Xabier Legaspi's Website

Xabier Legaspi Juanatey

I was a predoc researcher in mathematics both at ICMAT and Université de Rennes 1, under a joint supervision of Yago Antolín and Rémi Coulon. My research area was geometric group theory.

I was interested in the study of exponential growth rates in groups of non-positive curvature. The techniques I exploited included simple counting arguments; metric inequalities and geometric small cancellation theory. In particular I studied groups acting properly with a contracting element and groups acting acylindrically on hyperbolic spaces. I was also interested in monster groups.

My academic CV can be found here.

Research

Publications.

Growth of Quasi-Convex Subgroups in Groups with a Constricting Element arXiv:2206.06749 (40 pages). 2023. To appear in Groups, Geometry, and Dynamics.

Preprints.

/w M. Steenbock. Uniform Uniform Exponential Growth in Small Cancellation Quotients (53 pages). 2023. In preparation. Poster.

PhD thesis.

Growth in Groups of Non-Positive Curvature

Undergraduate work.

My second master thesis about the ergodicity of the geodesic flow in non-positive curvature, supervised by Rémi Coulon.
My first master thesis about Shor's algorithm and quantum computing, with Clément Louis. Slides of the talk.
My undergraduate thesis about the classification of quadratic forms over the p-adic numbers, supervised by Javier Majadas. Slides and "lyrics" of the talk. Everything is written in Galician.

Teaching

Université de Rennes 1.

Deuxième Semestre 2021/2022:

Algèbre et Géométrie 2.

Universidad Complutense de Madrid.

Primer Semestre 2021/2022:

Geometría Lineal.

Talks

Invited seminar talks.

07/06/23 — Group Theory Seminar, ICMAT.
18/10/22 — Geometry and Analysis on Groups Research Seminar, Universität Wien.
15/06/22 — Learning Seminar, IHP.
02/06/22 — Geometric Group Theory Seminar, Universität Münster.
17/01/22 — DAGGER Seminar, University of Warwick.
03/11/21 — Algebra Seminar, UPV/EHU.
26/10/21 — BRIJGES Seminar, University of Bristol.
30/09/21 — Group Theory Seminar, ICMAT.
26/11/20 — Séminaire Pampers, Université de Rennes 1.
11/06/20 — Séminaire Pampers, Université de Rennes 1.

Contributed conference talks.

20/10/21 — IX Encuentro de Jóvenes Topólogos, Sevilla.
17/10/19 — VIII Encuentro de Jóvenes Topólogos, Santiago de Compostela.

Where to find me

You may contact me at the following email address:

xabier[dot]legaspi[at]etudiant[dot]univ[dash]rennes1[dot]fr