Sergio Cruz Blázquez

Academic curriculum

Curriculum vitae

Assistant Professor in the Department of Mathematics at the Autonomous University of Madrid. Research in geometric analysis, nonlinear partial differential equations and conformal geometry.

Affiliation
Autonomous University of Madrid
Email
sergio.cruz@uam.es
Identifiers
ORCID 0000-0003-3401-5617
ResearcherID W-8913-2018
Personal details
Male · Born 13 November 1994 · Spanish nationality
01

Positions

January 2025 – January 2031

Assistant Professor · Autonomous University of Madrid

  • Department of Mathematics.

January 2023 – January 2025

Postdoctoral Researcher, Margarita Salas · University of Granada

  • Project: Nonlinear Analysis and Conformal PDEs from Geometry.
  • Dipartimento di Scienze di Base e Applicate per l’Ingegneria, Sapienza University of Rome, January 2023 – January 2024. Supervisor: Prof. Angela Pistoia.
  • Department of Mathematical Analysis, University of Granada, January 2024 – January 2025. Supervisor: Prof. David Ruiz.

January 2022 – January 2023

Assegnista di Ricerca · University of Campania

  • Project Equazioni differenziali alle derivate parziali non lineari, funded within PRIN 2017 – JPCAP. Supervisor: Prof. Giusi Vaira.
  • Department of Physics and Mathematics.
  • Ranked 1/4 in the first call.

October 2021 – January 2022

Postdoctoral Researcher · University of Almería

  • Funded by the Department of Economic Transformation, Industry, Knowledge and Universities of the Regional Government of Andalusia under project P18-FR-667.
  • Department of Mathematics.

October 2017 – Present

Member · GNAMPA Research Group

  • Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni, part of INdAM.
  • Research area: Equazioni differenziali e sistemi dinamici.

October 2017 – October 2020

Marie Skłodowska-Curie Fellow · Istituto Nazionale di Alta Matematica

  • PhD student in the INdAM Doctoral Programme Fellowships in Mathematics and/or Applications, cofunded by Marie Skłodowska-Curie Actions, INdAM-DP-COFUND-2015.
  • Project: Liouville equations, geometry and physics.
  • Ranked 9/20 in the first call.
  • Grant no. 713485.
02

Education and training

October 2017 – June 2021

Doctoral Program in Physics and Mathematics

International School for Postgraduate Studies, University of Granada

  • B04.56.1, RD 99/2011. Academic years 2017/18–2020/21.
  • PhD thesis in cotutelle with the Scuola Normale Superiore: Curvature Prescription Problems on Manifolds with Boundary. Defended on 29 June 2021; grade: Sobresaliente Cum Laude, with International Doctorate Mention.
  • Thesis advisor at the University of Granada: Prof. David Ruiz.

October 2017 – June 2021

Corso di Perfezionamento in Matematica, PhD in Mathematics

Classe di Scienze, Scuola Normale Superiore

  • INdAM-DP-COFUND 2015 Project.
  • Ciclo XXXIII, academic years 2017/18–2019/20.
  • Settore scientifico-disciplinare: MAT/05 – Analisi Matematica.
  • PhD thesis in cotutelle with the University of Granada: Curvature Prescription Problems on Manifolds with Boundary. Defended on 29 June 2021; grade: Cum Laude.
  • Thesis advisor at the Scuola Normale Superiore: Prof. Andrea Malchiodi.
  • Courses completed with a final exam: Geometric Flows, 29/30; Riemannian Geometry, 30/30 e lode; and Conformal Geometry, 30/30 e lode.
  • Additional PhD courses: Initial Data Sets in General Relativity, Variational Methods, and Elliptic Partial Differential Equations.

October 2016 – September 2017

Master’s Degree in Physics and Mathematics

International School for Postgraduate Studies, University of Granada

  • Master’s thesis: El problema de las curvaturas gaussiana y geodésica prescritas en D². Defended in September 2016; grade: Sobresaliente 10/10.
  • Thesis advisor: Prof. David Ruiz.
  • Overall grade: Sobresaliente 9.5/10. One Cum Laude grade in Nonlinear Dispersive Differential Equations.
  • Representative of the Master’s Degree students in the Consejo de Representantes de Máster, CRM; member of the Communications and Social Networking Committee.

