Luis C. García Lirola

I am an associate professor (PCD) at the University of Zaragoza and researcher at the IUMA. My research intelinks Geometry of Banach Spaces, Metric Geometry and Convex Geometry.
Email: luiscarlos (at) unizar.es

Publications
Talks

Thesis
Links

Publications

Preprints

R. Aron, V. Dimant, L. García-Lirola, M. Maestre. Linearization of holomorphic Lipschitz functions.

Papers

L. García-Lirola, G. Grelier, G. Martínez-Cervantes, A. Rueda Zoca. Extremal structure of projective tensor products. Results Math. 78 (2023), no. 5, Paper No. 196, 16 pp. Preprint version
L. García-Lirola, G. Grelier. Lipschitz-free spaces, ultraproducts, and finite representability of metric spaces, J. Math. Anal. Appl. 526 (2023), no. 2, Paper No. 127253, 14 pp. Preprint version
L. García-Lirola, C. Petitjean, A. Procházka. Injectivity of Lipschitz operators, Bull. Malays. Math. Sci. Soc. 46, 68 (2023). Preprint version
L. García-Lirola, G. Grelier, A. Rueda Zoca. Extremal structure in ultrapowers of Banach spaces, RACSAM, 116, Art. 161 (2022). Preprint version
S. Dantas, L. García-Lirola, M. Jung, A. Rueda Zoca. On norm-attainment in (symmetric) tensor products, Quaest. Math. 46 (2023), no. 2, 393–409. Preprint version
L. García-Lirola, C. Petitjean. On the Weak Maximizing Properties, Banach J. Math. Anal. 15, 55 (2021). Preprint version
L. García-Lirola, M. Raja. Uniformly convex renormings and generalized cotypes, Adv. Math. 383, 107679, 2021. Preprint version
M. Alexander, M. Fradelizi, L. García-Lirola, A. Zvavitch. Geometry and volume product of finite dimensional Lipschitz-free spaces. J. Funct. Anal. 280 (2021), no. 4, 108849. Preprint version
R. Chiclana, L. García-Lirola, M. Martín, A. Rueda Zoca. Examples and applications of the density of strongly norm attaining Lipschitz maps. To appear in Rev. Mat. Iberoam. Preprint version
G. Beer, L. García-Lirola, M. Garrido. Stability of Lipschitz-type functions under pointwise product and reciprocation. Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM 114 (2020), no. 3, Paper No. 120, 16 pp.
B. Cascales, R. Chiclana, L. García-Lirola, M. Martín, A. Rueda Zoca. On strongly norm attaining Lipschitz maps. J. of Funct. Anal. 277, no. 6 (2019) 1677-1717
L. García-Lirola, A. Procházka. Pelczynski space is isomorphic to the Lipschitz free space over a compact set. Proc. Amer. Math. Soc. 147, no. 7 (2019), 3057-3060.
L. García Lirola, C. Petitjean, A. Procházka and A. Rueda Zoca. Extremal Structure and Duality of Lipschitz Free Spaces. Mediterr. J. Math. (2018) 15: 69.
L. García-Lirola, A. Procházka and A. Rueda Zoca, A characterisation of the Daugavet property in spaces of Lipschitz functions. J. Math. Anal. Appl. 464, 1 (2018), 473-492
L. García-Lirola and M. Raja. On strong asymptotic uniform smoothness and convexity. Rev Mat Complut., 31(1):131-152, 2018.
L. García-Lirola and M. Raja. Maps with the Radon–Nikodým property. Set-Valued Var. Anal., 26(1):77-93, 2018.
L. García-Lirola, C. Petitjean, and A. Rueda Zoca. On the structure of spaces of vector-valued Lipschitz functions. Studia Math., 239(3):249–272, 2017.
L. García-Lirola and A. Rueda Zoca. Unconditional almost squareness and applications to spaces of Lipschitz functions. J. Math. Anal. Appl., 451(1):117–131, 2017.
L. García-Lirola, J. Orihuela, and M. Raja. Convex compact sets that admit a lower semicontinuous strictly convex function. J. Convex Anal., 24(3):987–998, 2017.

The preprint versions are available in arXiv.

Talks

Invited talks

Linearization of holomorphic Lipschitz functions. III Jornada en Espacios de Banach. Valencia, Octubre 2023
Linearization of holomorphic Lipschitz functions. ÆSY TO DEFINE, HARD TO ANALYSE: First conference on Lipschitz free spaces. Besançon, September 2023
Injectivity of Lipschitz operators. XVI EITA Meeting in Approximation Theory 2022, Huesca, October 2022.
Decompositions of polytopes and Banach-Stone-like theorems for metric spaces. Conference Current trends in Convex Geometry. Virtual, March 2021.
Volume product and metric spaces. Workshop on Geometric Tomography. BIRS, Banff, January 2020. Video
Extremal structure of Lipschitz free spaces. XVI Encuentros de Análisis Funcional Murcia-Valencia. Murcia, December 2018
Some results on duality of spaces of vector-valued Lipschitz functions. XV Encuentro de Análisis Funcional Murcia-Valencia. Alcoi, July 2016.
Compactos convexos que admiten una función estrictamente convexa. III Congreso de Jóvenes Investigadores de la RSME. Murcia, September 2015.

