IKERBASQUE Research Associate at BCAM
I work on inverse problems arising in PDEs, especially these with an analytical flavour. I am very interested in problems of regularity which require tools from harmonic and microlocal analysis. Recently, I have also got interested in problems where there is a specific uncertainty which is modelled by random fields.
PhD Student at BCAM
I am working on harmonic analysis topics. My research interests focus on weighted inequalities, Poincaré-type inequalities, fractional Poincaré-Sobolev inequalities and BMO spaces.
Postdoctoral researcher at BCAM
My primary research focus lies in the analysis of partial differential equations (PDE). Specifically, I am interested in the following areas of research:
On Functional Inequalities: Functional inequalities such as Hardy-Sobolev inequality, Hardy-Rellich inequality, logarithmic Sobolev inequality, serve as a major tool in partial differential equations, operator theory, and mathematical physics. I am interested in the following aspects on these functional inequalities: (a) Characterizing (or identifying) admissible space of weight functions, (b) Existence of minimizer associated with these functional inequalities, (c) Quantitative stability of functional inequalities.
Extremum problems associated to the eigenvalues of elliptic operators: Such problems are related to the Shape optimization problems. One can derive crucial information of a mathematical model of certain physical phenomena by studying an appropriate optimization problem related to the eigenvalues of the underlying elliptic operators. Hence the existence of optimizers is a natural question that arises in investigating such models. Also, it is important and interesting to analyze the qualitative properties of the optimizers of these optimization problems when they exist.
Analysis on discrete graphs: I am also interested in studying functional inequalities and certain unique continuation results in the discrete settings.
Marie Curie Postdoctoral Fellow at BCAM
My research lies broadly in the interaction of harmonic analysis and dispersive PDEs. I am particularly interested in problems that are motivated by physical phenomena like turbulence and optics. I have lately been thinking on:
Rigorously formalizing properties observed in fluid and wave turbulence, like multifractality and intermittency.
Derivation of kinetic equations from the corresponding microscopic model (like wave kinetic equations from NLS type equations).
Probabilistic approaches to tackle the questions above and other classical problems in harmonic analysis like the Carleson convergence problem for dispersive equations.
The Talbot effect, its formalization and physical interpretations.
PhD Student at BCAM
I am working on harmonic analysis. In particular, I am interested in the theory of singular integrals, directional singular integrals, square functions, and time-frequency analysis.
IKERBASQUE Research Associate at BCAM
My research interests mainly lie in the analysis of partial differential equations, with a special focus on models describing fluid dynamics. From a general perspective, I aim to capture effects due to large heterogeneities and lack of regularity.
I study questions linked with well-posedness of the models and asymptotic behaviour of solutions, especially singular perturbation problems and multiscale analysis.
Postdoctoral Researcher at BCAM
My research focuses on the regularity of weak solutions to differential equations arising from fluid mechanics, as well as the characterization of potential singularities. A particular emphasis is placed on the decomposition of the pressure term, which is non-local for the Navier-Stokes equations.
PhD student at BCAM
I am working with Luz Roncal in the analysis of PDEs on graphs. In particular, we look for Hardy uncertainty principles for functions over graphs, for which we study uniqueness properties for the Schrödinger equation with the graph Laplacian. My interests range from functional analysis, PDEs and geometry, to some questions in mathematical physics.
PhD Student at BCAM
I am working on harmonic analysis topics, in particular generalised Poincaré inequalities with Carlos Pérez Moreno and interpolation formulas with Mateus Sousa.
Postdoc at BCAM
I am a postdoctoral researcher working under the supervision of Dr. Luz Roncal and Dr. Mateus Sousa. My research focuses on harmonic analysis and partial differential equations, with particular interest in their interactions and their connections to geometry and probability. I investigate how classical results can be reformulated and how new phenomena arise when equations involve non-local diffusive operators and/or they are set in hyperbolic space.