September 2012 – September 2016

Undergraduate Degree in Mathematics

University of Granada

  • Final thesis: El Producto de Convolución y sus aplicaciones al Análisis Real, al Análisis de Fourier y al estudio de Ecuaciones en Derivadas Parciales. Defended in September 2016; grade: Sobresaliente 9.5/10.
  • Thesis advisor: Prof. Rafael Payá.
  • Overall grade: Sobresaliente 9.1/10.
  • 14 Cum Laude grades.
03

Publications

  1. S. Cruz-Blázquez and A. DelaTorre. Kazdan-Warner obstructions for a fourth-order boundary problem, Bulletin of the London Mathematical Society, 14 pages, accepted for publication in July 2026.

    doi:10.1112/blms.70461

  2. S. Cruz-Blázquez and A. DelaTorre. Conformal metrics on the four-dimensional half sphere with symmetric Q and T curvatures, Calculus of Variations and Partial Differential Equations, 65, Art. 236, 26 pages, July 2026.

    doi:10.1007/s00526-026-03402-5

  3. S. Cruz-Blázquez and G. Vaira. Positive blow-up solutions for a linearly perturbed boundary Yamabe problem, Discrete and Continuous Dynamical Systems, 45, no. 8, pp. 2518–2539, August 2025.

    doi:10.3934/dcds.2024174
    Bibliometric indicators

    JCR 2024, Clarivate: JIF = 1.1; Category: Mathematics; JIF Percentile = 78.2. SJR 2024, SCImago: SJR = 1.065, Q1. Scopus, February 2026: Total citations = 1; FWCI = 1.33. Google Scholar: Total citations = 2.

  4. L. Battaglia, S. Cruz-Blázquez and A. Pistoia. Prescribing nearly constant curvatures on balls, Proceedings of the Royal Society of Edinburgh, Section A: Mathematics, 155, issue 3, pp. 756–791, June 2025.

    doi:10.1017/prm.2023.111
    Bibliometric indicators

    JCR 2024, Clarivate: JIF = 0.9; Category: Mathematics; JIF Percentile = 67.6. SJR 2024, SCImago: SJR = 1.076, Q1. Scopus, February 2026: Total citations = 1; FWCI = 1.81. Google Scholar: Total citations = 5.

  5. S. Cruz-Blázquez. The role of the boundary in the existence of blow-up solutions for a doubly critical elliptic problem, Nonlinear Differential Equations and Applications, 32, no. 40, 24 pages, March 2025.

    doi:10.1007/s00030-025-01042-w
    Bibliometric indicators

    JCR 2024, Clarivate: JIF = 1.2; Category: Mathematics; JIF Percentile = 59.2. SJR 2024, SCImago: SJR = 1.110, Q1. Scopus, February 2026: Not indexed. Google Scholar: Total citations = 0.

  6. S. Cruz-Blázquez, A. Pistoia and G. Vaira. Clustering solutions for a boundary Yamabe problem, Annali della Scuola Normale Superiore di Pisa – Classe di Scienze, 48, October 2024.

    doi:10.2422/2036-2145.202309_002
    Bibliometric indicators

    JCR 2024, Clarivate: JIF = 1.3; Category: Mathematics; JIF Percentile = 85.7. SJR 2024, SCImago: SJR = 1.775, Q1. Scopus, February 2026: Not indexed. Google Scholar: Total citations = 4.

  7. S. Cruz-Blázquez and A. Pistoia. Non-degeneracy of critical points of the squared norm of the second fundamental form on manifolds with minimal boundary, Journal of Geometric Analysis, 33, paper 332, 16 pages, August 2023.

    doi:10.1007/s12220-023-01395-7
    Bibliometric indicators

    JCR 2023, Clarivate: JIF = 1.2; Category: Mathematics; JIF Percentile = 83.8. SJR 2023, SCImago: SJR = 1.203, Q1. Scopus, February 2026: Total citations = 0. Google Scholar: Total citations = 0.

