# Celebrating Professor Manfred Dugas' 70th Birthday

On Friday, April 22, 2022, friends and faculty of the Baylor Mathematics Department gathered to celebrate the 70th birthday of Dr. Manfred Dugas, his scientific achievements, and his 35 years of service to our Baylor Department of Mathematics. On this festive occasion, Dr. Kulumani Rangaswamy (University of Colorado, UCCS) shared about Manfred's life, his widespread career in algebra, and his prolific research contributions to realization theorems.

# Manfred Dugas at 70:

A Survey of his Research Contributions

Manfred Dugas was born on February 11, 1952 in Rhineland-Palatinate, Germany. He completed his college and Ph.D. studies at the University of Kaiserslautern, where he earned his Ph.D. (Doctorate) in 1974 under the supervision of Heinrich Lüneburg for his work on the geometry of Hjelmslev planes. In the same year, Manfred married his wife Karin, a happy relation that is closing in on its golden anniversary. After graduation, Manfred continued his studies in Kaiserslautern, completing another math diploma in 1975 with sponsorship of the German Science Foundation (DFG).

In 1976, on recommendation of Reinhold Baer, Manfred took a position as a postdoctoral associate and assistant at the newly founded University of Essen (now University of Duisburg-Essen) in the algebra research group of Rüdiger Göbel. Just two years earlier, Saharon Shelah, with over 1200 publications one of the most prolific mathematicians alive and the world's leading logician, had solved the Whitehead problem, the question as to whether every abelian group G with Ext(G,'?') = 0 is free. As Saharon demonstrated, this purely algebraic question is undecidable, and the answer depends profoundly on the chosen model of set theory. This result took the scientific world by total surprise and revolutionized our understanding of the interaction between algebra and logic. Manfred and Rüdiger decided to follow Saharon's lead and set out to apply set-theoretic methods to abelian groups, rings, and modules. In the early years, they concentrated on properties of subgroups and quotient groups of cartesian products '?'^{I} of the integers. Soon thereafter Manfred and Rüdiger developed their trademark of "realization theorems" – intricate constructions of groups, rings, and modules with unusual properties using infinite combinatorics and set-theoretic axioms. In 1982, they published their most celebrated realization theorem showing that every cotorsion-free ring is the endomorphism ring of an abelian group, a paper with 130 citations. In the same year, Manfred gave a lecture series on *"Endomorphism Rings"* at the University of Padua (Italy) on invitation of Luigi Salce. Manfred and Rüdiger would continue their extremely prosper collaboration over the years, publishing 28 papers until Rüdiger's untimely death in 2014.

In many other ways, his time in Essen has been a very remarkable one for Manfred. This is the launching pad for his extremely successful career spanning close to 50 active years, two continents, and over 100 publications. Essen is where Manfred first made his name. Realization theorems and set-theoretic constructions have become synonymous with Manfred. His groundbreaking contributions to this area of algebra are ubiquitous and fill a larger part of the book *"Approximations and Endomorphism Algebras of Modules"* (2006 1^{st} Edition / 2012 2^{nd} Edition) by Rüdiger Göbel and Jan Trlifaj. In 1980, he finished his Habilitation, achieving the highest university degree certifying "full professor" qualification. Essen is also where his two children were born: daughter Diana in 1981 and daughter Tanja in 1983.

Manfred's fame soon also made an impression on the algebra community across the pond. László Fuchs (Tulane), the leading expert in abelian groups took notice, and in 1984, Manfred was invited as a visiting associate professor to the University of Colorado (UCCS) by László's close friend and collaborator Kulumani Rangaswamy, also known affectionately as Ranga. Manfred was subsequently hired as a regular associate professor at UCCS in 1985. Manfred and Ranga have remained lifelong close friends. They have mostly worked on completely decomposable groups, Butler groups, and related topics.

In 1987, Manfred published with Adolf Mader and Charles Vinsonhaler another celebrated realization theorem: the existence of arbitrarily large E-rings, commutative rings R with End_{'?'}(R) ≅ R. E-rings and related structures would remain one of Manfred's major interests over the coming years. It was also in 1987 that Manfred was hired as associate professor at Baylor University with strong support by the algebraist Paul Hill, an expert in abelian groups and at that time the Ralph and Jean Storm Chair of our department. The presence of Manfred greatly enriched the research and teaching environment at Baylor on its way to a university with a strong and vibrant research program in mathematics. During this time, he has been working with Jutta Hausen (UH), John Irwin (Wayne State), Ed Oxford, and Saharon Shelah (HUJI, Rutgers).

