I received a Ph.D. in Mathematics from the University of California at Berkeley in 1998. My advisor was Prof. George M. Bergman. My thesis is about dominions (in the sense of Isbell) in varieties of groups. Another way to think about it, in terms perhaps more familiar to group theorists, is that I studied special amalgams and strong embedding of special amalgams in certain kinds of categories of groups, namely those which are closed under arbitrary direct products, subgroups, and quotients.

   After graduating I went back to Mexico's Universidad Nacional Autónoma de México (UNAM), where I had obtained my undergraduate degree, also in Mathematics. There, I held a temporary position as Investigador Asociado 'C' at the Instituto de Matemáticas (Fellow or Researcher).

   I was a Visiting Assistant Professor position at the Department of Mathematical Sciences of The University of Montana in 2002-2003, and an Adjunct Assistant Professor in 2003-2005. I am now an Assistant Professor at the University of Louisiana in Lafayette.

   My duties include teaching courses and continuing research. I have continued my thesis research, trying to cast it in more mainstream terms. Among the results I have obtained since graduating is a complete characterization of the special amalgamation bases for nilpotent groups of class at most two (the strong and special bases had been characterized earlier by D. Saracino). In 2001 I substantially extended B. Maier's work on embedding of amalgams of nilpotent groups of class two, giving a uniform characterization for embeddability in all subvarieties of the variety of all nilpotent groups of class two. From it, I also derived a description fo the weak, strong, and special amalgamation bases for each subvariety.

   I co-wrote a paper on Number Theory with David McKinnon from the University of Waterloo (which will be published in The American Mathematical Monthly). More recently, I have been working on the problem of capability of groups (whether a group, and particularly a finite p-group, is isomorphic to the inner automorphisms of some group), and have obtained several results. For more information, see my preprints page. I am also working on some problems relating to several classes of epimorphisms, with Robert Raphael from Concordia University.

   I have a very broad mathematical background, which allows me to teach a wide variety of courses. I also have a continuing interest in Number Theory, Arithmetic Geometry, and cryptology.