Intro SO 2022 – Topics proposed by researchers ICMAT

Makrina Agaoglou (ICMAT-CSIC): Chaotic Transport and mixing in Hamiltonian models of Fluids. (only in English)

Yago Antolín (ICMAT-UCM): Complexity of orders of orderable groups.

Jose María Arrieta (ICMAT-UCM): Large-time behaviour of solutions of differential equations.

Nuno Ricardo Freitas (ICMAT-CSIC):

  1. Public-key cryptography with elliptic curves.
  2. The local-global principle.

Mateo Bonforte (ICMAT-UAM):

  1. Introduction to Nonlinear Diffusion: Parabolic PDEs of degenerate and singular type, both in the local and nonlocal framework.
  2. Entropy Methods for Nonlinear Diffusion Equations: a bridge between long time asymptotics, functional inequalities and geometry.

Florentino Borondo (ICMAT-UAM), Laia Domingo Colomer (ICMAT-UAM): Integration of PDEs using reservoir computing.

Ana Bravo Zarza (ICMAT-UAM): Singularities and differential operators.

Caterina Campagnolo (ICMAT-UAM):

  1. Cup products in bounded cohomology. (only in English)
  2. Quasimorphisms and bounded cohomology. (only in English)

Ángel Castro (ICMAT-CSIC): Bressan’s problem.

Diego Córdoba (ICMAT-CSIC): Incompressible fluids.

Manuel de León (ICMAT-CSIC):

  1. Geometry of morphogenesis in materials.
  2. Contact hamiltonian systems.

Daniel Faraco (ICMAT-UAM):

  1. Hydrodynamics. Turbulent solutions.
  2. Inverse problems in electromagnetism.

Dominik Francoeur (ICMAT-CSIC): Groups of intermediate growth. (only in English)

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

Oscar García Prada (ICMAT-CSIC):

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

Maria del Mar González (ICMAT-UAM):

  1. The Willmore functional, geometry, modelling and optics.
  2. Optimal transport and geometric optics.

Ángel González Prieto (ICMAT-UCM):

  1. Topological quantum field theories.
  2. Introduction to the geometry of moduli spaces of representations.

Luis Guijarro (ICMAT-UAM):

  1. Subriemannian geometry.
  2. Geodesic flows.

Fernando Lledó Macau (ICMAT-UC3M):

  1. Mathematical structure of quantum physics.
  2. Groupoids.

Ignacio Luengo (ICMAT-UCM): Post-quantum cryptography.

Daniel Macías Castillo (ICMAT-UAM):

  1. Structure of Modell-Weil Galois groups.
  2. The Rubin-Stark conjecture.

Leo Margolis (ICMAT-CSIC):

  1. Units in group rings.
  2. Coset partitions of groups.

David Martín de Diego (ICMAT-CSIC): Symplectic optimization and Lie group theory with applications to machine learning.

Jesús Munarriz (ICMAT-UAM):

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

Daniel Peralta (ICMAT, CSIC): Introduction to geometric theory of dynamical systems.

David Ríos Insua (ICMAT-CSIC):

  1. Adversarial Machine Learning (AML).
  2. Applications of data science to banking.

Aníbal Rodríguez (ICMAT-UCM):

  1. Fourier series, Fourier transform and PDEs.
  2. Dynamical complexity and dimension.

Daniel Seco (ICMAT-UC3M):

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

Pedro Tradacete (ICMAT-CSIC):

  1. – Doubling constants in metric spaces and graphs.
  2. – Positivity in Operator Theory.

Ignacio Villanueva (ICMAT-UCM):

  1. Valuations, intrinsic volumes and Hadwiger’s Theorem.
  2. Transformers and convolutional neural networks.