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.



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

Undergraduate work.


Université de Rennes 1.

Universidad Complutense de Madrid.

  • Primer Semestre 2021/2022:
  • Geometría Lineal.


Invited seminar talks.

Contributed conference talks.

Where to find me

Upcoming conferences.

You may contact me at one of the following email addresses:
  • xabier[dot]legaspi[at]icmat[dot]es
  • xabier[dot]legaspijuanatey[at]univ[dash]rennes1[dot]fr

13-15 Nicolás Cabrera,
Campus de Cantoblanco,
28049, Madrid, España.

263 avenue du Général Leclerc,
Campus de Beaulieu,
35042 Rennes, France.