Research
My research interests are divided into two themes:
Nonlinear Functional Analysis:
Topological Degree Theory
Bifurcation Theory
Nonlinear Spectral Theory
Nonlinear Elliptic & Parabolic Partial Differential Equations
Applications to Spatial Ecology, Population Dynamics and Dispersive Waves.
Real and Harmonic Analysis:
Measures on Infinite Dimensional Spaces
Projective Limits of Probability Measures
Wiener Measure on Riemannian Manifolds
Path Integrals and conections with Constructive Quantum Field Theory
Published Articles
J. López-Gómez and J. C. Sampedro.
Bifurcation Theory for Fredholm Operators.
Journal of Differential Equations, Volume 404, (2024).
DOI: doi.org/10.1016/j.jde.2024.05.040
J. C. Sampedro.
On the L^p-spaces of Projective Limits of Probability Measures
Journal of Theoretical Probability, (2024).
DOI: doi.org/10.1007/s10959-024-01329-1
J. C. Sampedro.
On the colimits of certain Sobolev spaces,
Journal of Mathematical Analysis and Applications, Volume 535, Issue 2, (2024).
DOI: doi.org/10.1016/j.jmaa.2024.128141
J. C. Sampedro.
Existence of infinite product measures,
Real Analysis Exchange, Volume 42, (2023).
DOI: doi.org/10.14321/realanalexch.48.2.1643257005
J. López-Gómez and J. C. Sampedro.
Orientability through the algebraic multiplicity,
Journal of Fixed Point Theory and Applications, Volume 25, (2023).
DOI: doi.org/10.1007/s11784-023-01062-y
G. Feltrin, J. C. Sampedro and F. Zanolin.
Periodic solutions to superlinear indefinite planar systems: a topological degree approach,
Journal of Differential Equations, Volume 363, (2023).
DOI: doi.org/10.1016/j.jde.2023.03.042
J. López-Gómez and J. C. Sampedro.
Generating loops and isolas in semilinear elliptic BVP’s,
Nonlinear Analysis, Volume 232, 113268 (2023).
DOI: doi.org/10.1016/j.na.2023.113268
J. C. Sampedro.
Approximation schemes for path integration on Riemannian manifolds,
Journal of Mathematical Analysis and Applications,
Volume 512, Issue 2 (2022).
DOI: doi.org/10.1016/j.jmaa.2022.126176
J. López-Gómez and J. C. Sampedro.
Axiomatization of the degree of Fitzpatrick, Pejsachowicz and Rabier,
Journal of Fixed Point Theory and Applications, Volume 24, Number 8 (2022).
DOI: doi.org/10.1007/s11784-021-00916-7
J. López-Gómez and J. C. Sampedro.
New analytical and geometrical aspects of the algebraic multiplicity,
Journal of Mathematical Analysis and Applications, Volume 504, Issue 1 (2021).
DOI: doi.org/10.1016/j.jmaa.2021.125375
J. López-Gómez and J. C. Sampedro.
Global perturbation of nonlinear eigenvalues,
Advanced Nonlinear Studies, Volume 21, Issue 2 (2021), 229-249.
DOI: doi.org/10.1515/ans-2021-2127
J. López-Gómez and J. C. Sampedro.
Algebraic multiplicity and topological degree for Fredholm operators,
Nonlinear Analysis, Volume 201, 112019 (2020).
DOI: doi.org/10.1016/j.na.2020.112019
J. C. Sampedro.
On the space of infinite dimensional integrable functions,
Journal of Mathematical Analysis and Applications, Volume 488, Issue 1 (2020).
DOI: doi.org/10.1016/j.jmaa.2020.124043
J. C. Sampedro.
Some identities involving Inverse Gamma integrals,
The Ramanujan Journal, Volume 48, (2019), 577–583.
DOI: doi.org/10.1007/s11139-018-0082-z
J. C. Sampedro.
On a new constant related to Euler’s constant,
The Ramanujan Journal, Volume 46, (2018), 77–89.
DOI: doi.org/10.1007/s11139-017-9912-7
J. C. Sampedro.
Some unit square integrals,
The Ramanujan Journal, Volume 40, (2016), 541–555.
