Святой Б

My scientific trajectory from 1989 to the present has been framed within the field of Applied Computational Topology. In 1989, I was awarded a Spanish research training grant (FPI) at the Department of Algebra, Computation, Geometry, and Topology at the University of Seville. In 1993, I obtained my Ph.D. in Mathematics from the same university with the dissertation Effective Homology of Classifying Spaces, under the supervision of Professor Francis Sergeraert (Université de Grenoble I).

My first international publications include:

Real, P. (1996). On the computability of the Steenrod squares. Annali dell’Università di Ferrara.

Real, P. (1996). An algorithm for computing homotopy groups. Mathematics and Computers in Simulation.

From 1997 to 2016, I was the founder and director of the FQM-296: Computational Topology and Applied Mathematics research group (PAIDI). During this period, several significant advances were achieved, including:

The development, in collaboration with Ph.D. students, of new homological computation algorithms, based on the seminal paper Real, P. (2000). Homological Perturbation Theory and Associativity. Homology, Homotopy and Applications.

The AT-model representation of a cell complex, co-developed with Dr. Rocío González-Díaz.

The purely combinatorial descriptions of the AT-model in terms of graphs, and, in collaboration with Dr. Helena Molina-Abril, the creation of the Homological Spanning Forest (HSF) model for the representation of nD digital objects.

Since 2016, I have been the director of the TIC-245: Topological Pattern Analysis, Recognition and Learning (PAIDI) research group. During this period, my main research contributions have been:

Significant algorithmic advances in connected-component labeling and topological representation, analysis, and recognition of nD binary and color digital images.

The development of a topological scale-space framework for data analysis, called Boundary Scale Theory, which introduces novel topological descriptors that depend exclusively on the chosen connectivity relation of the data.

The Hom-Tree representation for 3D digital volumes, which generalizes the classical notion of the Adjacency Tree.

Throughout my career, I have accumulated 30 years of positive research evaluation, with five consecutive six-year research periods recognized by the Spanish National Commission (CNEAI). I have supervised or co-supervised 13 Ph.D. dissertations (9 women, 4 men), as well as 3 Andalusian research training scholarships. Additionally, I have led multiple research projects and R&D&I contracts, all related to Applied Computational Topology.

Currently, I am a member of the Institute of Informatics Engineering of the University of Seville (I3US) and a professor in the Department of Applied Mathematics I at the University of Seville, where I teach courses in Informatics and Biomedical Engineering.