Intro SO 2021 – Topics proposed by researchers ICMAT

Javier Aramayona (ICMAT-CSIC): Hyperbolic structures on manifolds.

Jose María Arrieta (ICMAT-UCM): Large time behavior of solutions of Differential Equations

Nuno Ricardo Barroso Freitas (ICMAT-CSIC): Public key cryptography with elliptic curves

Mateo Bonforte (ICMAT-UAM):

1. Introduction to the theory of Nonlinear Diffusion: Parabolic PDEs of degenerate and singular type, both in the local and nonlocal frameworks.
2. Entropy Methods for Nonlinear Diffusion Equations: a bridge between asymptotic behaviour of solutions, functional inequalities and geometry.

Ana Bravo Zarza (ICMAT-UAM): Calculating examples of Samuel functions.

Diego Córdoba (ICMAT-CSIC): Incompressible fluids.

Manuel de León (ICMAT-CSIC):

1. Hamiltonian contact systems: Theory and applications.
2. Groupoids: applications to theories of growth, remodeling, aging and morphogenesis.

Alberto Enciso (ICMAT-CSIC): Mathematical problems in fluid mechanics.

Oscar García Prada (ICMAT-CSIC):

1. Introduction to moduli spaces: Higgs bundles.
2. Introduction to moduli spaces: Character varieties.

Eva Gallardo Gutierrez (ICMAT-UCM): The shift operator on Hardy spaces: invariant subspaces.

Maria del Mar González (ICMAT-UAM):

1. From the wave equation to optical geometry.
2. A non-local notion of perimeter. Minimal surfaces.

Alberto Ibort Latre (ICMAT-UC3M): Introduction to the theory of groupoids, algebras and applications.

Andrei Jaikin Zapirain (ICMAT-UAM):

1. Golod-Shafarevich groups and algebras.
2. Introduction to carácter theory and Burnside’s (p,q)-theorem.
3. Domains and subrings of división rings.
4. The Hanna Neumann problem.
5. Parafree groups.
6. The isomorphism problema for group-rings. El problema de isomorfismo de anillos de grupo.
7. Weyl algebras.
8. The Atiyah conjecture.

Fernando Lledó Macau (ICMAT-UC3M):

1. Coarse geometry and operator algebras.
2. Mathematical structure of quantum physics.

David Martín de Diego (ICMAT-CSIC):

1. Discrete differential Geometry and applications.
2. Differential geometry methods in machine learning applications.

Maria Medina de la Torre (ICMAT-UAM): Equivalence of solutions in non-linear elliptic PDEs. Classical and fractional cases.

Jesús Munarriz (ICMAT-UAM):

1. Inequalities, maximal and of other types.
2. Bernstein polynomials and generalisations.

Daniel Peralta (ICMAT, CSIC):

1. Introduction to spectral geometry.
2. Geometry and fluid mechanics.

Aníbal Rodríguez Bernal (ICMAT-UCM):

1. Fourier Series, Fourier Transform and Partial Differential Equations.
2. Dynamical complexity and dimension.

Daniel Seco (ICMAT-CSIC):

1. Invariant spaces in complex analysis.
2. Cyclic functions.

Pedro Tradacete (ICMAT-CSIC):

1. Positivity in Operator Theory.
2. Free Banach Lattices.