, 2020.
Multiple Perspectives on Geometric Inequalities, Centre de Recerca Matemàtica, Barcelona, June 3-7, 2019.
Differential Geometry & Topology seminar, University of Cambridge, January 30, 2019.