I am a postdoc at IMPAN (Warsaw) as part of the Maestro project "Analysis on groups" led by Piotr Nowak since October 2023.

I study analytical aspects of group cohomology and applications to geometric and measured group theory. I have mostly worked with L^p-cohomology of groups and of geometric objects related to Lie theory (such as Lie groups, buildings, Coxeter groups or Kac-Moody groups).

Before, I defended my PhD on June 2023 under the supervision of Marc Bourdon (Université de Lille) and Bertrand Rémy (ENS Lyon) at École polytechnique.

Email: alopez at impan.pl

Preprints

(with Juan Paucar) On growth of cocycles of isometric representations on Banach spaces. arXiv

Vanishing of the second L^p-cohomology group for most semisimple groups of rank at least 3. Accepted in Annales de l'Institut Fourier. arXiv

Articles

Top degree ℓ^p-homology and conformal dimension of buildings. Geom Dedicata 218, 83 (2024). published, arXiv

Finitely presented simple groups and measure equivalence. Colloquium Mathematicum, 172 (2023), no. 2, 261-279. arXiv

Teaching

2022 -2023

Tutorials L2 Analyse et convergence 1 (Université Paris-Saclay)
Tutorials L1 Algèbre 1 (Université Paris-Saclay)
Tutorials Remise à niveau analyse et algèbre, 3ème année cycle ingénieur (Polytech Paris-Saclay)

2021-2022

Tutorials L2 Analyse et convergence 1 (Université Paris-Saclay)
Tutorials L1 Algèbre 1 (Université Paris-Saclay)

2020-2021

Tutorials L2 Analyse et convergence 1 (Université Paris-Saclay)
Tutorials L2 Analyse pour physiciens (Université Paris-Saclay)