Institutos Universitarios

  1. Portada
  2. Programmes
  3. 2023-present
  4. Interactions of Functional Analysis with Algebra, Geometry and Topology

Interactions of Functional Analysis with Algebra, Geometry and Topology

Brief description

 

This program falls within several interdisciplinary fields within Pure Mathematics. More precisely, Certain linear, non-linear, and geometric aspects of Analysis (such as Geometric Analysis, Differentiability, Geometry of Banach spaces, Lineability and Spaceability, and classical inequalities). Banach Spaces and Lattices, and operators between them. General Operator theory, Chaotic and Hypercyclic Operators. The study of General Topology and Group Theory (Lie groups, semisimple groups, compact groups, Topological abelian groups, among others) via many different techniques from many other areas in Mathematics (such as, for instance, techniques inherited from Functional Analysis).

 

Researchers

  • Juan Benigno Seoane Sepúlveda. Professor (Catedrático), School of Mathematical Sciences (Facultad de CC Matemáticas), UCM (PI)
  • Gustavo Adolfo Muñoz Fernández. Associate Professor (Profesor Titular), School of Mathematical Sciences (Facultad de CC Matemáticas), UCM (PI)

 

External Collaborators

  • Francisco Luis Hernández Rodríguez. Professor (Catedrático), School of Mathematical Sciences (Facultad de CC Matemáticas), UCM 
  • Daniel Luis Rodríguez Vidanes. PhD Teacher Assistant (Contratado Doctor), School of Mathematical Sciences (Facultad de CC Matemáticas), UCM
  • Mar Jimenez Sevilla. Associate Professor (Profesora Titular), School of Mathematical Sciences (Facultad de CC Matemáticas), UCM
  • María Isabel Garrido Carballo. Associate Professor (Profesora Titular), School of Mathematical Sciences (Facultad de CC Matemáticas), UCM
  • Elena Martín Peinador. Honorary Collaborator (Colaboradora Honorífica), School of Mathematical Sciences (Facultad de CC Matemáticas), UCM
  • Juan Ferrera Cuesta. Professor (Catedrático), School of Mathematical Sciences (Faculltad de CC Matemáticas), UCM
  • Vicente Velázquez Muñoz. Researcher (Investigador), School of Mathematical Sciences (Facultad de CC Matemáticas), UCM
  • Otto-Rudwig Campoamor Stursberg. Associate Professor (Profesor Titular), School of Mathematical Sciences (Facultad de CC Matemáticas), UCM

 

