I obtained a B.Sc. degree (UNAM, 1974) in actuarial sciences. Before that I held jobs related to actuarial sciences 1970-1973. Thanks to the influence of Alejandro Bravo, UNAM, I registered in a M.Sc. program (mathematics) in 1973. Under the supervision of Francisco J. González-Acuña (Fico), I obtained a M.Sc. degree (UNAM, 1975). Thanks to the support of Fico, I was accepted as a Ph.D. student at the University of Cambridge, UK in 1976. Under the supervision of W.B.R. Lickorish, I obtained a Ph.D. (mathematics) in Cambridge by January 1981 with a thesis “On Knot Primness’”. It is my pleasure to say that during my last year as a graduate student, I had the privilege to spend 1979-80 at UC Berkeley working under the supervision of R. Kirby.
In May 1981, I became an Assistant Professor at the Instituto de Matemáticas, UNAM. My research interest mainly stayed in knot theory until 1986. I published two papers on knot primness. My first incursion into the administration happened in 1984-85 when I served as Secretario Academico of the Instituto. After this short period as administrator, my research interest turned to the general problem of studying low dimensional manifolds complexity by the minimal number of (open) subspaces with a fixed property that cover the manifold. The classical example is the Lusternick-Schnirelmann (LS) category where the fixed property is being contractible in the manifold. It was when I had the honor to start a lifelong collaboration with my teacher Fico.
I took my first Sabbatical year 1987-88 at Ruhr Universität Bochum having the great opportunity to have Heiner Zieschang as a host. It was when I met Wolfgang Heil for the first time. Since 1989, I have had the privilege to have also a lifelong collaboration with him. Also, by 1991 I became Associate Professor at the Instituto.
While mainly working on LS type invariants introduced by Clapp and Puppe in 1986, two events occurred in 1992. I moved to CIMAT as Full Professor and my second period as academic administrator happened, as I became President of the Mexican Mathematical Society 1992-1996.
After those very interesting and stimulating four years, where I had the chance to meet and work for the Mexican mathematical community, I had the opportunity to become a Visiting Professor at Florida State University 1997-1999. I did research with W. Heil and I attended De Witt Sumners Seminar on application of topology. Since then and thanks to De Witt my interest in applications has been alive.
Back in CIMAT in 1999 and still doing research in LS type invariants I became director of CIMAT 2003-2008. This was my last incursion into academic administration and it was a difficult time for doing research.
After this period and thanks to Fico and W. Heil, I reassumed research on LS type invariants. By 2014, I had 26 papers published related to these invariants as coauthor mainly with them and some other colleagues like J. Hoste, Víctor Núñez and V. Turaev.
In 2014-2015, another important event occurred. I was invited to spend a Sabbatical year at CIDE. CIDE is another Mexican research center, similar to CIMAT but oriented to Social, Economy and Political Sciences. Researchers at CIDE require data analysis. It was when I became aware of TDA (Topological Data Analysis). Also, I remembered my attraction to DNA topology as Sumners taught me at FSU. As a consequence starting in 2015, I attended many activities related to applications of geometry and topology and then, I became interested in what we call 2-stratifolds and foams. At the time of writing, in collaboration with Fico and W. Heil, we have eight papers published related to these topics.
During all these years I have taught over 70 courses, mainly on topology, at UNAM, CIMAT, Universidad de Guanajuato, UAM, UAMex, CIDE, FSU and UT Dallas. Also, I have had thirteen students (2 Ph.D., 3 M.Sc., 6 B.Sc., 2 research undergraduate projects) and presently have five students (one Ph.D., 4 B.Sc.). Also, three postdocs and one Catedra Conacyt have worked and work at CIMAT under my leadership.
I have given over one hundred talks, at least half of them outside Mexico. I have been the lead organizer of over a dozen national and international congresses, workshops, or schools, some of them large (over 1500 people). I have co-organized over a dozen Seminars on Topology. Currently, I am co-organizer of the international web-seminar GEOTOP-A.