__Institute of Mathematical Sciences____ (ICMAT)__ is a joint research center of the Consejo Superior de Investigaciones Científicas – CSIC (Spanish National Research Council) and three Madrid universities: the Universidad Autónoma de Madrid (UAM), the Universidad Carlos III de Madrid (UC3M), and the Universidad Complutense de Madrid (UCM). The ICMAT is located on the UAM Campus in Madrid, its facilities are exceptional in the field of mathematical research. Its goal is to generate knowledge in all the areas of mathematics, particularly in Algebraic Geometry, Mathematical Physics, Differential Geometry, Geometric Mechanics, Mathematical Analysis, Differential Equations and Applications, Number Theory, Group theory, Statistics, Probability, Operations Research and Mathematics of Quantum Information.

Research groups are divided in three main areas: Algebraic Geometry, Mathematical Analysis and Differential Equations, and Applied Mathematics.

Research proposals shall cover the following lines:

** Algebra and Geometry.** The main lines can be grouped in:

– **Algebraic Geometry and Mathematical Physics.** Moduli spaces of vector bundles involving techniques from algebraic geometry, differential geometry, topology, Lie theory, geometric analysis and theoretical physics.

**– Differential Geometry, Symplectic Geometry and Geometric Mechanics.** Differential and contact topology, differential and riemannian geometry, geometric mechanics with applications to control theory, dynamical systems and the geometry of PDEs.

**– Group Theory.** Several areas of group theory with applications to other fields, such as ring theory, topology, dynamics, and logic.

**– Arithmetic Geometry:** The research in this line is devoted to problems at the core of arithmetic geometry, like the equivariant Tamagawa number conjecture or the development of Arakelov geometry, as well as its interplay with related fields like complex and non-Archimedean analysis, algebraic geometry and even theoretical physics.

** Mathematical Analysis and Differential equations.** With two sublines:

–**Mathematical Analysis.** Classical problems around the Kakeya conjecture and Bochner-Riesz multipliers, the Schrödinger and wave equations, elliptic PDE in rough domains and connections with geometric measure theory, harmonic analysis and geometric group theory for nonamenable groups, classical and abstract Calderón-Zygmund theory and problems around the invariant subspace problem. Other fields such as operator theory, geometry of Banach spaces, complex analysis, quantum probability and analytic number theory are also well represented.

**-Differential Equations and Applications.** Differential equations arising in fluid mechanics, spectral theory, mathematical physics and mathematical biology. This is an interdisciplinary subject, with significant applications to engineering, biology and physics.

__Applied Mathematics.__** **With the following research lines:

–**Mathematics of Quantum Information Theory.** Quantum technologies are nowadays one of the most promising technologies for the near future. They exploit quantum effects to develop new techniques in fields like cryptography, metrology, material science, pharmacology and many others, which have the potential to go far beyond the current (classical) state of the art. The group «Mathematics and Quantum Information» at ICMAT works in a wide variety of mathematical problems which are motivated by quantum technologies. Some of the topics considered in this line are: condense matter and many body systems, quantum control, foundational aspects of quantum mechanics and the theory of operator algebras.

**– Machine Learning and Data Science.** Machine learning and Data Science are disciplines that are at the core of many current significant societal developments. Embedded in the disciplines of Statistics, Probability, Optimization and Algebra, with strong support from Computer Science developments, this line emphasizes, methodological developments focusing on providing efficient Bayesian approaches to the treatment of large scale inference and prediction problems and methods to deal with the presence of adversaries ready to perturb the data and structure in a problem though adversarial risk analysis and adversarial machine learning. Moreover, it also emphasizes dealing with complex applied problems mainly in the areas of security and cybersecurity, with the aid of its DataLab. In particular, and with respect to the COVID-19, this group has been working with the tracking of fake news.

**– Mathematical Modelling and Simulation.** This covers a wide spectrum ranging from the multidisciplinary mathematical approach to the problems, with emphasis in numerical computation, to the promotion of applications by means of collaborations with other departments such as engineering, biology, physics and earth sciences all around the world. Research include topics such as microfluidics modelling and technological applications, geophysical fluid dynamics, etc..

Copyright © Mujeres por África 2024