Research Lines
Research Lines
A central theme in my research is the following question: given an algebraic structure, can it be realized by a topological space? This problem connects topology with algebra in a deep and constructive way. Together with several collaborators, I have obtained positive answers for a wide variety of algebraic structures, showing that many of them admit faithful realizations within suitable classes of topological spaces.
Pedro J. Chocano, Manuel A. Morón & Francisco R. Ruiz del Portal. Topological realization of groups in Alexandroff spaces. Rev. R. Acad. Cien. Serie A. Mat., 115(25). 2021. (Link)
Pedro J. Chocano, Manuel A. Morón & Francisco R. Ruiz del Portal. On some topological realizations of groups and homomorphisms. Trans. Amer. Math. Soc., 375(12), 8635-8649, 2022. (Link)
Pedro J. Chocano, Realization of finite groups as isometry groups and problems of minimality. Math.Nachr., 298(2):419-426, 2025 (Link)
Pedro J. Chocano, Realizing regular representations of finite groups. J. Algebra, 663: 454-467, 2025. (Link)
Pedro J. Chocano. Every group retraction can be realized as a topological retraction, (Link) 2025.
Pedro J. Chocano. Semiflows deforming automorphisms groups. (Under review).
In this part of my research, we study dynamical systems defined on Alexandroff spaces (finite topological spaces). Our goal is to develop a robust and meaningful notion of dynamical system within this combinatorial framework, allowing us to approximate classical continuous dynamics in a discrete setting. This perspective opens the door to new ways of analysing dynamical behaviour and provides a foundation for developing computational approaches to classical dynamical systems.
Pedro J. Chocano, Manuel A. Morón, D. Mondéjar & Francisco R. Ruiz del Portal. On the triviality of flows in Alexandroff spaces, Topol. Appl. 339 (Part A) 108580, 2023. (Link)
Pedro J. Chocano. On the dynamics of the combinatorial model of the real line. Dynamical Systems, 38 (3), 395-404, 2023. (Link)
Pedro J. Chocano, Manuel A. Morón & Francisco R. Ruiz del Portal. Coincidence theorems for finite topological spaces. Topol. Method Nonl. An., 65(1): 219-263, 2025 (Link).
Pedro J. Chocano. Semiflows on finite spaces. Indag. Math. 2025(Link)
Pedro J. Chocano, Conley Index for Finite Spaces. (In Preparation), 2025.
This part of my research brings together several problems connected through a strong topological perspective. Among the questions I investigate are the combinatorial description of shape theory, generalizations of homotopy for finite spaces, and the reconstruction of compact metric spaces from discrete or combinatorial data. I am also interested in the topological properties of Riordan matrices, as well as in questions related to topological groups and homotopy invariants arising in different settings.
Pedro J. Chocano, Manuel A. Morón & Francisco R. Ruiz del Portal. Computational approximations of compact metric spaces. Phys. D., 433, 133168, 2022. (Link)
Pedro J. Chocano, Ana Luzón, Manuel A. Morón & Luis Felipe Prieto Martínez. Characteristic curves and the exponentiation in the Riordan Lie group: A connection through examples. J . Math. Anal. Appl., 532(1), 127989, 2024. (Link)
Pedro J. Chocano, Manuel A. Morón & Francisco R. Ruiz del Portal. A category to classify compact Hausdorff spaces and finite spaces. Homol. Homotopy Appl., 27 (1), 17-28, 2025 (Link).
Pedro J. Chocano, Manuel A. Morón & Francisco R. Ruiz del Portal. A combinatorial perspective on shape theory. J. Math. Soc. Japan, (Link), 2025.
Pedro J. Chocano. Eigenvalues and signature of quadratic forms associated to finite topological spaces, Linear Algebra Appl., (Link) 2025.
Pedro J. Chocano. A Generalization of homotopy for finite spaces, (Preprint), 2024.
Pedro J. Chocano. Matrix Invariants as Homotopy Invariants in Finite T0-spaces, (Link), 2024.
Pedro J. Chocano. From Samples to Shape: A Finite Approach to Topological Invariants, (Preprint), 2025.
Pedro J. Chocano, Ana Luzón, Manuel A. Morón & Luis Felipe Prieto-Martínez. Riordan pattern's quest within simplicial complexes, (Link), 2025.
Pedro J. Chocano & Luis Felipe Prieto-Martínez. A formula for the Euler characteristic of a poset through the determinant of the order-complement matrix, (Link), 2025.
Tayomara Borsich & Pedro J. Chocano. On the existence and properties of Alexandroff paratopological groups, (Link), 2026.
Tayomara Borsich & Pedro J. Chocano. On continuous isomorphisms from sigma-compact paratopological groups onto topological groups, (Link), 2026.
Classical parametric statistical inference is often based on maximum likelihood estimation, which is optimal under correct model assumptions but highly non‑robust in the presence of outliers or model misspecification. By using divergence measures, we can construct alternative estimators and testing procedures that retain good statistical properties while offering significantly improved robustness across a wide range of models.
E. Castilla. & Pedro J. Chocano. On the choice of the optimal tuning parameter in robust one-shot device testing analysis. Balakrishnan, Gil, Martín, Morales and Pardo (eds.). Trends in Mathematical, Information and Data Sciences. Studies in Systems, Decision and Control. vol 445. Springer, Cham, pp. 169-180, 2023. (Link)
E. Castilla. & Pedro J. Chocano. A new robust approach for multinomial logistic regression with complex design model. IEEE trans. Inf. Theory, 86(11), pp. 7379-7395, 2022. (Link)
E. Castilla & Pedro J. Chocano. Robust copula estimation for one-shot devices with correlated failure modes. (Link)