COSAM News Articles 2020 August Q and A with Ulrich Albrecht

Q and A with Ulrich Albrecht

Published: 08/11/2020

By: Luke Oeding

Ulrich Albrecht joined Auburn University in 1984, became full professor in 1994, and has served as a department chair, graduate program officer, faculty senator, and has given his talents in many other roles in the department and university. He is currently nearing completion of his term as interim chair. Luke Oeding, assistant professor of mathematics and associate chair and undergraduate program officer, (digitally) sat down with him to get some of his perspectives on his 36-year career at Auburn.

Q: What was your trajectory [where you grew up, where you studied, and what other places you worked] that brought you to Auburn?

A:  I grew up in Essen, Germany.  I attended the University of Essen studying mathematics and physics and graduated in 1980 with a M.S. in Mathematics.  After graduation, I went to New Mexico State University from which I received my Ph.D. in Mathematics in 1982.  After two one-year post docs at the University of Duisburg, Germany, and Marshall University, W.V., I came to Auburn in 1984.  I obtained my German Habilitation in 1986.

Q: What is your favorite Mathematical Theorem (and why)?

A:  There are many interesting and beautiful theorems in Mathematics, so picking a favorite one is somewhat difficult.  However, the structure theorem for finitely generated modules over a principal ideal domain is probably my favorite.  In addition to being a beautiful result which classifies an important class of modules completely, it also has very interesting applications.  For instance, it is essential for proving the existence of canonical forms in Linear Algebra.  Even more important, it has opened a multitude of other research questions of which I only want to mention a few:

1)           Which domains have the property that all finitely generated modules are direct sums of cyclics?

2)           What happens if one has a domain other than those in 1)?

3)           What can be said about modules which are not finitely generated?

4)           What happens in the non-commutative case?

Q: What's your favorite experience teaching Math?

A:  My favorite moments teaching mathematics have been those when a student discovered that there is so much more to mathematics than just solving computational problems.  This may be a student in a calculus class who suddenly becomes interested in the theory behind the course material, or a graduate student who wants to know more about the material in a course and asks: where can I read more about this?

Q: Which of your research results are you most proud?

A:  Having written over 100 papers, there are quite a few results I am proud of, but there are two groups of results which I am most excited about.  The first can be found in my Habilitation thesis in Germany.  It introduced the notion of an A-solvable group as a central tool for investigating the relationship between Abelian groups and their endomorphism ring.  The results of this thesis have given rise to a series of papers in various areas of Abelian Group Theory, and still provide a central tool for everyone working on endomorphism rings of modules.

The second group of results began with a joint paper with Laszlo Fuchs and John Dauns from Tulane University in which we classify all rings for which the classes of non-singular modules and Hattori-torsion-free modules coincide. This result gave rise to a several additional publications addressing the question of how properties of modules over integral domains carry over to a non-commutative setting.

Q: Of your many accomplishments at Auburn, which are you most fond of?

A:  I am most fond of the fact that my colleagues trusted me to serve as Department Chair in 2000, and then again in 2018 and 2019.

Q: What do you want to do when you grow up (AKA Retire)?

A:  My immediate plans include travelling when the COVID-19 situation has improved.  Until this happens, I plan to work on my model railroad, and make some upgrades which I did not have time to do while working.  Also, there are a few research problems left which I will look at again since I have more time available now than in the last two years.

It may come as a surprise, but mathematics was only my second choice of a subject to study.  I would rather have become a historian when I graduated from high-school in 1976.  However, a look at the job market in history put a rapid end to that idea.  I plan to read and study various areas of history I am interested in, in particular Byzantine history and military history.  Maybe, I might even do some research.

Q: If I might be so bold to ask, what do you hope will be your legacy?

A:  I have always taken a holistic view of mathematics (and statistics).  While all mathematician have a specialty, we should see ourselves as mathematicians first, and only then as algebraists, statisticians and so on.  Both as a faculty member and as an administrator, I have strived to implement this vision, and it is my hope that my view of mathematics will prevail at Auburn University.

Q: Any advice for a young mathematician/statistician?

A:  I believe that young researchers should work on their projects with the goal to increase their knowledge and produce beautiful new results.  They should not worry about tenure and promotion, nor should they try to reach these by appearing to do what is “popular”.  If one does research for the love of research, then the advancement will come by itself.  On the other hand, agonizing too much about the future will interfere with one’s success.

Mathematics is great and wonderful, but there is another world out there.  Travel, enjoy your family (if you decide to have one), and develop other interests.  After all, you will be more productive as a mathematician if you can give your brain a chance to rest by focusing on something else.

Finally, try to be a good colleague.  There is so much more to be gained by helping, respecting, and understanding others.  Your colleagues will do things differently from you, but this does not mean that their work is more or less important than yours.

We're all very thankful for all you've given to DMS, COSAM, and Auburn. You will certainly be missed around Parker Hall. Don't be a stranger!