Phone
E-mail davidmp@mat.uab.cat
Position Associate Professor
Area Algebra, Geometry, Number Theory and Topology
Marín, David
Biosketch

Degree in mathematics from Universitat de Barcelona (1995) and PhD in mathematics from Universitat Autònoma de Barcelona (2001). Post-doctoral stage at Université de Bourgogne (2001-2002). Temporal position at Universitat Autònoma de Barcelona (1995-2006) and a permanent one from 2006 until now.

 

Interests

My research focuses on the theory of differential equations in the complex domain. I have worked in three main lines:

a) analytic and topological invariants of singular holomorphic foliations in the complex plane,

b) description and classification of the set of global singular foliations on the complex projective plane fulfilling a Zariski  closed property as being convex, Galois or having a flat dual web,

c) bifurcation of critical periodic orbits in families of real centers in the real projective plane.

Other Research Interests
  • Singularities
  • Ordinary Differential Equations
  • Holomorphic Foliations
  • Webs
Projects
  • Invariantes locales y globales en geometría, PGC2018-095998-B-I00, 2019-2021
  • Laboratori d’Interaccions entre Geometria, Àlgebra i Topologia, 2017SGR1725, 2017-2019
  • Estructuras geométricas, MTM2015-66165-P, 2016-2018 (Co IP)
  • Variedades complejas, dinámica holomorfa y singularidades, MTM2011-26674-C02-01, 2012-2014 (IP)
  • Variedades complejas, dinámica holomorfa y singularidades, MTM 2008-02294, 2009-2011 (IP)
  • Grup consolidat de geometria diferencial, 2009SGR1207, 2009-2013

 

Selected publications
  • S. Bedrouni, D. Marín, Convex foliations of degree 5 on the complex projective plane, Publicacions Matemàtiques 65 (2021), 409-429
  • D. Marín, J. Villadelprat, Asymptotic expansion of the Dulac map and time for unfoldings of hyperbolic saddles: general setting, Journal of Differential Equations 275 (2021) 684-732
  • D. Marín, J.-F. Mattei, E. Salem, Topological moduli space for germs of holomorphic foliations, International Reseach Mathematics Notices 2020, 9228-9292
  • A. Beltrán, M. Falla, D. Marin, M. Nicolau, Foliations and webs inducing Galois coverings, IMRN 2016, 3768-3827
  • D. Marín, M. Nicolau, A priori L^2-error estimates for approximations of functions on compact manifolds, Mediterranean Journal of Mathematics 12 (2015), 51-62
  • D. Marín, J.V. Pereira, Rigid Flat webs on the projective plane, Asian J. of Math. 17 (2013), 163-192
  • D. Marín, J.-F. Mattei, Monodromy and topological classification of germs of holomorphic foliations. Annales Scientifiques ENS 45 (2012), 405-445
  • P. Mardesic, D. Marín, J. Villadelprat, The period function of quadratic reversible centers, J. Differential Equations (2006), 120-171
  • D. Marín, Moduli spaces of germs of holomorphic foliations in the plane, Commentarii Math. Helv. 78 (2003), 518-539