Contributed talks

Convexidad uniforme y cotipos en espacios de Banach. Congreso Bienal RSME, Ciudad Real, January 2022
Lipschitz operators which preserve injectivity. Winter School in Abstract Analysis, Czech Republic, January 2022
The weak maximizing property and asymptotic geometry of Banach spaces. Entangling Non-commutative Functional Analysis and Geometry of Banach Spaces. CIRM Luminy, October 2020
Volume product and Lipschit-free Banach spaces. Workshop in Convexity and geometric aspects of Harmonic Analysis. Georgia Tech, Atlanta, December 2019
On strongly norm attaining Lipschitz maps. Banach spaces and optimization: Conference on the occasion of Robert Deville’s 60th birthday. Metabief, June 2019
Extremal structure of Lipschitz free spaces. Conference on Non Linear Functional Analysis. Valencia, October 2017.
A characterisation of the Daugavet property in spaces of Lipschitz functions. Septièmes journées Besançon-Neuchâtel d’analyse fonctionnelle, Besançon, June 2017.
Asymptotic uniform smoothness in spaces of compact operators. Banach Spaces and Operator Theory with Applications. Poznan, July 2017.
Maps with the Radon-Nikodym property. 45th Winter school in Abstract Analysis. Svratka, January 2017.
Asymptotic uniform smoothness in spaces of compact operators. Function Theory on Infinite Dimensional Spaces XIV. Madrid, February 2016.
On generalized type and cotype. 44th Winter School in Abstract Analysis. Svratka, January 2016.
Compact convex sets that admit a strictly convex function. XIV Encuentro de Análisis Funcional Murcia-Valencia. Valencia, September 2015.

Seminars

Descomposiciones de politopos y teoremas tipo Banach-Stone para espacios metricos. Seminario de Geometría Diferencial y Convexa. Murcia, February 2022
The weak maximizing property and asymptotic geometry of Banach spaces. Functional Analisis Seminar. University of Tartu, April 2021 Video
La propiedad maximizante débil y geometría asintótica de espacios de Banach. Seminario Rubio de Francia, Universidad de Zaragoza, Oct 2020
The weak maximizing property and asymptotic geometry of Banach spaces. Measure Theory Seminar. Kent State University, September 2020
Volume product and metric spaces. Seminar der Arbeitsgruppen Diskrete Mathematik/Geometrie & Diskrete Geometrie. Technische Universität Berlin, May 2020
Volume product and metric spaces. Analysis Seminar. University of Rochester, April 2020
Stability of Lipschitz-type functions under pointwise product and reciprocation. Karcher Colloquium. University of Oklahoma, March 2020
Volume product and metric spaces. Analysis Seminar. University of Oklahoma, March 2020
Volume product and metric spaces. Analysis and Applied Math Seminar. University of Toronto, February 2020
On strongly norm attaining Lipschitz maps. Analysis seminar. University of Illinois at Urbana-Champaign, December 2019
On strongly norm attaining Lipschitz maps. Geometry Luncheon Seminar. Penn State University, State College, November 2019
Volume product and metric spaces. Analysis and Probability Seminar. Case Western Reserve University, Cleveland, Oct 2019
Geometry and topology around extreme points. Graduate Student Seminar. Kent, Oct 2019
On strongly norm attaining Lipschitz maps. Workshop in Analysis and Probability Seminar. Texas A&M, July 2019
Producto de volúmenes para bolas de espacios de funciones Lipschitzianas. Seminario Rey Pastor. Murcia, December 2018
Extreme points in Lipschitz-free spaces. Colloquium. Kent, December 2018.
Lyapunov's theorem and application to fair cake-cutting. Non-Linear Analysis Seminar. Kent, November 2018.
Strongly norm-attaining Lipschitz maps. Measure Theory Seminar. Kent, Nov 2018.
Estructura extremal de espacios Lipschitz libres. Seminario de jóvenes investigadores en Matemáticas. Granada, February 2018.
Compact convex sets that admit a strictly convex function. I Jornadas de Doctorandos en Matemáticas. Murcia, September 2016.
Aplicaciones con la propiedad de Radon-Nikodym. Seminario del Departamento de Análisis Matemático. Granada, December 2016.
Puntos expuestos de continuidad para una función estrictamente convexa. Seminario de jóvenes investigadores en Matemáticas. Granada, November 2016.
Asymptotic uniform smoothness in spaces of compact operators. Séminaire d’Analyse fonctionnelle. Besançon, March 2016.

Posters

Volume product and Lipschitz-free Banach spaces. Local and Nonlocal Trends in Analysis and Geometry. Pittsburgh, October 2019 & Informal Analysis Seminar. Kent, November 2019.
A characterization of the Daugavet property in spaces of Lipschitz functions. Recent Advances in Functional Analysis. Kent, October 2018 & Informal Analysis Seminar. Kent, April 2019.
Extremal structure of Lipschitz free spaces. Non Linear Functional Analysis. CIRM Luminy, March 2018.

Thesis

Convexity, Optimization and Geometry of the Ball in Banach Spaces

The research done during my PhD involves several topics in the framework of the geometry of Banach spaces. The guiding theme is the structure of convex sets. Several properties based on the notions of extreme and exposed points are analyzed. This includes classical properties as the Radon-Nikodym property, which is studied from a non-linear point of view, as well as the study of the geometry of the norm in tensor products. Moreover, some isometric properties (in particular, the Daugavet property and the extremal structure) are studied in spaces of Lipschitz functions and their preduals. These last spaces, known as Lipschitz-free spaces, are a very active research topic by their applications in non-linear analysis. The research has been done in collaboration with the reasearch groups of Murcia and Granada (Spain) and Besançon (France). To this end, a three months research stay was done in Besançon, and a two-weeks research stay was done in Granada.

My thesis was supervised by Bernardo Cascales and Matías Raja.

(comics from xkcd and Spiked Math)