David González Álvaro

Profesor Contratado Doctor

Universidad Politécnica de Madrid
ETSI de Caminos, Canales y Puertos
Departamento de Matemática e Informática Aplicadas a las Ingenierías Civil y Naval

Delegado del Director de la EPES para la Calidad del Grado en Matemáticas y del Máster Universitario en Matemáticas Avanzadas.

NEWS:

New preprint: arXiv:2606.21417

Teaching

2026/2027: Álgebra Lineal (Grado en Matemáticas)
2026/2027: Matemáticas I (Grado en Ingeniería de Materiales)

Past teaching

Research

UPM research group: Geometría y sus aplicaciones.
Research project: Análisis y Geometría con Aplicaciones a los Problemas Inversos (AGAPI).

Research interests: Riemannian Geometry, and more specifically, manifolds of non-negative or positive sectional curvature.
My MathSciNet profile and my zbMATH profile.
I received the prize "Vicent Caselles 2018" from the RSME (Spanish math society) and the Fundación BBVA. Some links: RSME, FBBVA, FBBVA.
Organization of events, visiting positions, list of talks and conferences attended.

Preprints

15. (With J. DeVito and M. Zarei) Ricci Flow Preserves Positive Sectional Curvature on Homogeneous Spheres. arXiv:2606.21417
14. (With J. DeVito, M. Domínguez-Vázquez and A. Rodríguez-Vázquez) Positive Ric2 curvature on products of spheres and their quotients via intermediate fatness. arXiv:2410.18846

Articles (here you can find the arXiv versions)

13. (With M. Albanese and J. DeVito) Examples of biquotients whose tangent bundle is not a biquotient vector bundle. Comm. Anal. Geom. 33 (2025), no. 5, 1135-1171.
12. (With M. Zarei) Positive sectional curvature is not preserved under the Ricci flow in dimensions seven and thirteen. J. Geom. Anal. 35 (2025), no. 8, Paper No. 241, 30 pp.
11. (With M. Zarei) Positive intermediate curvatures and Ricci flow. Proc. Amer. Math. Soc. 152 (2024), 2637-2645.
10. (With M. Domínguez-Vázquez and L. Mouillé) Infinite families of manifolds of positive k-th intermediate Ricci curvature with k small. Math. Ann. 386 (2023), no. 3-4, 1979-2014.
9. (With J. DeVito) Biquotient vector bundles with no inverse. Math. Z. 302 (2022), no. 2, 1267-1278.
8. (With M. Amann and M. Zibrowius) Vector bundles of non-negative curvature over cohomogeneity one manifolds. Adv. Math. 405 (2022), Paper No. 108477, 51 pp.
7. (With I. Belegradek) Diffeomorphic souls and disconnected moduli spaces of nonnegatively curved metrics. Ann. Inst. Fourier (Grenoble) 72 (2022), no. 1, 109-122.
6. (With M. Zibrowius) The stable converse soul question for positively curved homogeneous spaces. J. Differential Geom. 119 (2021), no. 2, 261-307.
5. (With A. Dessai) Moduli space of metrics of nonnegative sectional or positive Ricci curvature on homotopy real projective spaces. Trans. Amer. Math. Soc. 374 (2021), no. 1, 1-33.
4. (With M. Zibrowius) Open manifolds with non-homeomorphic positively curved souls. Math. Proc. Cambridge Philos. Soc. 169 (2020), no. 2, 357-376. Link to the C++ program Eschenburg calculator.
3. (With M. Radeschi) A note on the Petersen-Wilhelm conjecture. Proc. Amer. Math. Soc. 146 (2018), no. 10, 4447-4458.
2. Nonnegative curvature on stable bundles over compact rank one symmetric spaces. Adv. Math. 307 (2017), 53-71.
1. (With L. Guijarro) Soft restrictions on positively curved Riemannian submersions. J. Geom. Anal. 26 (2016), no. 2, 1442-1452.

Survey

(With L. Guijarro) On the double soul conjecture. New Trends in Geometric Analysis, 227-244, RSME Springer Ser., 10, Springer, Cham, 2023.

Short CV

Education (all at Universidad Autónoma de Madrid):

2006-2010: Licenciatura en Matemáticas.
2010-2011: Máster en Matemáticas y Aplicaciones.
2011-2016: Ph.D. degree in Mathematics, under the supervision of Luis Guijarro. You can find here a copy of my Ph.D. thesis.

Employment:

2009-2013: Various scholarships.
2013-2016: FPI grant at ICMAT.
2016-2017: Profesor Ayudante at UAM.
2017-2019: Postdoctoral researcher at the University of Fribourg (Switzerland), under the supervision of Anand Dessai. Member of the DFG-Priority Program Geometry at infinity.
2019-2022: Profesor Ayudante Doctor at UPM.
2022-------: Profesor Contratado Doctor at UPM.

Contact and address

E-mail: david.gonzalez.alvaroATupm.es

Office: Planta 2ª (torre)

Calle del Profesor Aranguren, 3
ETSI de Caminos, Canales y Puertos
Universidad Politécnica de Madrid
28040 Madrid (Spain)