Postdoctoral researcher at BCAM
I work on nonlinear effects in mechanics of solids. My master thesis was related to contact problem emerged in simulation of assembly of aircrafts and my PhD thesis was about simulation of wrinkles in bacterial biofilms. My research interests are:
Functional analysis
Nonlinear PDEs
Finite element method
Optimization methods
Phd. student at BCAM
I am a first-year Ph.D. student at BCAM, under the supervision Dr. Mateus Sousa. My research interests span across Harmonic Analysis, Complex Analysis, Geometric Measure Theory and several related subjects with applications and interactions with other branches of mathematics either applied or pure.
PhD Student at BCAM
I am a first-year Ph.D. student at the Basque Center for Applied Mathematics, under the supervision of Professor Luz Roncal and Professor Mateus Sousa. My research interests include Harmonic Analysis, Functional Inequalities, and Partial Differential Equations.
PhD Student at BCAM
Many problems in PDEs can be attacked introducing a suitable probability on the solutions space (for instance Gibbs measures). I am interested in the implementation of this statistical approach to the study of the pointwise behavior of dispersive PDEs. More specifically, in the context of nonlinear wave models, I study the almost everywhere pointwise convergence of the solutions to the initial data, as time goes to zero, namely the nonlinear/probabilistic version of the celebrated Carleson problem.
Postdoc fellow at at BCAM
I am interested in fluid mechanics in general, investigating issues such as existence, regularity, time-periodicity.
Lately I've been working on the fluid-structure interaction, studying fluids that interact with elastic membranes.
PhD Student at BCAM
My research interests lie in between Calculus of Variation and PDEs, with applications to physical models. At the moment I am studying the propagation of a light beam through a liquid crystal. I am also interested in Geometric Measure Theory and analysis on Manifolds
Postdoctoral researcher at BCAM
My research focuses on problems from harmonic analysis and geometric measure theory. In particular, I like those that lie within the limit of these two areas. Currently, I am interested in Poincaré trace inequalities and the improving behavior of self-similar measures in Lebesgue spaces.
PhD Student at BCAM
I'm working between the areas of harmonic analysis and PDEs. More specifically, I apply analytical tools to the study of changes in the topology of the flux lines over time of the solutions to Navier-Stokes and MHD equations, i.e. vortex reconnection and magnetic reconnection, respectively. I also study well-posedness for these equations.
Post-doctoral researcher at BCAM
In my PhD I worked on improving multilinear inequalities for the extension operator, which is the Fourier transform of a measure supported on a manifold. Currently, I am interested in inverse problems.
PhD student at BCAM
My research interests concerns the applications of operator algebras in quantum statistical mechanics, in particular to the theory of first order phase transitions in quantum systems.
IKERBASQUE Research Associate and Ramón y Cajal fellow
My research concerns problems from harmonic analysis and partial differential equations.
In particular, my most recent interests include spherical means, square functions, directional operators, analysis in the infinite torus, analysis in the Heisenberg group, non-local equations, and unique continuation.
IKERBASQUE Research Fellow and Ramón y Cajal fellow
My research deals with the problems from nonlinear partial differential equations relating to fluid mechanics, control theory, liquid crystals and porous media. In particular, my research focuses on the mathematical analysis (existence, uniqueness, singular limits and long time behaviour of the solutions) and control aspects (controllability, stabilizability) of fluid-structure interaction problems.
Ramón y Cajal Fellow at BCAM
I am broadly interested in mathematical analysis, especially topics in harmonic analysis. My interests include sharp inequalities, regularity of maximal operators and the restriction theory of the Fourier transform, uncertainty principles, Fourier interpolation formulas and related topics.
Postdoctoral fellow at BCAM
My research interests lie in harmonic analysis and their applications to the dispersive equations. Especially, I study the dispersive, Strichartz, and resolvent estimates associated with Schrödinger operator with potential. And I combine these estimates and harmonic analysis tools to study the well-posedness, scattering theory and blow-up dynamics for the nonlinear dispersive equations.
IKERBASQUE research professor at BCAM
Current research is concerned with the analytical study of physically motivated systems of partial differential equations. So far it has concentrated on several major directions:
The Q-tensor theory describing liquid crystals
Models describing complex non-Newtonian fluids
Aspects of classical Newtonian fluids
Visitor PhD at BCAM
I am working on harmonic analysis. In particular, I am interested in
the topic of weighted inequalities, commutators of singular integrals and spherical means.