BBVA-Project

PROJECT INFORMATION

  • BBVA Foundation Description (in Spanish): available here.
  • Title: From Integrability to Randomness in Symplectic and Quantum Geometry
  • Amount: 149996 euros
  • Duration: 2022-2025
  • Principal Investigator: Álvaro Pelayo
  • Team Members: Sean Curry (Oklahoma State University, USA), Fraydoun Rezakhanlou (UC Berkeley, USA) and San Vu Ngoc (Rennes 1, France)
  • Brief Description: The goal is to use techniques from symplectic geometry, combinatorics, algebra and analysis to study classical/quantum integrable systems and random systems. Integrable systems are a crucial family of dynamical systems (i.e. systems which evolve with time) for which many quantities are preserved under the motion, and they play an essential role in both mathematics and physics. The project aims to introduce new perspectives and methods to solve several fundamental problems concerning integrable systems, including understanding their invariants and singularities, existence of fixed points, as well as making connections with symplectic geometric aspects of stability and randomness.


BBVA FOUNDATION ANNOUNCEMENT

On May 31, 2022, the BBVA (Banco Bilbao Vizcaya Argentaria Bank) Foundation announced that it had awarded 35 Research Grants for Scientific Research Projects in the areas of Mathematics, Climate Change and Ecology and Conservation Biology, Biomedicine, Social Sciences and Philosophy.

A total of 35 projects were selected among 620 submissions, including 4 projects in Mathematics, including the project above.

On June 7, 2022, the BBVA Foundation published a press note, available here,  which includes a description (in Spanish) of the selected projects aimed at a general audience.


PRESS ANNOUNCEMENTS


CONFERENCES FUNDED BY THIS PROJECT


LECTURES DELIVERED DURING THE TENURE OF THIS PROJECT

  • BBVA Foundation Project Opening Lecture at Conference Symplectic and Algebraic Geometry of Real and p-adic systems, Complutense University of Madrid 2024 Spain.
  • Joint CRM-Montréal/Princeton/Institute for Advanced Study/Tel Aviv/Paris Symplectic Zoominar (online) 2024 USA. Video
  • Spanish Royal Academy of Sciences – Entry Speech as Corresponding Member in the Mathematical Sciences Division,  Madrid 2024 Spain. Video
  • Lecture at Congress deLeonfest 2023, an interdisciplinary conference on Geometric Mechanics and Related Fields, in honor of Manuel de León at ICMAT Madrid, 2023 Spain.
  • BBVA Foundation Project Opening Lecture at Conference Stability, Quantization and Randomness in Symplectic Geometry – Dedicated to Professor Pedro Luis García Pérez on his 85th birthday, Complutense University of Madrid, 2023 Spain. Video
  • University of Cantabria, MATESCO Seminar 2023 Spain.
  • University of Cantabria, MATESCO Seminar 2022 Spain.


ARTICLE FOR A GENERAL PUBLIC  FUNDED BY THIS PROJECT

  • Geometría simpléctica: de los movimientos planetarios a las misiones espaciales (Symplectic geometry: from planetary motions to space missions).
    BBVA Foundation Web


RESEARCH ARTICLES FUNDED BY THIS PROJECT

  • Ewald’s Conjecture and integer points in algebraic and symplectic toric geometry (with L. Crespo and F. Santos), Preprint.
    arxiv:2310.10366
  • The structure of monotone blow-ups in symplectic toric geometry and a question of McDuff (with F. Santos), Preprint.
    arxiv:2308.03085
  • The random Arnold Conjecture: a new probabilistic Conley-Zehnder Theory for symplectic maps (with F. Rezakhanlou), Preprint.
    arxiv:2306.15586
  • Moduli spaces of Delzant polytopes and symplectic toric manifolds (with F. Santos), Preprint.
    arxiv:2303.02369
  • Semitoric systems of non-simple type (with J. Palmer and X. Tang), Preprint.
    arXiv:1909.03501
  • Symplectic geometry: applications and challenges (in Spanish), La Gaceta de la Real Sociedad Matemática Española 27 (2024) 285-311.
    Publisher Website
  • Vu Ngoc’s Conjecture on focus-focus singular fibers with multiple pinched points (with X. Tang), Journal of Fixed Point Theory and Applications 26, 6 (2024).
    Publisher Website   arXiv:1803.00998
  • Symplectic and inverse spectral geometry of integrable systems: a glimpse and open problems. Topology and its Applications 339 Part A (2023) 108577.
    Publisher Website


RELATED WORKS FUNDED BY THIS PROJECT

  • Extended abstract (2024): On Ewald’s and Nill’s Conjectures about smooth polytopes (with L. Crespo, F. Santos), Conference Discrete Mathematics Days, Alcalá de Henares, July 3-5, 2024.

Life is not easy for any of us. But what of that? We must have perseverance and above all confidence in ourselves. We must believe that we are gifted for something and that this thing must be attained.
M. Curie