Research Interests
Low dimensional geometry and topology, Hyperbolic geometry, Teichmüller and moduli spaces, Random surfaces, Random 3-manifolds.
Research Interests
Low dimensional geometry and topology, Hyperbolic geometry, Teichmüller and moduli spaces, Random surfaces, Random 3-manifolds.
Preprints
1. Lengths of closed geodesics on random surfaces of large genus,
with Maryam Mirzakhani
Preprint.
[arXiv version]
2. Counting non-commensurable hyperbolic manifolds and a bound on homological torsion,
Preprint.
[arXiv version]
Accepted articles
1. Hyperbolic surfaces with long systoles that form a pants decomposition,
Proc. Amer. Math. Soc., to appear.
[arXiv version] [Journal version]
2. 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, to appear.
[arXiv version] [Journal version]
3. Poisson approximation of the length spectrum of random surfaces,
with Christoph Thäle
Indiana Univ. Math. J., to appear.
[arXiv version] [Journal version]
4. Mapping class group orbits of curves with self-intersections,
with Patricia Cahn and Federica Fanoni
Israel J. Math., to appear.
[arXiv version]
5. Graphs of Large Girth and Surfaces of Large Systole,
with Alexander Walker
Math. Res. Lett., to appear.
[arXiv version]
6. The genus of curve, pants and flip graphs,
with Hugo Parlier
Discrete Comput. Geom., to appear.
[arXiv version] [Journal version]
7. Finite length spectra of random surfaces and their dependence on genus,
J. Topol. Anal., 09 (4): 649 - 688, 2017.
[arXiv version] [Journal version]
8. Random regular graphs and the systole of a random surface,
J. Topol., 10 (1): 211 - 267, 2017.
[arXiv version] [Journal version]
Conference organization
Geometric Group Theory in Bonn II, Dec 3-4, 2015
Click here for more infomation
Talks
| 11 May 2017 | Geometric Topology Fair 2017, KAIST, Daejeon |
| 24 Apr 2017 | Ergodic Theory Seminar, Université de Rennes |
| 16 Mar 2017 | Workshop on Enumerative Geometry, IHP, Paris |
| 23 Nov 2016 | EPF Lausanne |
| 16 Jun 2016 | Hebrew University of Jerusalem |
| 13 Jun 2016 | Statistics & Topology Seminar, Technion, Haifa |
| 03 May 2016 | Universität Heidelberg |
| 20 Apr 2016 | Topology Seminar, UC Berkeley |
| 19 Apr 2016 | Topology Seminar, Stanford University |
| 31 Mar 2016 | MPI-Oberseminar, MPIM, Bonn |
| 19 Mar 2016 | Special Session on Invariants of Closed Curves on Surfaces, |
| AMS Spring Eastern Sectional Meeting, Stony Brook University | |
| 15 Mar 2016 | Séminaire de Géométrie et Topologie, University of Toulouse |
| 07 Dec 2015 | MPIM Toplogy Seminar , MPIM, Bonn |
| 19 Nov 2015 | Geometry and Topology Seminar, University of Warwick |
| 16 Nov 2015 | GT3, Université de Strasbourg |
| 11 Nov 2015 | Universität Bielefeld |
| 10 Nov 2015 | Geometric Analysis & Differential Geometry Short talks, MPIM, Bonn |
| 02 Nov 2015 | Universität Bochum |
| 04 Jun 2015 | Discrete Geometry Seminar, Freie Universität Berlin |
| 01 Jun 2015 | Journée de géométrie, Université Paris-Est - Créteil |
| 15 May 2015 | Complex Analysis and Dynamics Seminar, Graduate Center, CUNY |
| 12 May 2015 | Stony Brook University |
| 25 Mar 2015 | Special Year in Hyperbolic Geometry, Hunter College, CUNY |
| 18 Feb 2015 | Graduate student seminar, Brown University |
| 29 Jan 2015 | Boston College Geometry/Topology seminar, Boston College |
| 20 Jan 2015 | Geometric Group Theory and Topology Seminar, Tufts University |
| 25 Nov 2014 | Discrete math and geometry seminar , Brown University |
| 09 Oct 2014 | Combinatorics seminar, University of Fribourg |
| 31 May 2014 | GEAR Junior Retreat, University of Michigan at Ann Arbor |
| 21 Nov 2013 | Séminaire de Topologie et Géométrie, University of Geneva |
| 10 Sep 2013 | Graduate Colloquium, University of Fribourg |
| 08 Mar 2012 | Oberseminar Geometrie, University of Fribourg |
| 14 Dec 2011 | Oberseminar Geometrie, University of Fribourg |
| 01 Mar 2011 | Mathematical Physics Seminar, Radboud University Nijmegen |
| 20 Dec 2010 | Mathematikon, University of Fribourg |
| 20 Oct 2010 | Oberseminar Analysis und Spektraltheorie, TU Clausthal |
Theses
On Random Surfaces
PhD Thesis, Written under the supervision of Hugo Parlier, University of Fribourg, 2015.
Entanglement of states with unitary and permutation symmetry
Master Thesis, written under the supervision of Dr. J.D.M. Maassen, Radboud Universiteit Nijmegen, 2011.