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

Eva Miranda is a Full Professor in Geometry and Topology at Universitat Politècnica de Catalunya-IMTech and member of CRM-Barcelona. She is the director of the Laboratory of Geometry and Dynamical Systems at UPC and the group leader of the UPC Research group GEOMVAP (Geometry of Varieties and Applications). Miranda is the Co-Principal investigator of the Maria de Maeztu program CEX2020-001084-M at CRM. She has been distinguished with an ICREA Academia Prize in 2016 and a Chaire d'Excellence de la Fondation Sciences Mathématiques de Paris in 2017.

Eva Miranda is an active member of the mathematical community and created an important school by supervising 9 PhD theses so far. She has also been a member of international scientific panels, prize committees (UMALCA prize, Lichnerowicz Prize and Vicent Caselles Prize) and other scientific committees. She served as the EMS-SCM corresponding member in 2011-2017 and a former member of the Scientific Advisory Board of the CRM-Barcelona (2017-2020). Since 2020 she is a member of the scientific committee at the RSME. Since May 2018 she is a member of the Governing Board of the Barcelona Graduate School of Mathematics and since 2020 she is a member of the Conseil d'Administration de l'Institut Henri Poincaré in Paris.

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 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.