Profile (CV) of the research teaching staff

García Lirola, Luis Carlos
Department: Departamento de Matemáticas
Field: Análisis Matemático
Faculty: Facultad de Ciencias

Research Institute: INSTITUTO UNIVERSITARIO DE MATEMÁTICAS Y APLICACIONES (IUMA)
Group: E48_23R: Análisis y física matemática

UNESCO codes
  • Álgebra y espacios de Banach

Number of 6-year periods of research productivity evaluation
  • CNEAI agreement periods of research evaluation. 03/05/22
Academic position: Prof. Titular Univ.

Academic position
  • Profesor Secretario del Departamento de Matemáticas
Office phone: 876553226
Mobile phone: 679085628
Email: luiscarlos@unizar.es
Personal web page: http://personal.unizar.es/luiscarlos
ORCID number: 0000-0001-9211-4475

Research interests
  • Geometría métrica
  • Convexidad
  • Análisis funcional
  • Espacios normados lineales y espacios de banach

University degrees
  • Máster Universitario en Matemática Avanzada y Profesional. Universidad de Murcia. 2014
  • Licenciado en Matemáticas. Universidad de Murcia. 2013

PhDs
  • Doctor en Matemáticas. Universidad de Murcia. 2017

Go to personal website Go to ORCID page

 
               
I am Associate Professor at the University of Zaragoza. My research interlinks Functional Analysis, Convex Geometry, and Metric Geometry, and includes topics as uniform convexity, the Radon-Nikodym property, the Daugavet property, extreme points, and convex bodies. I particularly focus on spaces of Lipschitz functions and Lipschitz-free spaces, which had become a very active research topic because of its applications on Non-Linear Analysis, Computer Science and Optimal Transportation.
I received a bachelor's degree in Mathematics from the University of Murcia (UM) in 2013, with a GPA of 9.84/10 and the End of Studies Award. After that, I earned a master's degree in Advanced and Professional Mathematics, again in Murcia, with a GPA of 9.94/10.
My Ph.D. dissertation, supervised by B. Cascales and M. Raja at the UM focus on several topics on the theory of Banach spaces where Geometry and Topology are interlaced. The thesis was defended in December 2017, with a distinction Cum Laude, the International Mention and the Exceptional Award for a Ph.D. in Mathematics at the UM.

In 2016, I did a three-month stay in Besançon (France) with G. Lancien, and initiated a collaboration with the research group there. I also collaborate regularly with the group at Granada. I have done several research visits to both places, hosted members of those groups in Murcia and Zaragoza, and published several papers in collaboration with C. Petitjean and A. Procházka (Besançon), and R. Chiclana, M. Martín and A. Rueda Zoca (Granada).  
After my thesis defense, I enjoyed a postdoctoral fellowship of the UM. From June 2018 to June 2020, I was a postdoctoral fellow at Kent State University (USA), where I worked on questions in the framework of Convex Geometry with A. Zvavitch.  
My research has led to 19 papers in JCR journals. I have presented them in both national and international conferences, as well as in seminars in several universities in Europe and America. I want to highlight the following results:
- The Banach-Stone-like theorem for metric spaces and its relation with the Mahler conjecture for certain convex polytopes
- The metric spaces such that the space of Lipschitz functions has the Daugavet property are precisely the length spaces, this improves a result by Kadets, Ivakhno and Werner from 2007
- The study of the denseness of the set of Lipschitz functions which attain their Lipschitz constant, including the solution to a problem posed by Godefroy
- The existence of a renorming with modulus of uniform convexity greater than its cotype for Banach spaces with the UMD property
- A characterization of Orlicz spaces such that the space of compact operators between them is asymptotically uniformly smooth, extending the lp case done by Dilworth, Kutzarova, Randrianarivony, Revalski and Zhivkov

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