Current Research Interests:
· Symplectic Geometry
· Poisson Geometry
· Integrable systems and group actions
· Foliation theory
· Geometric quantization
· Groupoids and Algebroids
· Hamiltonian Dynamics
· and Differential
Geometry/Mathematical Physics in the large....
My research deals with geometrical and dynamical aspects of singularities. In particular, I am interested in Hamiltonian systems and their singularities. I study normal forms and equivariant geometric problems arising in Symplectic, Contact, and Poisson manifolds. I am also interested in rigidity problems for group actions on these manifolds. I also work in geometric quantization of real polarizations. Some years ago, I started to consider geometrical problems on b-manifolds (inspired by
My research is financed by the Catalan Institution for Research and Advanced Studies via an ICREA Academia 2016 Prize and partially supported by several research projects. I am the principal investigator of the AGAUR SGR research project GEOMVAP with code 2017SGR932 (21 members) and the MTM research project MTM2015-69135-P/FEDER, Geometría y Topología de variedades, álgebra y aplicaciones (together with Marta Casanellas).
From September 2017 until February 2018, I have been a Chaire d'Excellence de la Fondation Sciences Mathématiques de Paris and my work has been supported by a public grant overseen by the French National Research Agency (ANR) as part of the "Investissements d'Avenir" program (reference: ANR-10-LABX-0098). I am also a member of the research project EXPLORA ciencia MTM2015-72876-EXP based at ICMAT-CSIC (Members: Alberto Ibort, Eva Miranda and Francisco Presas(IP)). I am a collaborator of the National Science Foundation project New Avenues in Symplectic Geometry DMS 12/11819 (PI: Jonathan Weitsman).
Since December 2016 I am in the head of the Laboratory of Geometry and Dynamical Systems. Since May 2018 I am the group leader of the UPC research group GEOMVAP (Geometry of varieties and applications).
My academical trajectory in a glimpse:
Ph.D thesis "On symplectic linearization of singular Lagrangian foliations" at the University of Barcelona in September 2003.
October 2004-May 31, 2007, Marie Curie EIF postdoc at Laboratoire Émile Picard, Université Paul Sabatier.
June 1st, 2007 – August 31, 2009, Juan de la Cierva Fellow at the Departament de Matemàtiques at Universitat Autònoma de Barcelona.
September 2009-August 2013- Professor Lector (Lecturer) at the Department of Applied Mathematics I, UPC.
September 2013-September 2015- Professor Agregat Interí/Interim Associate Professor at Universitat Politècnica de Catalunya.
Currently (since October 2015), Associate Professor (Professor Agregat) at UPC.
Since January 2016, I am principal investigator of the MTM Research project MTM2015-69135-P, Geometría y Topología de variedades, álgebra y aplicaciones with 24 members.
Since December 2016, I am in charge of the Laboratory of Geometry and Dynamical Systems at EPSEB.
Since January 2017 and for 5 years I am an ICREA Academia Professor.
From September 2017 until February 2018, I have been a Chaire d'Excellence de la Fondation Sciences Mathématiques de Paris and my work has been supported by a public grant overseen by the French National Research Agency (ANR) as part of the "Investissements d'Avenir" program (reference: ANR-10-LABX-0098).
I have been selected under the Programa Càtedres-UPC 2017 for promotion to Full Professor.
I am the principal investigator of the AGAUR SGR research project 2017SGR932 (21 members).
Since May 2018 I am the group leader of the UPC research group GEOMVAP (Geometry of varieties and applications).
Affiliations and memberships:
1. Associate Professor at UPC, member at ICMAT (via Ginzburg lab) and member of Barcelona Graduate School of Mathematics BGSMath.
2. I am a member of the European Mathematical Society and a member of Societat Catalana de Matemàtiques.
3. Since 2011 I am the corresponding member for the SCM and EMS.
I am qualified as Full Professor in the area of Geometry and Topology by AQU since October 2016.
