Julien Boulanger

Since September 2024 I am a postdoc researcher at the Centro de Modelamiento matematico in Santiago de Chile, with Rodolfo Gutiérrez-Romo. Prior to that I did my PhD at the Université Grenoble alpes under the supervision of Erwan Lanneau and Daniel Massart, on some geometric problems around translation surfaces.

I am interested in dynamics and geometry of surfaces. I specifically study translation surfaces and their Veech groups, but I am also interested in interval exchange transformations, continued fractions, combinatorics on words and Anosov dynamics. Here is my CV, and a research statement.

News

I’ll be in France in may and june. Don’t hesitate to contact me if you are interested in my research!

I was in Montevideo between February 17 and March 7 and I gave a talk at the dynamical systems seminar on my work on connection points. See the slides (in spanish) or a very close english version which I used for the (online) number theory seminar of Oregon state University in january.

Preprints

(7) Connection points on double regular polygons, 2025.
Arxiv

We study connection points on the double regular n-gon translation surface, for n≥7 odd and its staircase model. For n≠9, we provide a large family of points with coordinates in the trace field that are not connection points. This family includes the central points, and for n=7 we conjecture that all the remaining points are connection points. Further, in the case where n≥7 is a prime number, we provide a constructive proof by exhibiting an explicit separatrix passing through a central point that does not extend to a saddle connection.

(6) Algebraic intersections on Bouw-Möller surfaces, and more general convex polygons, with Irene Pasquinelli, 2024.
Arxiv

Publications

(5) Algebraic intersection, lengths and Veech surfaces, To appear in the Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (2025).
Arxiv or Journal

(4) Lower bound for KVol on the minimal stratum of translation surfaces. Geometria Dedicata 218, 88 (2024).
Arxiv or Journal

(3) Algebraic intersection in regular polygons, with Erwan Lanneau and Daniel Massart, 2022. Annales Henri Lebesgue . Volume 7 (2024), pp. 787-821.
Arxiv or Journal

(2) There are no primitive Teichmüller curves in Prym(2,2), with Sam Freedman, 2022. Comptes rendus de l’académie des sciences. Volume 362 (2024), pp. 167-170.
Arxiv or Journal

(1) Central points of the double heptagon translation surface are not connection points. Bulletin de la SMF, Vol.150(2) (2022), pp. 459-472.
Arxiv or Journal

PhD defense

I started my PhD on September 2021 under the supervision of Erwan Lanneau and Daniel Massart and defended in December 2023 at the Institut Fourier, Université Grenoble Alpes. The slides are available here as well as the manuscript. You can also find here a small explication of my work which was meant for non-matematicians attending my PhD defense.

A fundamental domain for the SL(2,R)-orbit of the golden L in the moduli space of translation surfaces.