modeling nature from nano to macro
STAFF / COLLABORATOR RESEARCHER
Miguel Martin defended his PhD in 2000 at the University of Granada under the supervision of Rafael Paya. He has been assistant and associate professor at the University of Granada and earned a full professorship in 2016 at the same University, a position which is his current one. He has undertaken several short and mid-term research stays abroad, including a six-month stay at Kent State University (OH, USA) in 2012 as visiting scholar, funded by the Spanish Ministry of Education.
The main research lines of Miguel Martin fall inside the linear and non-linear functional analysis, focusing on the study of the geometry of Banach spaces and of the geometry of the spaces of the operator between them. Concrete lines of research include the study of the numerical range of operators, surjective isometries, Daugavet and Daugavet-like properties, and norm-attaining operators (both linear and Lipschitz). As a sample of some of the recent goals obtained, Miguel Martin proved in 2014 that there are compact operators between Banach spaces which cannot be approximated by norm attaining operators, answering a question open since 1970s. Let us also mention the developing in 2018-2020 of a complete theory of numerical indices with respect to operators, extending the classical theory of numerical index, in collaboration with Vladimir Kadets, Javier Meri, Antonio Perez, and Alicia Quero. The research of Miguel Martin has been published in more than 80 papers within the JCR journals and two monographs, one in Springer’s Lecture Note in Mathematics and one in Dissertationes Mathematicae. He has a wide network of frequent collaborators and has published papers with more than 50 coauthors from all over the world.
He has a long experience teaching many different topics inside Mathematical Analysis in many studies as Civil Engineering, Chemistry Engineering, Computer Sciences, Physics, Biotechnology, and Mathematics. He also has conducted some courses within the PhD and Master Program FISYMAT. He has developed an extensive experience leading research projects funded by both the Spanish Government and the Andalusian Government and was deputy coordinator of the Spanish Network of Functional Analysis and Applications from 2006 till 2011. He has advised or co-advised four PhD students (two of them at the University of Granada, one at the University of Valencia, Spain, and one at Pohang University of Science and Technology, Republic of Korea), and he is
co-advising three more PhD students nowadays. Besides, he is part of the Editorial Board of the Journal of Function Spaces and of Advances in Operator Theory and has co-edited a special volume published by De Gruyter. He is a reviewer for Zentralblatt Math and Mathematical Reviews.
He has served as a scientific evaluator of research projects in Functional Analysis for the Spanish Research Agency (AEI), for ANCP and FONCyT of Argentina, for FONDECyT of Chile, and for Czech Science Foundation, Czech Republic, and he has been an external expert for promotions at Universities of Czech Republic, India, Italy, and the USA. Finally, Miguel Martin is involved in scientific dissemination activities, giving talks and presentations for the general public.