Publications

  • R. Campoamor-Stursberg. Polynomial algebra associated to the Cartan subalgebra of G2 in its enveloping algebra. Journal of Physics: Conference Series. 2883 (1). 2024. DOI: 10.1088/1742-6596/2883/1/012003.
  • R. Campoamor-Stursberg, M. Reginatto, D. Schuch. Preface. Journal of Physics: Conference Series. 2883 (1). 2024. DOI: 10.1088/1742-6596/2883/1/011001.
  • R. Campoamor-Stursberg, O. Carballal, F. J. Herranz. A representation-theoretical approach to higher-dimensional Lie–Hamilton systems: The symplectic Lie algebra sp(4,R). Communications in Nonlinear Science and Numerical Simulation. 141. 2025. DOI: 10.1016/j.cnsns.2024.108452
  • R. Monjo, Á. Rodríguez-Abella, R. Campoamor-Stursberg. From colored gravity to electromagnetism. General Relativity and Gravitation, 56. 2024. DOI: 10.1007/s10714-024-03307-8.
  • F. L. Hernández, C. Ruiz, M. Sanchiz. Remarks on weak compactness criteria in variable exponent Lebesgue spaces. Quaestiones Mathematicae, 47 (S1), 195-211. 2024. DOI: 10.2989/16073606.2023.2287839.
  • R. Campoamor-Stursberg, A. Marrani, M. Rausch de Traubenberg. An infinite–rank Lie algebra associated to SL(2, R) and SL(2, R)/U(1). Journal of Mathematical Physics, 65, (8). 2024. 10.1063/5.0223755.
  • S. G. Low, R. Campoamor-Stursberg. Jacobi group symmetry of Hamilton's mechanics. Journal of Geometry and Physics, 203. 2024. 10.1016/j.geomphys.2024.105249.
  • J. Fernández-Sánchez, S. Maghsoudi, D. L. Rodríguez-Vidanes, J. B. Seoane-Sepúlveda. Some properties of differentiable p-adic functions. Revista Matemática Complutense, 37, 391–411. 2024. https://doi.org/10.1007/s13163-023-00458-1.
  • G. da Silva Araújo, L. Bernal González, J. L. Gámez Merino, M. Martínez Gómez, G. A. Muñoz Fernández, D. L. Rodríguez Vidanes, J. B. Seoane Sepúlveda. Real Analysis: An Undergraduate Problem Book for Mathematicians, Applied Scientists, and Engineers. CRC Press, 2024. ISBN: 978-1-032-50461-2.
  • D. Azagra, M. García-Bravo, M. Jiménez-Sevilla. Approximate Morse-Sard type results for non-separable Banach spaces. Journal of Functional Analysis, 287, (4). 2024. DOI: 10.1016/j.jfa.2024.110488.
  • G. Araújo, M. Fenoy, J. Fernández-Sánchez, J. López-Salazar, J. B. Seoane-Sepúlveda, J. M. Vecina. Modes of convergence of random variables and algebraic genericity. Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales - Serie A: Matemáticas, 118 (2). 2024. DOI: 10.1007/s13398-024-01561-8.
  • M. Jiménez-Sevilla, S. Lajara. Operator ranges in Banach spaces with weak star separable dual. Journal of Mathematical Analysis and Applications, 531 (2, part 2). 2024. DOI: 10.1016/j.jmaa.2023.127881.
  • L. Bernal-González, M. C. Calderón-Moderno, G. A. Muñoz-Fernández, D. L. Rodríguez-Vidanes, J. B. Seoane-Sepúlveda. Coneability of Anti-Fubini Functions and Other Lineability Properties. Results in Mathematics, 79 (2). 2024. DOI: 10.1007/s00025-023-02121-z.
  • R. Campoamor-Stursberg, I. Marquette. Decomposition of Enveloping Algebras of Simple Lie Algebras and their Related Polynomial Algebras. Journal of Lie Theory, 34 (1), 17–40. 2024. Link: https://www.heldermann.de/JLT/JLT34/JLT341/jlt34002.htm.
  • J. Ferrera, M. R. Pouryayevali, H. Radmanesh. Local Minimality of Weak Geodesics on Prox-Regular Subsets of Riemannian Manifolds. Mediterranean Journal of Mathematics, 21 (3). 2024. DOI: 10.1007/s00009-024-02648-7.
  • E. Martín-Peinador, X. Domínguez, T. C. Stevens, M. Tkachenko (eds.). Axioms | Special Issue: Advance in Topology and Functional Analysis——In Honour of María Jesús Chasco's 65th Birthday. MDPI, 2024. Link: https://www.mdpi.com/journal/axioms/special_issues/topology_and_functional_analysis.
