Xabier Legaspi

Xabier Legaspi Juanatey

I am a final year 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 is geometric group theory.

I am interested in growth and combinatorial problems in groups that involve the following ingredients: simple counting arguments; metric inequalities imposing non-positive curvature conditions such that Gromov’s inequality or Behrstock’s inequality; and geometric small cancellation theory. One of the goals of my research is to understand better some collections of exponential growth rates for groups acting properly with a contracting element and groups acting acylindrically on hyperbolic spaces. I am also interested in monster groups.

My CV can be found here. This year I am applying for positions.

Research

Preprints.

• Constricting elements and the growth of quasi-convex subgroups. arXiv:2206.06749. Submitted.

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.

• 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

Upcoming conferences.

• 12-16/12/22 — II Encuentro RSME-UMA, Ronda.
• 13-17/02/23 — Young Geometric Group Theory XI, Münster.

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