Sergio López-Permouth was born and raised in Guatemala City, Guatemala, where he studied mathematics at Universidad del Valle de Guatemala. He then moved to the United States and completed graduate degrees from Ohio University and North Carolina State University. While living in the United States, Sergio has remained involved with mathematics in Latin America, mentoring undergraduate theses in Guatemala and El Salvador, organizing special sessions for joint meetings of AMS and SMM and participating in conferences in Brazil, Colombia, Costa Rica, Guatemala, Mexico, and Uruguay.

After completing his doctorate in 1985, Sergio has been with the faculty of Ohio University, where he has served terms as chair of the department of mathematics and of the university faculty senate. He is currently the John F. and Rita L. Wilson Professor of Mathematics and the director of the Ohio University Center of Ring Theory and its Applications (OUCRA).

At Ohio University, Sergio has advised more than 25 doctoral students, and, with OUCRA, he has mentored many postdoctoral visitors from all over the world.

Sergio is the author of about 100 papers and has edited several research volumes. He has been an executive editor for Journal of Algebra and its Applications and a member of the editorial board of several other journals.

Sergio has enjoyed a nice partnership with Ohio State University, where they organize a biweekly ring theory seminar that attracts mathematicians from throughout Ohio. With OSU, Sergio handled the algebra portion of SAMMS, a collaborative program of OSU and Universidad de Puerto Rico, Río Piedras, which offered a taste of graduate level mathematics to students from underrepresented areas. One of Sergio’s proudest accomplishments was to publish a research paper in the Pi Mu Epsilon journal of mathematics, a venue dedicated to undergraduate research, which resulted from collaborating with SAMMS participants.

Sergio’s research displays an eclectic taste as he tackles a variety of algebraic structures. He is just as likely to be considering foundational questions about modules over non-commutative rings, as he is to be pondering questions about what happens when you let binary operations to create new ones, or to be trying to expand structures from infinite sums to infinite products via summability notions. In the middle of it all, he also frequently finds the time to consider applications in the realm of information and coding theory.

Early on, Sergio emphasized the study of modules over noncommutative rings, focusing largely, but not exclusively, on injectivity and related properties. A unique twist that Sergio and his collaborators have offered within module theory is the development of a sort of gauging theory for properties; the profiles and portfolios they have introduced have offered a tantalizing template for researchers in module theory and other areas.

The distinctive feature of Sergio’s approach is an emphasis on studying, not only modules that satisfy a given property, but, rather, in measuring the extent to which other modules satisfy it. Sergio’s program has paid extensive attention to those modules which, in some sense, are farthest possible from satisfying a given property. This focus led them, for example, to introduce the notions of poor modules, those which are the least injective, in the sense that they have the smallest possible domain of injectivity. Sergio’s team has championed the notion that there is an inherent interest in these poor modules, which are just as ubiquitous as their injective counterparts.

From Sergio’s perspective, the category of modules over a ring can be divided into strata which are characterized by their portfolio within the profile of the ring. Understanding the distribution of the portfolios allows the characterization of the rings themselves.

One of the most remarkable features of this philosophy is that the template can be extended to other properties of modules such as projectivity and flatness. While alternative profiles and gauging theories may be motivated by the injective template, the specific structures obtained in alternative settings can be strikingly different from each other. These differences will provide insight to better understand the diverse nature of the various concepts and properties in this discipline.

In fact, the applications do not stop with module theory and the patterns have been used to analyze concepts in other projects. For example, another area of Sergio’s work, the basic module extensions induced by amenable bases of infinite dimensional modules over arbitrary algebras, can be significantly enhanced with this type of philosophy. Looking at things under such prism has given rise to the notion of contrarian bases which, as was the case with poor modules, seem to be as ubiquitous as amenable bases are. The study of amenability of bases considers the feasibility of extending the module structure of some infinite direct sums to the equally indexed products so that the basis for the sum acts as a surrogate for a basis for the product.

“Hispanic Heritage Month is an opportunity to celebrate the accomplishments of Latin people in the United States and their contributions to all aspects of life. As a Guatemalan working in the United States, I am proud to represent my country in the area of mathematics. Anything I achieve is rooted in my formative years at home and in the professional opportunities that I have received as a resident of the United States. I am extremely proud to celebrate and thank both, every step of the way.”

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