The research of this group is divided into four main lines. The first one concerns different aspects of differential topology, as Engel structures, foliations and extensions of h-principle, as well as contact topology, specifically groups of contactomorphisms, Legendrian submanifolds and higher dimensional problems. The second one is focused on differential and Riemannian geometry, in particular on spectral problems, Poisson and symplectic geometry, field theories, Kahler geometry, geometric analysis and geometric theory of information.

Mathematical Analysis is a very active field of research that places itself in a fundamental position within the mathematical sciences. Mathematical Analysis has many different branches and turns out to be fundamental in the understanding of several problems in the fields of combinatorics, complex variables, differential geometry, functional analysis, geometric group theory, geometric measure theory, harmonic analysis, metric geometry, operator theory, operator algebras, partial differential equations and probability (among others).

The group of Differential Equations and Applications is deeply involved both with theory and its use in fluid mechanics, mathematical physics and mathematical biology. The members of the group cover a wide spectrum ranging from the multidisciplinar mathematical approach to the problems to the promotion of applications by means of collaborations with other departments such as engineering, biology, physics and earth sciences. The research carried out in the group is closely related with that of the group on Mathematical Analysis.

One of the features of number theory is the interplay of a great variety of mathematical techniques, including combinatorics, representation theory, harmonic analysis, probability theory, algebraic geometry, motives, p-adic and complex analytic geometry or ergodic theory, all of them applied to solve arithmetic problems. The Number Theory group works on several problems in analytic, combinatorial and algebraic number theory and in arithmetic geometry.

Our research revolves around combinatorial, geometric, and algebraic properties of finite and infinite groups, often viewed through the spaces upon which they act. As such, we are framed within IMCAT's "Algebra and Geometry" research group. Some of our particular research lines include: asymptotic, combinatorial and geometric group theory; groups acting on trees; profinite groups; Artin-Tits groups; mapping class groups; order able groups, and representation theory. The group hosts several early-career researchers (Ayudante Doctor and postdocs) as well as several graduate students.

The main aspects addressed in the research are: - Mechanisms of reinforcement corrosion and physic-chemical attack to concrete - Life cycle of structural concrete and performance evolution - Numerical simulation and laboratory validation - Non destructive techniques and on-site monitoring of deterioration through embedded sensors. - Evaluation of deteriorated structures - Rehabilitation, industrialization and standardization - Sustainability and evaluation of innovation

The research group ISCMA was created in the year 2002 and currently consists of 7 people: a research scientist, a scientific holder, 1 hired researcher in the Ramon y Cajal Spanish program, 1 predoctoral fellow and 3 hired It is a young group, dynamic and enthusiastic with multidisciplinary spirit (2 Dr. Chemical sciences, 1 Dr. Mechanical and Materials Engineer, 1 Bachelor in environmental science, 1 arquitect, 1 Industrial engineer and a technical analysis and control).

Group of multidisciplinary profile, highlights its experience in topics in which converges science-technology-engineering aimed at the construction sector, relying mainly on the risk-safety binomial. Its activity is developed from an analytical, numerical and experimental aspect. Long career path in cooperation with industry and the university to achieve its objectives in research, training and transfer.

Development and application of analytical methodologies for assessment of the presence, fate and impact of organic contaminants, especially emerging contaminants, in the aquatic and terrestrial environment. KEY resources required in 2019-2021: - 3 Titular Scientists - 2 Laboratory Technicians Positioning within the three global areas (SOCIETY, LIFE, MATTER) in their intersection S-V-M. Interest in new Interdisciplinary Thematic Platforms : PTI15-AG2BIO, PTI22, PTI2-SUSPLAST, PTI5-SOILBIO, PTI14-POLARCSIC. Collaboration in open science initiatives: Science Week, Open Door Days.

Study of natural organic matter and contaminants as a source of knowledge of the evolution of ecosystems, including climate change and transport processes, distribution, transformation and effects of organic pollution in organisms and humans