Bram Petri

photo

About me:
I am a maître de conférences in the Complex Analysis and Geometry group of the IMJ-PRG at Sorbonne Université.

Before that, I was in Bonn. First as a post-doctoral fellow at the Max Planck Institute for Mathematics and later as a post-doc in the Geometry group at the University of Bonn, where my mentor was Ursula Hamenstädt.

I did my doctoral studies under the supervision of Hugo Parlier at the Department of Mathematics at the University of Fribourg.

My CV and Publication list.

Address:
Institut de Mathématiques de Jussieu-Paris Rive Gauche
Sorbonne Université - Campus Pierre et Marie Curie
4, place Jussieu - Boite Courrier 247
75252 Paris Cedex 05
France

Office: 16-26 526
E-mail: bram dot petri at imj-prg dot fr

Research

Research interests

Low dimensional geometry and topology, Hyperbolic geometry, Teichmüller and moduli spaces, Random surfaces, Random 3-manifolds, subgroup growth.

Preprints

5.      A model for random three-manifolds
with Jean Raimbault
Preprint.
[arXiv version]

4.     Statistics of finite degree covers of torus knot complements
with Elizabeth Baker
Preprint.
[arXiv version]

3.     Kissing numbers of regular graphs
with Maxime Fortier Bourque
Preprint.
[arXiv version]

2.     Kissing numbers of closed hyperbolic manifolds
with Maxime Fortier Bourque
Preprint.
[arXiv version]

1. Counting non-commensurable hyperbolic manifolds and a bound on homological torsion
Preprint.
[arXiv version]

Accepted articles

15.     The diameter of random Belyi surfaces
with Thomas Budzinski and Nicolas Curien
Algebr. Geom. Topol., to appear.
[arXiv version]

14.     On the minimal diameter of closed hyperbolic surfaces
with Thomas Budzinski and Nicolas Curien
Duke Math. J., to appear.
[arXiv version]

13. On distinct finite covers of 3-manifolds
with Stefan Friedl, JungHwan Park, Jean Raimbault and Arunima Ray
Indiana Univ. Math. J., to appear.
[arXiv version]

12.   Universality for random surfaces in unconstrained genus
with Thomas Budzinski and Nicolas Curien
Electron. J. Combin., 26 (4): Paper 4.2, 2019
[arXiv version] [Journal version]

11. Subgroup growth of right-angled Artin and Coxeter groups
with Hyungryul Baik and Jean Raimbault
J. Lond. Math. Soc. (2), 101 (2): 556 - 588, 2020.
[arXiv version] [Journal version]

10.   Subgroup growth of virtually cyclic right-angled Coxeter groups and their free products
with Hyungryul Baik and Jean Raimbault
Combinatorica, 39 (4): 779 - 811, 2019.
[arXiv version] [Journal version]

9. Lengths of closed geodesics on random surfaces of large genus
with Maryam Mirzakhani
Comment. Math. Helv., 94 (4): 869 - 889, 2019.
[arXiv version] [Journal version]

8. Hyperbolic surfaces with long systoles that form a pants decomposition
Proc. Amer. Math. Soc., 146 (3): 1069 - 1081, 2018.
[arXiv version] [Journal version]

7. Exponential Torsion Growth for Random 3-Manifolds
with Hyungryul Baik, David Bauer, Ilya Gekhtman, Ursula Hamenstädt, Sebastian Hensel, Thorben Kastenholz and Daniel Valenzuela
Int. Math. Res. Not. IMRN, 21: 6497 - 6534, 2018.
[arXiv version] [Journal version]

6. Poisson approximation of the length spectrum of random surfaces
with Christoph Thäle
Indiana Univ. Math. J., 67 (3): 1115 - 1141, 2018.
[arXiv version] [Journal version]

5. Mapping class group orbits of curves with self-intersections
with Patricia Cahn and Federica Fanoni
Israel J. Math., 223 (1): 53 - 74, 2018.
[arXiv version] [Journal version]

4. Graphs of Large Girth and Surfaces of Large Systole
with Alexander Walker
Math. Res. Lett., 25 (6): 1937 - 1956. 2018.
[arXiv version] [Journal version]

3. The genus of curve, pants and flip graphs
with Hugo Parlier
Discrete Comput. Geom., 59 (1): 1 - 30, 2018.
[arXiv version] [Journal version]

2. Finite length spectra of random surfaces and their dependence on genus
J. Topol. Anal., 09 (4): 649 - 688, 2017.
[arXiv version] [Journal version]

1. Random regular graphs and the systole of a random surface
J. Topol., 10 (1): 211 - 267, 2017.
[arXiv version] [Journal version]



PhD Thesis

On Random Surfaces
Written under the supervision of Hugo Parlier, University of Fribourg, 2015.

Conference organization

Groups and Dynamics in Geometry, Jul. 18 - 23, 2021
Click here for more infomation

Geometric Group Theory in Bonn III, Jan. 31 - Feb. 1, 2019
Click here for more infomation

Geometric Group Theory in Bonn II, Dec. 3-4, 2015
Click here for more infomation

Mini course

For the lecture notes of the mini course "Extremal problems and probabilistic methods in hyperbolic geometry", click here.

Teaching

Current

2020 - 2021 / Autumn:
Topology and differential calculus
Course page
Remote teaching

Past

2019 - 2020 / Spring:
Introduction to probability theory
Course page
Remote teaching

2019 - 2020 / Autumn:
Linear and bilinear algebra
Course page

2018 - 2019 / Summer:
Teichmüller Theory
Course code: V5D3 - Advanced Topics in Geometry

2018 - 2019 / Winter:
Random walks on linear groups
Course code: S4D3 - Graduate Seminar on Advanced Geometry

Simplicial volume
Course code: V5D6 - Selected Topics in Differential Geometry

2017 - 2018 / Summer:
Arithmetic groups
Course code: V5D3 - Advanced Topics in Geometry

2017 - 2018 / Winter:
Property (T)
Course code: S4D3 - Graduate Seminar on Advanced Geometry

Quantum ergodicity
Course code: S4D1 - Graduate Seminar on Differential geometry

Advanced Geometry I V4D2
Exercises week 8

2016 - 2017 / Summer:
Random methods in geometry
Course code: V5D4 - Selected Topics in Geometry

2013 - 2014 / Spring:
Assistant for Analysis IV

2013 - 2014 / Autumn:
Assistant for Analysis III

2012 - 2013 / Spring:
Assistant for Mathematical Methods in Computer Science

2012 - 2013 / Autumn:
Assistant for Mathematical Methods in Computer Science

2011 - 2012 / Spring:
Assistant for Mathematical Methods in Computer Science