Submitted Papers
J. C. Sampedro.
Periodic solutions to nonlocal pseudo-differential equations. A bifurcation theoretical perspective, Submitted.
ArXiv: arxiv.org/abs/2409.04253v1
J. López-Gómez and J. C. Sampedro.
Blow-up estimates and a priori bounds for the positive solutions of a class of superlinear indefinite elliptic problems, Submitted.
ArXiv: arxiv.org/abs/2402.01519
Research Stays
July 2023
Research Stay at Università degli Studi di Palermo.
Under the supervision of Professor Francesca Dalbono. (Palermo, Italy)
November 2022 - May 2023
Research Stay at BCAM (Basque Center for Applied Mathematics).
Under the supervision of Professor Luis Vega. (Bilbao, Spain)
September 2022
Invited Stay at Swansea University (Prifysgol Abertawe).
Under the supervision of Professor Elaine Crooks. (Swansea, United Kingdom)
May 2022
Invited Stay at Dipartimento di Scienze Matematiche, Politecnico Turin.
Under the supervision of Professor Jacobo Pejsachowicz. (Turin, Italy)
April 2022 - July 2022
Research Stay at Dipartimento di Scienze Matematiche, Informatiche e Fisiche of the Universit‘a degli Studi di Udine.
Under the supervision of Professors Fabio Zanolin and Guglielmo Feltrin. (Udine, Italy)
Research Projects
2022 - Present.
Project PID2021-123343NB-I00: Ecuaciones Diferenciales Heterogéneas: Dinámica y Numérico,
PI: Julián López-Gómez,
Ministerio de Ciencia, innovación y universidades, Gobierno de España.
2019 - 2022.
Project PGC2018-097104-B-I00: Sistemas de Reacción Difusión,
PI: Julián López- Gómez,
Ministerio de Ciencia, innovación y universidades, Gobierno de España.
Research Institutions & Groups
2024 - Present
Research Group: Análisis Matemático y Aplicaciones (A.M.A)
PI: Dolores Barrios Rolanía
Universidad Politécnica de Madrid (UPM).
2022 - Present.
Research Group: Linear and Non-Linear Waves (WAVE) — Analysis of partial differential equations (APDE),
PI: Luis Vega,
Basque Center for Applied Mathematics (BCAM).
2021 - Present.
Instituto de Matemática Interdisciplinar (IMI),
Universidad Complutense de Madrid (UCM).
2020 - Present.
Research group UCM-GR17-970846: Nonlinear Elliptic and Parabolic Equations,
PI: Julián López-Gómez,
Universidad Complutense de Madrid (UCM).
Fellowships and Awards
2024. Acreditación como Profesor Contratado Doctor y Profesor de Universidad Privada.
Agencia Nacional de Evaluación de la Calidad y Acreditación (ANECA).
2023. Juan de la Cierva 2022 grants.
Ministerio de Ciencia e Innovación, Gobierno de España.
Expedient Code: JDC2022-048469-I
2nd position in the area of Mathematics.
2022. Acreditación como Profesor Ayudante Doctor.
Agencia Nacional de Evaluación de la Calidad y Acreditación (ANECA).
2022. Egonlabur Fellowship of the Basque Country Government.
Gobierno Vasco
Grant for predoctoral stays.
Expedient Code: EP_2022_1_0063.
2021. Kovalevskaya Fellowship for the ICM2022.
Grants for the attendance of young researchers to the ICM2022.
2020. Predoctoral Fellowship of Basque Country Government.
Gobierno Vasco.
Expedient Code: PRE_2019_1_0220.
The unique grant in the field Mathematics.
2019. PhD initialization Award.
Facultad de Ciencias Matemáticas, Universidad Complutense de Madrid (UCM).
2018. Collaboration Fellowship IKASIKER of the Basque Country Government.
Gobierno Vasco
Director: Luis Escauriaza Zubiria.
Expedient Code: IkasC_2017_1_0191
2018. Academic Excellence Grant of the Basque Country Government 2017-2018.
Gobierno Vasco
Third position in Science.