Manfred's research received continuous NSF support during the years 1987–1990. In May 1990, he organized an NSF funded weeklong workshop *"Set Theoretic Methods in Algebra"* at Baylor that attracted many outstanding mathematicians. In the same year, Manfred became full professor, while David Arnold succeeded Paul Hill with Manfred's strong support as the Ralph and Jean Storm Chair, a position that Dave would hold until his retirement in 2015. Dave was widely renown for his research in torsion-free abelian groups of finite rank and related subjects. Manfred and Dave turned Baylor into an algebra powerhouse, working mostly on Butler groups, near-isomorphisms, and representations of finite posets. Together they published over a dozen articles and were the recipients of another two NSF grants in 1991/92 and 1994/95. Manfred and Dave would remain close friends and collaborators until Dave's passing in 2021.

Manfred relates well with students. During his time at Baylor he has regularly been engaging in undergraduate research and has directed close to a dozen Master's Theses. Two of his students, Amy Maddox and Jeff DaCunha, would continue to earn their Ph.D.s from Baylor. One of his greatest successes in undergraduate research was his work with Bruce Olberding that resulted in a joint publication in 1991. After graduating from Baylor with a B.S. in 1990, Manfred encouraged Bruce to seek a doctoral degree at Wesleyan University. All of this occurred long before Baylor would start its own math doctoral program. Bruce went on to obtain his Ph.D. from Wesleyan as a student of the algebraist James Reid and has since had an outstanding career in mathematics. He is now himself a full professor at NMSU.

Since Baylor started its own math doctoral program in 2001, Manfred has also been very successfully engaging in graduate research. Up to date, he has supervised or co-supervised a total of six Ph.D. students many of whom would continue to pursue their own university careers. This includes Klaus Kowalski (FOM University of Applied Sciences), Kelly Aceves (College of the Canyons), Bradley Wagner (William Jessup University), Jordan Courtemanche (Harding University), and Jackson Rebrovich (Texas State). During these years, Manfred worked with Shalom Feigelstock (Bar-Ilan University) on E-rings and generalizations. With his graduate student Joshua Buckner, he published a total of eight papers on a variety of topics including co-local subgroups, left rigid rings, quasi-localizations, and Zassenhaus algebras. In 2014 history repeating did come full circle with Manfred strongly supporting the hire of Daniel Herden, Rüdiger Göbel's last assistant. Currently, Manfred is primarily working on incidence algebras, finitary incidence algebras, and generalizations in a series of publications with Badley Wagner, Jordan Courtemanche, Daniel Herden, and Jackson Rebrovich. Manfred has been one of the main speakers of the Southwest Local Algebra Meeting (SLAM 2022), a high-profile algebra conference hosted by our department in February 2022.

Manfred is beloved by his students, friends, and colleagues. Thank you for all your help and wise advice throughout these years! Thank you for your great humor that seems to come right out of *All in the Family*! (Have you ever asked your class to negate the statement "Everybody Loves Somebody Sometime"? Well, Manfred has!) Thank you for all your dedication in these past 35 years, shaping and steering our department.

** Manfred, congratulations to your 70th birthday! Thank you for spending half of these years with us! Here is to you and to many more active years to come!**

- Daniel Herden

Associate Professor of Mathematics, Baylor University

## Words About Manfred from our Faculty

Fritz Gesztesy

The very first time I met Manfred was during my interview at the Baylor Mathematics Department in March of 2016. I had been assigned one of the windowless offices near the entrance to the left wing of Sid Rich and suddenly, there he was, a bear of a man barging into my office, striking up an interesting conversation without much ado or small talk. It turned out to be a very typical encounter with Manfred, one I learned to treasure over the following years. Manfred doesn't suffer fools lightly and quickly gets to the point, and when he speaks, he always has something important on his mind. During my brief tenure at Baylor I quickly learned to appreciate his down to earth demeanor and constant voice of reason he represented in our department, especially, in important departmental meetings. His subtle sense of humor, and his collegiality are qualities we will all sorely miss.

A Very Happy Birthday, Manfred, and the very best for your retirement and all your future endeavors!

Baxter Johns

Manfred and I have been friends and office neighbors for many years. Manfred has a great sense of humor. We were talking about smoking one time and he said that he's actually in much better shape because he smokes. He said that every time he smokes a cigarette, he has to walk down three flights of stairs and then back up three flights of stairs. So, the more cigarettes the better!

Manfred actually did my family a great favor many years ago. My wife was a high school geometry teacher and some students (who had been complaining about low grades) went to the headmaster and said that the course and book were too hard. Manfred was clearly the outstanding geometry consultant in Waco (and probably the world) so we got him to look at the text and some of her assignments. He gave a very favorable report and my wife was able to keep her job. So, our standard of living would clearly be lower if it weren't for Manfred!

At one time some of us senior professors, including Manfred, would go to the Faculty Center for lunch. Then I noticed that Manfred was missing for several weeks so I asked him if anything was the matter. He said that he had decided to go to lunch with the lecturers instead because they were a whole lot more fun!

Despite the above comment, I wish Manfred a great retirement and appreciate all he has done for Baylor.