  8. S. Cruz-Blázquez, A. De la Torre and D. Ruiz. Qualitative Properties for Solutions of the Fractional Yamabe Problem, Discrete and Continuous Dynamical Systems, 43, issue 11, November 2023.

    doi:10.3934/dcds.2023077
    Bibliometric indicators

    JCR 2023, Clarivate: JIF = 1.1; Category: Mathematics; JIF Percentile = 80.1. SJR 2023, SCImago: SJR = 1.104, Q1. Scopus, February 2026: Total citations = 1; FWCI = 0.25. Google Scholar: Total citations = 2.

  9. S. Cruz-Blázquez, A. Malchiodi and D. Ruiz. Conformal metrics with prescribed scalar and mean curvature, Journal für die reine und angewandte Mathematik, 789, pp. 211–251, June 2022.

    doi:10.1515/crelle-2022-0026
    Bibliometric indicators

    JCR 2022, Clarivate: JIF = 1.5; Category: Mathematics; JIF Percentile = 80.2. SJR 2022, SCImago: SJR = 2.310, Q1. Scopus, February 2026: Total citations = 7; FWCI = 1.15. Google Scholar: Total citations = 18.

  10. S. Cruz-Blázquez and D. Ruiz. Prescribing Gaussian and geodesic curvatures on disks, Advanced Nonlinear Studies, 18, no. 3, pp. 453–468, July 2018.

    doi:10.1515/ans-2018-2021
    Bibliometric indicators

    JCR 2018, Clarivate: JIF = 1.650; Category: Mathematics; JIF Percentile = 91.56. SJR 2018, SCImago: SJR = 1.422, Q1. Scopus, February 2026: Total citations = 19; FWCI = 0.83. Google Scholar: Total citations = 30.

Preprints

  • X. Cabré and S. Cruz-Blázquez. Michael-Simon type Sobolev inequality and applications to non-local mean curvature, preprint.
04

Teaching

  • The Direct Method of Calculus of Variations in one dimension – Final degree dissertation. Degree in Mathematics. Student: Fernando Ibáñez Clemente. Autonomous University of Madrid, Academic Year 2025–2026.
  • Calculus I – Degree in Computer Engineering. First year, first semester. CFU 6, 60 hours. Held in Spanish at the Autonomous University of Madrid during the Academic Year 2025–2026.
  • Calculus I – Degree in Mathematics. First year, first semester. CFU 6, 60 hours. Held in Spanish at the Autonomous University of Madrid during the Academic Year 2025–2026.
  • Statistics – Degree in Chemical Engineering. First year, second semester. CFU 3, 30 hours. Held in Spanish at the Autonomous University of Madrid during the Academic Year 2024–2025.
  • Calculus II – Degree in Computer Engineering. First year, second semester. CFU 6, 60 hours. Held in Spanish at the Autonomous University of Madrid during the Academic Year 2024–2025.
  • Mathematical Analysis II – Degree in Physics, Group C. First year, second semester. CFU 4, 40 hours. Held in Spanish at the University of Granada during the Academic Year 2023–2024.
  • Calculus II – Double Degree in Computer Engineering and Mathematics, unique group. First year, second semester. CFU 2, 20 hours. Held in Spanish at the University of Granada during the Academic Year 2023–2024.
  • Mathematical Analysis I, COLL.DOC., Groups I and II, 1015374, SSD MAT/05 – Degree in Clinical Engineering. First year, first semester. CFU 3+3, 60 hours. Held in Italian at Sapienza University of Rome during the Academic Year 2023–2024. Duration: 30+30 hours.
  • Introduction to Mathematical Analysis. Held in Italian at the University of Bari during the Academic Year 2021–2022. Duration: 40 hours. Lecture notes in Italian.
05

