Mathematical Analyis
Scientific Sectors
- SSD: MAT/05 Mathematical Analysis.
- ERC: PE1_6 Topology, PE1_8 Analysis, PE1_9 Operator algebras and functional analysis, PE1_10 ODE and dynamical systems, PE1_11 Theoretical aspects of partial differential equations, PE1_19 Control theory and optimisation, PE1_20 Application of mathematics in sciences, PE6_11 Machine learning, statistical data processing and applications using signal processing, PE7_7 Signal processing.
Research Topics
- Analysis of minimal surfaces, mean curvature flows, and harmonic maps.
- Asymptotic analysis and Γ-convergence theory.
- Free boundary problems.
- Shape optimization and spectral theory.
- Boundary value problems in ordinary differential equations.
- Complex solutions in Celestial Mechanics, Hamiltonian partial differential equations, and the N-body problem.
- Global geometrical and topological properties of partial differential equations.
- Pattern formation in reaction-diffusion systems, phase separation, and optimal partition problems.
- Perturbative aspects of nonlinear differential problems.
- Well-posedness of the Cauchy problem for hyperbolic systems.
- Analysis on manifolds.
- Fourier analysis and signal processing.
- Microlocal analysis for linear and nonlinear operators.
- Pseudo-differential operators, Fourier integral operators, and spectral analysis.
- Time-frequency analysis, localisation operators, and uncertainty principles.
Research Groups