Brief Vita & Scientific Interests

Proud survivor of the excessively selected (supposedly elitist) 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 . The same year I became Associate Professor (Profesor Titular) of "Algebra" at 25. In January 1988, I had to leave the the University, returning to the academic system in January 1989. I returned with the firm intention of devoting most of my time and effort to the scientific formation of young mathematicians through a high quality doctoral program in Cantabria. I was advising my first PhD Student (J. L. Montaña ) at 27. Since then I have tried to interpret my research as a pathfinder, seeking less traveled roads in the frontiers of mathematical knowledge, accompanied by a PhD Student who then gets a formation as researcher.

My Research Interests are in 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 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 60 scientific manuscrits. Some of them have been well treated by colleagues, yielding an h-index 16 in Thomson Reuters Web of Science (with more than 600 citations), and an h-index 19 in Google Scholar (with more than 1600 citations in this data basis). I have completed 24 years of positive evaluation ( 4 periods of 6 years each, called "sexenios" in the Spanish academic system). I will apply for next evaluation (of the period 2012-1017) on December, 2017.

Some Milestones of my scientific contributions 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 (also 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 Carlos 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 Teresa 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 conjeture 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 bock of existencial quantifiers (most of them with J. Heintz and G. Matera ).

I also liked Editing, being a member of the Editorial Board of the Journal of Complexity since 2004 and of the Editorial Board of Applicable Algebra in Engineering Communications and Computing since 2014. I have also edited several books and Special Issues of Journals.

I have leaded several national Research Grants and participated in many since my youngest years. I also 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 or invited talks and I presented a few referred communication along these years. I have also been invited to visit several scientific Laboratories and Universities.

I have already completed 30 years of positive evaluation in teaching ( 6 periods of 5 yers each, called "quinquenios" in the Spanish academic system) in December 31st, 2014. This is the maximum number of evaluable periods of teaching, although it does not mean that you don't teach anymore at Spanish universities. It simply means that you may avoid any future teaching evaluation, if you wish. In all these years, I have taught many courses either of undergraduate or graduate programs. Among undergraduates courses 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 and Formal Languages Theory), 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 other duties and services to the Academic Community both in different structures of the University of Cantabria, in national and internatonal Scientific Committees or as chosen delegate of the union CC.OO. .
and 24 years of

Scientific Production

Teaching and Advisory

Service, Committees and Other Duties


  • Address:
    Depto. de Matemáticas, Estadística y Computación
    Facultad de Ciencias, Universidad de Cantabria
    Avda. Los Castros s/n
    E-39071 SANTANDER, Spain.
  • E-mail:
    luis.m.pardo at (preferred)
    luis.pardo at (otherwise)