Lance Littlejohn

When I became Chair in January 2007, the first colleague I sought out for advice and perspective on the department was Manfred. After all, Manfred had been at Baylor since 1987 and if anybody had the 'lay of the land,' it was Manfred. He came to Baylor at a time when research in the department – actually, research *anywhere* on campus – was an exceptionally low priority. He came to the department highly recommended by some of the best algebraists in the world. His hiring signaled the beginning of a fundamental change in direction for the department. Manfred excelled in research and his reputation in algebra helped put Baylor mathematics on the national 'mathematics map.' Manfred's presence at Baylor was the main reason David Arnold joined the department in 1990 as the Ralph and Jean Storm Chair of Mathematics. Together, Manfred and David were a 'force' in algebra; they published over a dozen papers together. Over his productive career, Manfred published more than 160 research papers. He also played a significant role in helping develop our young graduate program; he produced six Ph.D. students. Manfred was also instrumental in attracting Daniel Herden to our department, a hire that markedly strengthened our algebra group.

Manfred has always been a quiet, but effective, leader in the department. He is a man of few words but when he spoke in a faculty meeting, we all intently listened. From early on, I leaned heavily on him for his sage advice. I asked Manfred to serve as search committee chair for several consecutive years; I needed someone with common sense and a shared vision for the department. Manfred was the perfect search chair; he was always courteous but he could combine that with a sarcastic bluntness that helped the department stay on course in hiring the best possible people. When it came to deciding which candidate to hire, Manfred will be forever known for introducing the 'Dugas Rule' for voting, a method which continues to serve the department well.

Manfred, I wish you all the best in your retirement. I could not ask for a better colleague. I hope that good health follows you, Karin, and your wonderful family. We are all going to miss you, Manfred... very much!!

Ed Oxford

Manfred is a friend. He was a very supportive colleague during our years together on the faculty of the Department of Mathematics at Baylor University.

Thank you Manfred, Karin, Diana, and Tanja for sharing your lives with us in Central Texas.

Tao Mei

Happy 70th birthday, Manfred! Thank you for being a quiet neighbor (I hope I was not too loud), for being a considerate and supportive colleague, and for lending me your double sided mobile white board. (It worked perfectly well for my seminar, and it was the only one that the whole department had at that time.)

Happy birthday, Manfred, we will miss you!

Ron Morgan

Manfred Dugas has been so important to the Baylor Math Department. He was one of just a few of the very good research mathematicians who helped convert the department into a real research department in the 1980's and 1990's. He obviously produced a lot for Baylor in terms of papers, grants, and reputation, but I also remember how hard he worked at it. For many years, if I came to work on days that faculty were not required to be here, it would be only me and Manfred here working. But guess what, students really like Manfred also. One of my kids took him for Calculus II and liked him (he did not like his Calculus I teacher so much), but other evidence is how students always like to take his classes. Finally, I will add that Manfred has always added character to the department. I remember when I was first at Baylor, while we were having lunch, Manfred gave some whacky opinion about something (maybe how prisoners could be cheaply kept in the desert), and I said to another faculty member later about how funny Manfred was, and he said, "no, he wasn’t joking." I may never know if he was serious, but I know he is interesting.

Bob Piziak

When Baylor decided to go to a research institution, we had an election for the new Chair. Ed Oxford came in first, I came in second. Ed and I lunched nearly every day. There always seemed to be an issue to discuss concerning the new Ph.D. program in Mathematics. But this is about Manfred. Many times, he joined the two of us for lunch. Now Manfred was hired for his research ability which was huge. He came to Baylor from Colorado Springs, and he was up to date on how issues were resolved. He probably doesn’t even realize how influential he was in helping us formulate our new program. Thank you, Manfred.

Daniel Herden

I owe Manfred a whole lot! First and foremost, Manfred has been a hero since my earliest days as an undergraduate and graduate student with Rüdiger Göbel in Essen. Literally every result in our research area is either directly attributable to Manfred or it is related to Manfred's enormous research output and trailblazing efforts. Working with Manfred at Baylor has been an amazing experience! It is simply impressive to see the strength and determination with which he has been pushing forward our work with Jordan Courtemanche and Jack Rebrovich on a day-to-day basis. We have been spending plenty of hours every week on research meetings – and always quite productive ones, thanks to Manfred's ideas and intuition! Manfred is a showcase of German efficiency! There is hardly any day that Manfred does not spend the morning either reading through a fresh pile of papers or typing up some of his most recent notes.

I am very grateful to both Manfred and Karin for all their help and support with taking my first steps in this new country. It is not just that Manfred has been invaluable as a mentor, helping me understand the inner workings of a US university. Manfred has also been helping with all the bare essentials. Manfred was there when I filed for my social security card. And he was there when I opened my first bank account. Gosh, Manfred even helped me with buying my first car! (Which I am still driving, as Manfred predicted correctly! :P)

Manfred, thank you for always having an open ear! I am grateful for all your advice and wisdom throughout these years!