BBVA-Project

The announcement above was prepared and posted on May 31, 2022, at the website of the School of Mathematics of the Complutense University of Madrid, and then in early June at the front page of the main website of the Complutense University.

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

  • Combinatorial Problems in Algebraic and Symplectic Geometry (co-organized by R. Campoamor, M. de León and A. Díaz-Cano, in collaboration with the UCM Algebra, Geometry and Topology Seminar Organizers M. Castrillón and R. Mallavibarrena), November 8 of 2023.
  • Stability, Quantization, and Randomness in Symplectic Geometry (co-organized with R. Campoamor, M. de León and A. Díaz-Cano), dedicated to Professor Pedro Luis García Pérez on his 85th Birthday,  June 28, 29 and 30 of 2023 at the Complutense University of Madrid. A video of the Opening of the Conference by the Dean of the School of Mathematics Antonio Brú and my opening lecture may be found in the section in Videos.


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
  • 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

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