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 and a junior member of the Institut Universitaire de France.

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.      Random surfaces with large systoles
with Mingkun Liu
Preprint.
[arXiv version]

4.      Two counterexamples to a conjecture of Colin de Verdière on multiplicity
with Maxime Fortier Bourque, Émile Gruda-Mediavilla and Mathieu Pineault
Preprint.
[arXiv version]

3.      Linear programming bounds for hyperbolic surfaces
with Maxime Fortier Bourque
Preprint.
[arXiv version]

2.      On Cheeger constants of hyperbolic surfaces
with Thomas Budzinski and Nicolas Curien
Preprint.
[arXiv version]

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

Accepted articles

20.     Statistics of finite degree covers of torus knot complements
with Elizabeth Baker
Ann. H. Lebesgue, to appear
[arXiv version]

19.      The Klein quartic maximizes the multiplicity of the first positive eigenvalue of the Laplacian
with Maxime Fortier Bourque
J. Differential Geom., to appear
[arXiv version]

18.      A model for random three-manifolds
with Jean Raimbault
Comment. Math. Helv., 97 (4), 729 - 768, 2022.
[arXiv version] [Journal version]

17.     Kissing numbers of regular graphs
with Maxime Fortier Bourque
Combinatorica, 42 (4), 529 - 551, 2022.
[arXiv version] [Journal version]

16.     Kissing numbers of closed hyperbolic manifolds
with Maxime Fortier Bourque
Amer. J. Math., 144 (4), 1067 - 1085, 2022.
[arXiv version] [Journal version]

15.     The diameter of random Belyi surfaces
with Thomas Budzinski and Nicolas Curien
Algebr. Geom. Topol., 21: 2929 - 2957, 2021.
[arXiv version] [Journal version]

14.     On the minimal diameter of closed hyperbolic surfaces
with Thomas Budzinski and Nicolas Curien
Duke Math. J., 170 (2): 365 - 377, 2021.
[arXiv version] [Journal version]

13. On distinct finite covers of 3-manifolds
with Stefan Friedl, JungHwan Park, Jean Raimbault and Arunima Ray
Indiana Univ. Math. J., 70 (2): 809 - 846, 2021.
[arXiv version] [Journal 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]



Students

Current:
Anna Roig-Sanchis, PhD thesis, Sorbonne University, 2021 - current

Former:
Mingkun Liu, PhD thesis, Paris Cité University, 2019 - 2022
Co-supervised with Vincent Delecroix and Anton Zorich

Sofia Amontova, MSc thesis, 2019, University of Bonn

Elizabeth Baker, MSc thesis, 2019, University of Bonn

Muhammad Ardiyansyah, MSc thesis, 2018, University of Bonn

Theses

HDR thesis: Extremal and random hyperbolic geometry
Defended at the Institut de Mathématiques de Jussieu - Paris Rive Gauche on 21 Feb. 2024.

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

Conference organization

Probability and Geometry in, on and of non-Euclidian spaces, Oct. 2 - 6, 2023
Click here for more infomation

Geometry and spectra of random hyperbolic surfaces Jun. 12 - 16, 2023
ISM Discovery School
Click here for more infomation

Groups and Dynamics in Geometry, May 29 - Jun. 2, 2023
Click here for more infomation

Combinatorics of finite-index subgroups, Nov. 2 - 4, 2022
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

2022 - 2023 / Winter:
Introduction to Teichmüller theory

Past

2022 - 2023 / Spring:
Mathematics for the Sciences 2

2022 - 2023 / Autumn:
Differential Geometry

2022 - 2023 / Autumn:
Renforcement Mathématiques
Course page

2021 - 2022 / Spring:
Introduction to probability theory
Course page

2021 - 2022 / Autumn:
Topology and differential calculus
Course page

2021 - 2022 / Autumn:
Renforcement Mathématiques
Course page

2020 - 2021 / Spring:
Introduction to probability theory
Course page
Remote teaching

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

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