Mathematician
Prof. Dr. of Algebra (ret.), luis.m.pardo at gmail.com
lm.pardo.vassallo(at)gmail.com, luis.m.pardo(at)gmail.com
Phone: +34 630552300
Some links to my profile as author:
Not all of them are exhaustive but all together yield a profile. I have excluded MathSciNet and Clarivate's WoS (full version) because both of them required payment to access to my own profile. In some of them, my affiliation with the University of Cantabria is, of course, obsolete, because I am already retired, but I don't want to waste time changing it everywhere.
Most of my research interests belong to the field of Computational Mathematics. I focussed on Computational Complexity, Foundations of Computational Mathematics, either Symbolic or Numeric Effective Methods in Algebraic Geometry. Obviously, these interests also include related fields as Commutative Algebra, Algebraic, Arithmetic and Diophantine Geometry, Numerical Analysis, Linear Algebra, Theoretical Computer Science, Integral Geometry and many others. In my poor opinion, there is no isolated field of knowledge in Mathematics, there is just a missed path which connects it to the others.
I have published more than 70 scientific manuscripts.
Concerning the impact and influence of these publications, some have been well-recieved by my colleagues, achieving (as of early 2026) an h-index 18 in Clarivate's Web of Science, an h-index 21 in Google Scholar (with more than 2250 citations in this data basis) and an h-index 23 in Research Gate (with more than 2000 citations). Although all these measurements are of dubious meaning, according to Google Scholar as of early 2026, the i100 index of my production is 6 (i.e. six of my research original works have reached at least 100 citations), whereas the i50 index (i.e. number of articles with more than 50 citations) is 16.
I like editing, which I consider an essential task in support of science and the deepening of knowledge.
I'm a member of the Editorial Board of the Journal of Complexity since 2004.
I'm also a member of the Editorial Board of Applicable Algebra in Engineering Communications and Computing since 2014 and member of the Managing Board of the same journal since 2019.
I have also edited several books and Special Issues of Journals.
I have supervised several Ph.D Students and have always tried to encourage many others.
Some moments in my scientific activity include the TERA Project (which I co-directed with Joos Heintz and Marc Giusti) in the nineties of the past century. The manuscripts we published (together with my former student J.E. Morais) in this period yielded the most efficient symbolic method that solves universally systems of multivariate polynomial equations. Another milestone was the solution of Smale's 17th Problem toghether with my former student C. Beltrán, obtained after several joint publications in the first decade of the present century. Other milestones were the works on the Arithmetic Nullstellensatz ( firstly developped with T. Krick , and, later on, also with M. Sombra and my former student K. Hägele). Last but not least, I have devoted an special effort to understand lower complexity bounds of several problems in several contexts as Algebraic Complexity Theory (including a solution to M. Ben-Or's conjecture on the usage of higher order Betti numbers as lower complexity bound, published with J.E. Morais and J.L. Montaña) or to prove exponential lower complexity bounds for universal, geometrically robust algorithms for eliminating a single block of existencial quantifiers (most of them with J. Heintz and G. Matera).
I organized (either in the scientific committe or in the local committee) scientific meetings and conferences. Colleagues found interesting to invite me to give several plenary and invited talks. Throughout these years, as far as I had financial support, I presented a more than considerable number of notable referred communications in many conferences related to Computational Mathematics.
I have been invited to visit several scientific Laboratories and Universities.
I have leaded several National Research Grants (Competitive Projects) and participated in many since 1985.
Proud survivor of the overly selected, supposedly elitist and somehow traumatized, 1st Promotion of Mathematicians ever formed in Cantabria (October 1979-June 1984). I did my PhD Thesis in Mathematics under the smart advising of Tomás Recio, winning an FPI Predoctoral Grant (Jan., 1985-Sept., 1987). I defended my PhD Thesis in February 1987. On October, 1st of 1987, I became a (tenured) "Profesor Titular" of "Algebra" (25 years old). On January, 1988, I had to leave the the University, returning to the academic system in February 1989. I became "Catedrático" of Algebra in 2010. I returned in 1989 with the firm conviction of devoting most of my time and effort to the scientific training of young mathematicians through a high quality doctoral program in Mathematics at the University of Cantabria (the program no longer exists). I was advising my first PhD Student (J. L. Montaña) when I was 27 years old and my first supervised PhD Thesis was defended when I was only 30 years old. Since then I have tried to interpret my research as a search for less traveled paths on the frontiers of mathematical knowledge, accompanied by a doctoral student who thus gains training as a researcher.
In December 2024, after more than 45 years serving to University of Cantabria and more than 40 years of teaching, I decided to retire as Professor Dr.. My retirement was intended to be an active retirement in scientific research, continuing, at a different pace, to explore the paths of knowledge, both as author or as editor of scientific material.
I have taught at the University of Cantabria for 40 years. I began in February 1985 with a full course on "Galois Theory" (in those times, pre-doctoral students on FPI scholarships were responsible for full teaching duties) and concluded my teaching tasks in November 2024, my last teaching task being an introductory course on "Commutative Algebra". In all these years, I have taught many courses either of undergraduate or graduate programs. I have devoted more than 5500 hours lecturing in a classroom, not counting the preparation, correction of excercises and topics, exams or tutorial hours, which, obviously, were much more than these. Among undergraduate teaching duties, I have also advised 15 TFG's (graduation thesis that students must develop before obtaining their degree). I was committed with courses in Mathematics Studies (as Commutative Algebra, Linear Algebra, Computer Algebra, Algebraic Geometry, Geometry or General Topology), Computer Engineering (as Introduction to Logic for Computer Scientists or Automata Theory and Formal Languages), Physics (Linear Algebra) or Nautic Studies (Linear Algebra and Spheric Trigonometry). Among graduate courses I was committed with several courses in the Master Program of "Mathematics & Computation" as Computational Complexity. Effective Methods in Algebraic Geometry, since its occurence in 2008. In former Doctoral Program in Mathematics courses I taught many different courses as Introduction to Computational Complexity, Real Algebraic Geometry, Algebraic Complety Theory, Algorithmic Algebra and others.
I have also assumed several duties and services to the Academic Community in different structures of the University of Cantabria, in national and internatonal Scientific Committees or as chosen delegate of the unions CCOO and UGT in several 4-year election periods. I was also the founder and first director the Research Group M&CFLAI (Mathematics & Computation: Foundations, Learning and Artificial Intelligence) until December, 2024.
Along my scientific career, I also have obtained Finantial Support for my Research Group through several sources.