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.
- 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.
- C. García-Azpeitia. Traveling and standing waves in coupled pendula and Newtons 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.