Since February 2010, I am qualified as Professeur des Universités en Section 25 (Mathématiques) by the French CNU (Conseil des Universités). I was qualified as MCF in February 2008.
I am qualified as Professor agregat by AQU since 2010.
I am qualified as Profesor Titular de Universidad since April 2015
Chaire d'Excellence 2017 de la Fondation Sciences Mathématiques de Paris.
Giovanni Prodi Chair at Würzburg 2017-2018 (declined).
Complete cv in English (last update May 2018)
· My thesis:
Eva Miranda, "On symplectic linearization of
singular Lagrangian foliations" , June, 2003, edicions de
· My research papers (the versions posted here might differ slightly from the final published versions):
Publications (as author):
Open Problems, Questions, and Challenges in Finite-Dimensional integrable systems, (with A. Bolsinov, V. Matveev and S. Tabachnikov), arXiv:1804.03737, to appear at Philosophical Transactions of the Royal Society A, 2018.
Equivariant classification of $b^m$-symplectic surfaces(with A. Planas), https://arxiv.org/abs/1607.01748, to appear at Regular and Chaotic Dynamics, Volume 23, Issue 4 of 2018.
Convexity of the moment map image for torus actions on b^m-symplectic manifolds (with V. Guillemin and J. Weitsman), https://arxiv.org/abs/1801.01097, to appear at Philosophical Transactions of the Royal Society A, 2018.
Singular fibers of the Gelfand--Cetlin system on u(n)* (with D. Bouloc and N.T Zung), arXiv:1803.08332, preprint 2018, submitted.
On geometric quantization of b-symplectic manifolds (with V. Guillemin and J. Weitsman), arXiv:1608.08667, Advances in Mathematics, to appear, 2018.
On geometric quantization of $b^m$-symplectic manifolds, (with V. Guillemin and J. Weitsman), arXiv:1801.03762 preprint, 2018, submitted.
Classification of b^m-Nambu structures of top degree (with A. Planas), C. R. Math. Acad. Sci. Paris 356 (2018), no. 1, 92–96.
Zeroth Poisson homology, foliated cohomology and perfect Poisson manifolds (with D. Martínez-Torres), Regul. Chaotic Dyn. 23 (2018), no. 1, 47–53.
An invitation to Singular Symplectic Geometry (with R. Braddell, A. Delshams, C. Oms and A. Planas), arXiv:1705.03846, accepted at International Journal of Geometric Methods in Modern Physics, 2017.
Desingularizing b^m-symplectic structures (with V. Guillemin and J. Weitsman), arXiv:1512.05303, accepted at IMRN, International Mathematics Research Notices
Cotangent models for integrable systems (with A. Kiesenhofer), http://arxiv.org/abs/1601.05041 Communications in Mathematical Physics,10.1007/s00220-016-2720-x Comm. Math. Phys. 350 (2017), no. 3, 1123–1145.
Geometric Quantization of Semitoric Systems and almost toric manifolds (with F. Presas and R. Solha), preprint 2017, arXiv:1705.06572, submitted.
Non-commutative integrable systems on b-symplectic manifolds (with A. Kiesenhofer), https://arxiv.org/abs/1606.02605, Regul. Chaotic Dyn. 21 (2016), no. 6, 643–659.
I am currently working on a book project entitled "Geometry and Dynamics of singular symplectic manifolds" (by invitation of the Societé Mathématique de France jointly with Fondation Sciences Mathématiques de Paris) for the collection Cours Spécialisées of the SMF. By special agreement with FSMP the publication will be made available in open access.
This book aims to be an enhanced and (hopefully) comprehensive version of the course I delivered in October-November-December 2017 at Institut Henri Poincaré during my Chaire d'Excellence de la Fondation Sciences Mathématiques de Paris. The webpages of the course are available here: https://www.sciencesmaths-paris.fr/fr/le-cours-deva-miranda-933.htm https://mat-web.upc.edu/people/eva.miranda/coursIHP.htm
Publications (as editor):