New Mexico Researchers Network


Description: This is a group of junior

researchers from many parts of the world, with

strong ties to the mathematical activity in New

Mexico. Our works cover many aspects of

Nonlinear PDE’s, Applied Harmonic Analysis 

and related topics.


Research Interests: Our areas of expertise include: Bifurcation problems, Compressed sensing, Frame theory, Gamma  convergence, Geometric flows, Geometric measure theoretic approaches to concentration phenomena, Ginzburg-Landau theory,  Gluing Constructions, KAM methods, Liquid-Crystals, Microlocal Analysis, Multi Scale problems, N-body related problems, Nash-Moser methods,  Nonlinear Analysis, Nonlocal variational problems, Pseudo-differential Operators, Segregation models, Signal processing, Singular perturbations, Stability of solitary waves, Statistical mechanics, Strichartz estimates, Variational methods in mathematical physics, etc.



Recent Preprints:

  • A. Contreras, R. Jerrard.  Nearly Parallel Vortex Filaments in the 3D Ginzburg-Landau Equations, submitted 2016.
  • C. Garcia-Azpeitia, Manuel Tejada-Wriedt. Molecular chains interacting by Lennard-Jones and Coulomb forces.
  • R. Calleja, A. Celletti, R. de la Llave. Domains of analyticity of Lindstedt expansions of KAM tori in dissipative perturbations of Hamiltonian systems, preprint.

Recently Accepted:

  •  C. García-Azpeitia. Traveling and standing waves in coupled pendula and Newton’s cradle. Journal of Nonlinear Science (2016) (arXiv:1503.07391).
  • Jameson Cahill, Peter G. Casazza, and Ingrid Daubechies, Phase retrieval in infinite-dimensional Hilbert spaces. To appear in Transactions of the AMS. Preprint available online at arXiv:1601.06411.    
  • A. Burchard, R. Choksi, I. Topaloglu. Nonlocal shape optimization via interactions of attractive and repulsive potentials. To appear in Indiana Univ. Math. J.
  • A. Contreras, C. Garcia-Azpeitia, C. Garcia-Cervera, S. Joo.  The onset of layer undulations in smectic A liquid crystals due to a strong magnetic field. To appear in Nonlinearity.
  • S. Alama, L. Bronsard, X. Lamy. Minimizers of the Landau-de Gennes energy around a spherical colloid particle. To appear in Arch. Ration. Mech. Anal,. 2016.
  • R. Calleja, A. Celleti, L. Corsi, R. de la Llave.  Response solutions for quasi-periodically forced, dissipative wave equations.  To appear in SIAM Journal on Mathematical Analysis.
  • A. Contreras, D. Pelinovsky, Y. Shimabukuro. L^2 orbital stability of Dirac solitons in the massive Thirring model. To appear in Comm. Part. Diff. Eq.  Preprint available at arXiv:1312.1019.
  • A. Contreras, X. Lamy, R. Rodiac. Boundary regularity of weakly anchored harmonic maps.  To appear in Comptes Rendus Mathematique. Preprint available at arXiv:1509.04155.
  • S. Alama, L. Bronsard, J. Dadok, A. Contreras, P. Sternberg.  A Degenerate Isoperimetric Problem and Traveling Waves to a Bi-stable Hamiltonian System (2015). To appear in Communications on Pure and Applied Mathematics. Preprint available at arXiv:1504.00423.
  • M. Blair, C. Sogge. On Kakeya-Nikodym averages, L^p -norms and lower bounds for nodal sets of eigenfunctions in higher dimensions. To appear in Journal of the European Mathematical Society.