Participation in projects

  • INdAM-GNAMPA Project · CUP_E53C23001670001. Double curvature problems on manifolds with boundary and their relation with PDE of elliptic type, Istituto di Alta Matematica – Gruppo Nazionale per l'Analisi Matematica. PI: Marco Ghimenti, University of Pisa. Call 2024. Duration: January–December 2024. Amount granted: €3,500. Role: Researcher. Research line: Q-T curvature prescription problems.
  • INdAM-GNAMPA Project · CUP_E53C22001930001. Proprieta qualitative delle soluzioni di equazioni ellittiche, Istituto di Alta Matematica – Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni. PI: Luca Battaglia, University of Roma Tre. Call 2023. Duration: May 2023–May 2024. Amount granted: €3,500. Role: Researcher. Research line: Curvature Prescription Problems on Surfaces with Boundary and Concentration Phenomena for Equations in Two Dimensions.
  • PRIN 2017 – JPCAP. Quantitative and qualitative aspects of nonlinear PDEs, MIUR. PI 1: Berardino Sciunzi, University of Calabria. Local PI: Giusi Vaira, University of Bari. Call 2017. Duration: August 2019–February 2023. Amount granted: €133,500. Role: Assegnista di Ricerca. Research line: Nonlinear Partial Differential Equations.
  • INdAM-GNAMPA Project · CUP_E55F22000270001. Fenomeni di Blow-up per Equazioni non Lineari, Istituto di Alta Matematica – Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni. PI: Gabriele Mancini, University of Bari. Call 2022. Duration: May 2022–May 2023. Amount granted: €4,500. Role: Researcher. Research line: Curvature Prescription Problems on Surfaces with Boundary.
  • P18-FR-667. Nonlinear Analysis and PDEs from Physics and Geometry, Consejería de Transformación Económica, Industria, Conocimiento y Universidades. PI 1: José Carmona, University of Almería. PI 2: Salvador Villegas, University of Granada. Call 2019. Duration: January 2020–December 2022. Amount granted: €94,800. Role: Researcher. Research line: Singular Solutions of the Nonlocal Yamabe Problem.
06

Talks seminars and posters

  • Invited talk. Oscillating Solutions to the Fractional Yamabe Problem. XXIX CEDYA. Valencia, Spain, July 2026.
  • Invited talk. Existence and Obstructions in the Q- and T-Curvature Prescription Problem in S⁴₊. GeoPDEs Meeting. Granada, Spain, July 2026.
  • Invited talk. Boundary blow-up for a doubly critical elliptic problem. PDEs at Grand Paradis – V Edition. Cogne, Italy, January 2026.
  • Invited talk. The Kazdan-Warner problem on Manifolds with Boundary. Conformal and CR Geometry, Banff International Research Centre. Banff, Canada, December 2024.
  • Seminar. Conformal metrics in the upper four-dimensional hemisphere with symmetric Q and T curvatures. Seminar of Differential Equations, University of Granada, 15 October 2024.
  • Invited talk. Conformal metrics in the upper four-dimensional hemisphere with symmetric Q and T curvatures. Variational and Geometrical Methods in PDEs. Bedlewo, Poland, August 2024.
  • Seminar. Prescribing nonconstant scalar and mean curvatures on manifolds with boundary. Department of Mathematics and Physics, Università di Roma Tre, 13 December 2023.
  • Seminar. Infinite Morse Index Solutions to the Fractional Yamabe Problem on ℝⁿ. Seminario a tutto SBAI, 30 November 2023.
  • Invited talk. Oscillating Singular Solutions to the Fractional Yamabe Problem. Chiaccherate Nonlineari. Alghero, Italy, October 2023.
  • Seminar. Clustering Solutions for a Boundary Yamabe Problem. Department of Mathematics, University of Pisa, 29 November 2022.
  • Invited talk. Clustering Solutions for a Boundary Yamabe Problem. Qualitative and Quantitative Aspects of Nonlinear PDEs, University of Bari Aldo Moro, Italy, 5–9 September 2022.
  • Seminar. The Scalar-Mean Curvature Prescription Problem on Compact Manifolds with Boundary. Sapienza University of Rome, 24 February 2022.
  • Seminar. Conformal Metrics with Prescribed Scalar and Mean Curvatures. Department of Mathematics, Università degli Studi di Bari, 11 February 2022.
  • Seminar. Conformal Metrics with Prescribed Scalar and Mean Curvatures. Differential Equations Seminar, University of Granada, 15 December 2021.
  • Seminar. Métricas conformes con curvaturas escalar y media prescritas. Seminar of Young Researchers, University of Granada, 4 November 2021.
  • Invited talk. Curvature Prescription Problems on Manifolds with Boundary. Non-linear and Non-local Partial Differential Equations session, 5th Congress of Young Researchers RSME, Universitat Jaume I. Castelló, Spain, 30 January 2020.
  • Seminar. Curvature Prescription Problems on Manifolds with Boundary. Séminaire Jeunes Chercheurs, University of Cergy-Pontoise. Pontoise, France, 11–13 June 2019.
  • Seminar. Problemas de curvatura prescrita en variedades con borde. Seminar of Young Researchers, IEMath-GR, University of Granada. Granada, Spain, 28 May 2019.
  • Poster. Prescribing Gaussian and geodesic curvature on Disks. Bienal Congress of the Royal Spanish Mathematical Society, University of Cantabria. Santander, Spain, 7–9 February 2019.
07

