Ph.D. in mathematics, Universitat Autònoma de Barcelona, 1988.
Postdoc at Department of mathematics, Ohio State University, Columbus, Ohio, 1989-90, and Mathematisches Institut, Heidelberg, 1990-91.
Associate Professor, Departament de Matemàtiques, Universitat Autònoma de Barcelona, 1992-2004.
Professor at same Department since 2004.

• Unstable homotopy theory
• Finite groups
• Compact Lie groups
• Finite loop spaces
• Fusion systems

(1) PDI2020-116481GB-100. Homotopy theory of combinatorial and algebraic structures.
o Funding entity and call: Ministry of Science and Innovation
o IP: Wolfgang Pitsch
o Period: 2021 to 2025

(2) 2021 SGR 01015. Laboratory of Interactions between Geometry, Algebra and Topology (LIGAT)
o Funding entity and call: AGAUR
o IP: Dolors Herbera
o Period: 2023 to 2025

1. C. Broto, J. Møller, B. Oliver, and A. Ruiz. Realizability and tameness of fusion systems, Proc. Lond. Math. Soc. 127 (2023), 1816–1864
2. C. Broto, J. Møller, and B. Oliver. Automorphisms of fusion systems of finite simple groups of Lie type, Memoirs of the American Mathematical Society, 126 (2019) pp. 1¬–117
3. C. Broto, R. Levi, and B. Oliver. An algebraic model for finite loop spaces. Algebraic and Geometric Topology, 14 (2014) pp. 2915¬–2981
4. C. Broto, J. Møller, and B. Oliver. Equivalences between fusion systems of finite groups of Lie type. J. Amer. Math. Soc. 25 (2012), 1–20
5. C. Broto and J. Møller. Chevalley p-local finite groups. Algebraic and Geometric Topology, 7 (2007) pp. 1809-1919
6. C. Broto, R. Levi, and B. Oliver. Discrete models for the p-local homotopy theory of compact Lie groups and p-compact groups. Geometry and Topology, 11 (2007) pp. 315–427