  • G. Godefroy, M. Moslehian, J. B. Seoane-Sepúlveda (eds.). Proceedings of Symposia in PURE MATHEMATICS. Volume 106: Geometry of Banach Spaces and Related Fields. American Mathematical Society, 2024. ISBN: 978-1-4704-7570-3.
  • G. Muñoz, S. Ruiz, J. Seoane. Geometry of trinomials revisited. In Proceedings of Symposia in PURE MATHEMATICS. Volume 106: Geometry of Banach Spaces and Related Fields, G. Godefroy, M. Moslehian, J. B. Seoane-Sepúlveda (eds.), Chapter 11, American Mathematical Society, 2024. ISBN: 978-1-4704-7570-3.
  • R. Campoamor-Stursberg, D. Latini, I. Marquette, Y-Z. Zhang. Polynomial algebras from commutants: Classical and Quantum aspects of A3. Journal of Physics: Conference Series, 2667 (1). 2023. DOI: 10.1088/1742-6596/2667/1/012037.
  • E. Fernández-Saiz, R. Campoamor-Stursberg, F. J. Herranz. Generalized time-dependent SIS Hamiltonian models: Exact solutions and quantum deformations. Journal of Physics: Conference Series, 2667 (1). 2024. DOI: 10.1088/1742-6596/2667/1/012083.
  • R. Campoamor-Stursberg, E. Fernández-Saiz, F. J. Herranz. Exact solutions and superposition rules for Hamiltonian systems generalizing time-dependent SIS epidemic models with stochastic fluctuations. AIMS Mathematics, 8 (10), 24025-24052. 2023. DOI: 10.3934/math.20231225.
  • M. Isabel Garrido, A. S. Meroño. A result concerning the Lipschitz realcompactification of the product of two metric spaces. Topology and its Applications, 339, part A. 2023. DOI: 10.1016/j.topol.2023.108585.
  • G. Beer, M. Isabel Garrido. Reciprocation and Pointwise Product in Vector Lattices of Functions. In IMFACO 2022: Functional Analysis and Continuous Optimization, J. M. Amigó, M. J. Cánovas, M. A. López-Cerdá, M. López-Pellicer (eds.), pp. 65-85, Springer, 2023. ISBN: 978-3-031-30013-4. DOI: 10.1007/978-3-031-30014-1_3.
  • R. Campoamor-Stursberg, D. Latini, I. Marquette, Y.-Z Zhang. Polynomial algebras from Lie algebra reduction chains g ⊃ g′. Annals of Physics, 459. 2023 DOI: 10.1016/j.aop.2023.169496.
  • M. Jiménez-Sevilla, S. Lajara. Quasicomplemented Subspaces of Banach Spaces and Separable Quotients. Results in Mathematics. 2023, 78 (6), art. no. 244. DOI: 10.1007/s00025-023-02022-1.
  • R. Monjo, R. Campoamor-Stursberg. Geometric perspective for explaining Hubble tension: theoretical and observational aspects. Classical and Quantum Gravity, 40 (19). 2023. https://doi.org/10.1088/1361-6382/aceacc
  • R. Campoamor-Stursberg, F. O. García. Construction of Rank-One Solvable Rigid Lie Algebras with Nilradicals of a Decreasing Nilpotence Index. Axioms, 12 (8), article No. 754. 2023. https://doi.org/10.3390/axioms12080754
  • M. J. Chasco and E. Martín-Peinador. Bounded Duality in Topological Abelian Groups. In Functional Analysis and Continuous Optimization. Editors: José M. Amigó, María J. Cánovas, Marco A. López-Cerdá, Manuel López-Pellicer. Springer-Verlag, 2023. 113-121. https://doi.org/10.1007/978-3-031-30014-1_5
  • L. Bernal-González, J. L. Gámez-Merino, G. A. Muñoz-Fernández, V. M. Sánchez-de los Reyes, J. B. Seoane-Sepúlveda. Análisis de variable real, Paraninfo, 2023. ISBN: 978-84-283-6246-7

  • J. Ferrer, D. García, M. Maestre, G. A. Muñoz, D. L. Rodríguez, J. B. Seoane. Geometry of the Unit Sphere in Polynomial Spaces. Springer. 2023. ISBN: 978-3-031-23675-4


  • M. Jiménez-Sevilla, S. Lajara. Operator ranges and endomorphisms with a prescribed behaviour on Banach spaces. Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM, 2023, 117, no. 1, Paper No. 33, 29 pp. https://doi.org/10.1007/s13398-022-01368-5