Additional training

Courses

  • Toward a geometric theory of fractional Laplacians, Prof. Rafe Mazzeo. International Doctoral Summer School in Conformal Geometry and Non-Local Operators, IMAG – University of Granada, 19–30 June 2023. Duration: 4.5 hours.
  • Exterior value problems and regularity for nonlocal operators, Prof. Moritz Kassmann. International Doctoral Summer School in Conformal Geometry and Non-Local Operators, IMAG – University of Granada, 19–30 June 2023. Duration: 4.5 hours.
  • On the nonlocal mean curvature, Prof. Xavier Cabré. International Doctoral Summer School in Conformal Geometry and Non-Local Operators, IMAG – University of Granada, 19–30 June 2023. Duration: 4.5 hours.
  • Fractional GJMS operators and applications, Prof. Sun-Yung Alice Chang. International Doctoral Summer School in Conformal Geometry and Non-Local Operators, IMAG – University of Granada, 19–30 June 2023. Duration: 4.5 hours.
  • An introduction to Liouville Equations and applications. Online course, Department of Mathematics, University of Rome Tor Vergata, 8 November–2 December 2021. Duration: 20 hours.
  • Geometric Flows, Prof. Andrea Malchiodi. PhD course, Scuola Normale Superiore, academic year 2017/18. Duration: 40 hours. Final exam grade: 29/30.
  • Riemannian Geometry, Prof. Luciano Mari. PhD course, Scuola Normale Superiore, academic year 2017/18. Duration: 40 hours. Final exam grade: 30/30 e lode.
  • Elliptic Partial Differential Equations, Prof. Luigi Ambrosio. PhD course, Scuola Normale Superiore, academic year 2017/18. Duration: 40 hours.
  • Initial Data Sets in General Relativity, Prof. Alessandro Carlotto. PhD course, Scuola Normale Superiore, academic year 2017/18. Duration: 20 hours.
  • Metodi Variazionali, Prof. Andrea Malchiodi. PhD course, Scuola Normale Superiore, academic year 2018/19. Duration: 40 hours.
  • Conformal Geometry, Prof. Andrea Malchiodi. PhD course, Scuola Normale Superiore, academic year 2019/20. Duration: 40 hours. Final exam grade: 30/30 e lode.
  • CIME – Geometric Analysis. Centro Internazionale Matematico Estivo, 18–22 June.
  • Some classical properties of minimal surfaces, Laurent Mazet, Université Paris-Est-Créteil. IE-Math, University of Granada, 4–5 March 2017. Duration: 5 hours.