Welcome to my website! I am passionate about a wide array of mathematical topics, from special functions and orthogonal polynomials to mathematical analysis and geometry.  I am currently an Associate Professor at the Department of Mathematics at Universidad Carlos III de Madrid. I am also a member of the Instituto de Ciencias Matemáticas (ICMAT – Institute of Mathematical Sciences). Before, I was Full Professor at the Department of Pure and Applied Mathematics at Universidad Simón Bolívar. 

For over a decade, my research has focused on extending classical approximation theory results to function spaces with Sobolev norms. Recently, I have been exploring the algebraic and analytic properties of special functions like hypergeometric Bernoulli and Euler polynomials, as well as generalized mixed type Bernoulli-Gegenbauer polynomials. Through innovative methods, I have developed practical tools such as operational matrix techniques and quadrature formulae, offering fresh insights into these fascinating mathematical areas.

Another facet of my current research interests is devoted entirely to the study of  molecular graphs by means the determination (when possible) of upper and lower bounds for their corresponding topological indices. Since such bounds allow to establish the approximate range of the topological indices in terms of molecular structural parameters, it is possible to provide a wide range of applications in the setting of fractional calculus.

CONTACT INFORMATION

My office number is 2.2.D.04A, Sabatini building at the UC3M,  Leganés campus.

E-mail: yaquinta[at]math[dot]uc3m[dot]es