Research

I work in the field of mathematical physics and my research deals with symplectic geometry, integrable systems and quantization. I have worked on rigidity of group actions, cotangent models, geometric quantization and gauge theories.

I am currently interested in the study of the singular class of b-symplectic manifolds, which is the appropriate setting to examine many different physical models such as boundary problems and dissipative sistems.

Articles

  1. Rigidity of cotangent lifts and integrable systems. Journal of Geometry and Physics 157 (2020). With E. Miranda.

  2. Geometric quantization via cotangent models. Analysis and Mathematical Physics 11 (2021). With E. Miranda.

  3. Bohr-Sommerfeld quantization of b-symplectic toric manifolds. To appear in Pure and Applied Mathematics Quarterly. With E. Miranda and J. Weitsman.

  4. Singular cotangent models and complexity in fluids with dissipation. Physica D: Nonlinear Phenomena 446 (2023). With B. Coquinot and E. Miranda.

  5. Hamiltonian facets of classical gauge theories on E-manifolds. To appear in Journal of Physics A: Mathematical and Theoretical. With E. Miranda and P. Nicolás.

  6. Constructions of b-semitoric systems. Preprint. With J. Brugués, S. Hohloch and E. Miranda.

Talks

  • Geometric quantization via cotangent models. February 2021. Talk at the Barcelona-Würzburg Mathematical Physics Factory (Universität Würzburg).

  • Rigidity of cotangent lifts and integrable systems. July 2021. Talk at the Symposium 2021: New Developments in Momentum Polytope Theory (ICMAT).

  • Geometric quantization of b-symplectic toric manifolds. January 2022. Talk at the XXIII Encuentro de Invierno of the GMC Network (Universidad de Zaragoza).

  • Bohr-Sommerfeld quantization of b-symplectic toric manifolds. July 2022. Talk at the Poisson CRM Days 2022 (CRM).

  • Classification of symplectic toric manifolds I & II. November 2022. Talks at the Arbeitsgemeinschaft Symplektische Topologie (Universität zu Köln).

  • Bohr-Sommerfeld quantization of b-symplectic toric manifolds. December 2022. Talk at the Seminar semiklassische Analysis und Darstellungstheorie (Universität zu Köln).

  • A b-symplectic Hamiltonian model for dissipative dynamics. January 2023. Talk at the 43rd Winter School Geometry and Physics (Masaryk University).

  • Classification of symplectic toric manifolds. January 2023. Talk at the Seminari Informal de Matemàtiques de Barcelona (Universitat Politècnica de Catalunya).

  • Bohr-Sommerfeld quantization of b-symplectic toric manifolds. February 2023. Talk at the VI Congreso de Jóvenes Investigadores de la Real Sociedad Matemática Española (Universidad de León).

  • Constructions of b-semitoric systems. May 2023. Talk at the Analysis & Geometry Seminar (Universiteit Antwerpen).