The research group was created in 2014 and is currently made up of eight PhD in Mathematics, investigating about the following research lines: models of random matrices and orthogonal polynomials; control theory; symmetries of differential equations, both ordinary and partial differential equations; and integrability of distributions.
Some of the members of the group have extensive teaching and research experience, recently incorporating two doctors, whose doctoral theses, led by group members, collect the latest advances in some of the group's research lines.
Among the five members of the group who can get six-year terms of investigation, they accumulate a total of sixteen six-year terms recognized by CENAI. The research activity of the group has generated 143 publications in JCR indexes scientific journals, 30 book chapters from prestigious publishers, 11 books and more than 100 contributions to congresses, mostly international.
The members of the group have jointly directed 16 doctoral theses and numerous final and master's degree works in Mathematics. As a whole, the group has been the beneficiary of a total of 40 grants and R + D + i projects. Currently, there are two projects currently financed by the Ministry of Science and Innovation, Innovation and Universities through the State Program for Generation of Knowledge and Scientific and Technological Strengthening of the R + D + i System, (projects PGC2018-101514-B-I00 and PGC2018-094898-B-I00) in which group members participate as co-principal investigator or as part of the research team.
Integrability of Distributions
Random Matrix Models. Orthogonal Polynomials
Differential Equations Through Symmetry
Control Theory
Symmetries, λ-symmetries, exact solutions, reductions, linearization, first integrals and new techniques to solving partial differential equations and ordinary differential equations. Solvable structures and integrability of distributions.
Characterization of eigenvalue distributions in the Penner and Gross-Witten-Wadia models, phase transitions and electrostatic interpretation. Applications to the determination of the position of the images in gravitational lensing. Existence of separatrices in cosmological models.
Control Theory, switched systems, stabilization and control of these systems, design of stabilizing switching laws and research about conditions under which the stabilization is assured. Development of theory of switched systems applied to real models.