Presentation
I am a postdoctoral fellow in the Department of Mathematics at the University of Toronto, under the supervision of Prof. Jacopo De Simoi. I did my Ph.D. at the Université Paris Diderot (Université Paris 7), under the supervision of Prof. Artur Avila and Prof. Julie Déserti, and my M.Sc. at Sorbonne Université (former Université Paris 6), under the supervision of Prof. Artur Avila.
Contact
Martin Leguil Department of Mathematics, University of Toronto 40 St George St. Toronto, ON Canada M5S 2E4 St. George Office: PG303A (PGB - 45 St. George St.) UTM Office: DH 3019 E-mail: martin.leguil@utoronto.ca
Curriculum Vitae
You can find my CV here: CV (in French), CV (in English).
Publications
- On harmonic diffeomorphisms from conformal annuli to Riemannian annuli, joint with Harold Rosenberg, Matemática Contemporânea 43, Sociedade Brasileira de Matemática (2014), pp. 171-222.
- Dynamics of a Family of Polynomial Automorphisms of C^3, a Phase Transition, joint with Julie Déserti, J. Geom. Anal. 28 (2018), pp. 190-224.
- Weak mixing properties of interval exchange transformations & translation flows, joint with Artur Avila, Bull. Soc. Math. France 146 (2) (2018), pp. 391-426.
- Marked Length Spectrum, homoclinic orbits and the geometry of open dispersing billiards, joint with Péter Bálint, Jacopo De Simoi, Vadim Kaloshin, to appear in Commun. in Math. Phys.
- Exponential decay of the size of spectral gaps for quasi-periodic Schrödinger operators (the results of this paper were included in the next paper with Jiangong You, Zhiyan Zhao, Qi Zhou).
- Asymptotics of spectral gaps of quasi-periodic Schrödinger operators, joint with Jiangong You, Zhiyan Zhao, Qi Zhou.
- C^r prevalence of stable ergodicity for a class of partially hyperbolic systems, joint with Zhiyuan Zhang.
- On the centralizer of vector fields: criteria of triviality and genericity results, joint with Davi Obata, Bruno Santiago (submitted).
- Marked Length Spectral determination of analytic chaotic billiards with axial symmetries, joint with Jacopo De Simoi, Vadim Kaloshin.
- Invariant graphs and spectral type of Schrödinger operators, joint with Artur Avila, Kostya Khanin.
Published
Preprints/Submitted
PhD Thesis
You can find here the manuscript of my PhD Thesis under the supervision of Prof. Artur Avila and Julie Déserti.Teaching:
University of Toronto at Mississauga, Canada
- Winter/Spring 2019: Introduction to Discrete Mathematics (co-instructor with Stanley Xiao / Syllabus / Course evaluations)
- Fall 2018: Introduction to Discrete Mathematics (instructor)
- Winter/Spring 2018: Introduction to Partial Differential Equations (instructor)
- Fall 2017: Complex Variables (co-instructor with Raluca Tanase)
Université Paris Diderot (Paris 7), France
- Winter/Spring 2017: Calculus/Linear Algebra (teaching assistant - ATER)
Sorbonne Université (UPMC), France
- 2015-2016: Calculus/Linear Algebra (teaching assistant)
- 2014-2015: Calculus/Linear Algebra + Preparation for oral examinations in Mathematics (teaching assistant)
- 2013-2014: Linear Algebra (teaching assistant)