E-mail eva.miranda@upc.edu
Position Professor
Research interests Geometry
Group Algebra Geometry Number Theory And Topology
Miranda, Eva
Biosketch

Eva Miranda is a Full Professor at Universitat Politècnica de Catalunya in Barcelona and member of the Centre de recerca Matemàtica-CRM. She is the director of the Laboratory of Geometry and Dynamical Systems. Distinguished with two consecutive ICREA Academia Prizes in 2016 and 2021, she was awarded a Chaire d'Excellence de la Fondation Sciences Mathématiques de Paris in 2017 and a Friedrich Wilhelm Bessel Prize by the Alexander Von Humboldt Foundation in 2022. Miranda is the recipient of the quadrennial François Deruyts Prize in 2022, a prize awarded by the Royal Academy of Belgium. She has been named the 2023 London Mathematical Society Hardy Lecturer.

Miranda's research is at the crossroad of Differential Geometry, Mathematical Physics and Dynamical Systems. Miranda is an active member of the mathematical community, a member of several international scientific panels and prize committees. She created an important school by supervising 10 Ph.D. theses and several postdocs.

Interests

Her research deals with several aspects of Differential Geometry, Mathematical Physics and Dynamical Systems such as Symplectic and Poisson Geometry, Hamiltonian Dynamics, Group actions and Geometric Quantization. Almost a decade ago she started the investigation of several facets of b-Poisson manifolds (also known as log-symplectic manifolds). These structures appear naturally in physical problems on manifolds with boundary and in Celestial mechanics such as the 3-body problem (and on its restricted versions) after regularization transformations. She recently got interested in Fluid Dynamics and the study of their complexity (computational, topological, logical, dynamical) by looking through a contact mirror unveiled two decades ago by Etnyre and Ghrist. She is currently working in extending Floer homology to a class of Poisson manifolds including b-Poisson manifolds and the classical Weinstein conjecture in this set-up. Her motivation comes from the search of periodic orbits on regularized problems in Celestial Mechanics.

Other Research Interests
  • Differential Geometry
  • Symplectic Geometry
  • Poisson Geometry
  • Contact Geometry
  • Mathematical Physics
  • Fluid Dynamics
  • Dynamical Systems
  • Hamiltonian Dynamics
  • Quantization
Projects
  • ICREA Academia 2021
  • ICREA Academia 2016
  • Co-Principal investigator of the Maria de Maeztu program CEX2020-001084-M
  • AEI project Geometría, Álgebra, Topología y Aplicaciones Multidisciplinares code PID2019-103849GB-I00 / AEI / 10.13039/501100011033
  • MTM2015-69135-P (MINECO/FEDER)
  • 2017SGR932 (AGAUR)
  • AFR-Ph.D. project 2016-2019
Selected publications

10 most important publications in the last 10 years. Complete list in this link: https://web.mat.upc.edu/eva.miranda/nova/#PublishedPapers

  • 1. R. Cardona, E. Miranda, D. Peralta-Salas and F. Presas, Constructing Turing complete Euler flows in dimension 3. Proc. Natl. Acad. Sci. USA 118 (2021), no. 19, Paper No. e2026818118, 9 pp.
  • 2. E. Miranda and C. Oms, The singular Weinstein Conjecture, Adv. Math. 389 (2021), Paper No. 107925, 41 pp.
  • 3. V. Guillemin, E. Miranda and J. Weitsman, Jonathan Desingularizing bm-symplectic structures. Int. Math. Res. Not. IMRN 2019, no. 10, 2981–2998.
  • 4. V. Guillemin, E. Miranda and J. Weitsman, On geometric quantization of b-symplectic manifolds, Adv.
    Math. 331 (2018), 941–951.
  • 5. A. Bolsinov, V. Matveev, E. Miranda and S. Tabachnikov, Open problems, questions and challenges in
    finite-dimensional integrable systems Phil. Trans. Roy. Soc. A, 376 (2018), no. 2131, 20170430, 40pp.
  • 6. A. Kiesenhofer and E. Miranda, Cotangent models for integrable systems, Communications in Mathematical Physics, Comm. Math. Phys. 350 (2017), no. 3, 1123–1145.
  • 7. A. Kiesenhofer, E. Miranda and G. Scott, Action-angle variables and a KAM theorem for b-Poisson manifolds, J. Math. Pures Appl. (9) 105 (2016), no. 1, 66–85.
  • 8. V. Guillemin, E. Miranda, A. Pires and G. Scott, Toric actions on b-manifolds, Int Math Res NoticesIMRN (2015) 2015 (14): 5818–5848.
  • 9. V. Guillemin, E. Miranda and A. Pires, Symplectic and Poisson Geometry on b-manifolds, Adv. Math. 264 (2014), 864–896.
  • 10. E. Miranda, P. Monnier and N.T. Zung, Rigidity for Hamiltonian actions on Poisson manifolds, Adv. Math. 229 (2012), no. 2, 1136-1179.