Fourier Analysis and Partial Differential Equations Research groups

The project covers a wide scope ranging from theoretical aspects of Fourier or Harmonic Analysis (Uncertainty principle, Singular Integrals) to Geometric Measure Theory (Harmonic Measure) or Quantum Mechanics (Many-body system, Dirac equation) and passing from Analysis of Partial of Differential Equations (Control theory, Unique continuation) as well as more applied aspects like Numerical Analysis of problems from fluid mechanics. Being more precise we propose to study the following topics:

(A) Mathematical Physics
1) Mathematics of Quantum Many-Body Systems.
2) Dirac Equation3) Vortex Filament Equation
4) Kinetic equations5) Navier Stokes equations with Navier or Navier type boundary conditions

(B) Analysis of Partial Differential Equations
1) Unique continuation properties related to Uncertainty Principles
2) Control Theory and Unique continuation

(C) Numerical Analysis
1) Pseudo-spectral methods for nonlocal operators
2) Pseudo-spectral methods for the shallow water equation
3) Hermite spectral methods

(D) Harmonic Analysis
1) Operators on weighted Morrey spaces
2) Harmonic measure for second order elliptic operators and rectifiability
3) Poincaré Inequalities for general measures and geometry.
4) Singular integrals and the A1 log A1 conjecture.