31 January 2023

Obituary for Christian U. Jensen


Professor emeritus Christian Ulrik Jensen has died. His life is described here by Jørn Børling Olsson and his research by Søren Jøndrup, with contributions by Ian Kiming.

Chr. U. JensenChristian Ulrik Jensen (known as Chr.U), professor emeritus of mathematics at the University of Copenhagen, was born on November 6th, 1936 in Frederiksberg, Denmark, and died on January 12th, 2023 in Holte.

In many ways, Christian was an unusual and eccentric person who travelled his own path. Yet at the same time, he meant so incredibly much to so many of his colleagues and students.   He was an excellent mathematics researcher, who for more than 50 years, was a committed lecturer at the University of Copenhagen, which many students found very inspiring. After this tribute, Søren Jøndrup and Ian Kiming write about his research.

Christian grew up in Frederiksberg and graduated from Frederiksberg Gymnasium in 1955. By 1959, he had graduated with a cand.mag. and a mag.scient. degree in mathematics from the University of Copenhagen's Department of Mathematics. He would be affiliated with the department for the rest of his life. While studying at the University of Hamburg in 1959-60, he met H. Hasse and E. Artin. He became an amanuensis (assistant lecturer) in 1960 and a lecturer (associate professor) in 1962. From 1972 until his retirement in 2006, he was a full professor. Christian was invited to be a guest lecturer at US and Canadian universities on several occasions from1975-1990. In 1975, it was at the suggestion of the National Science Foundation.

Christian was a man of the old school, equipped with an incredible general education, of a quality that has long since vanished. He dressed conservatively at the department, wearing a suit and tie. Though he wasn't fond of changes, he generally embraced them in the end. One notable exception was that he clung to the pre-1948 reform of Danish orthography until the end of his days, in which Nouns are capitalized, among other things.

He mastered the main languages, as well as both spoken and written Russian. Despite an occasionally sulky appearance, he was a friendly and outgoing person. Talking to him was easy. Those who conversed with him benefited from his vast knowledge, phenomenal memory and genuine interest in whoever he was speaking with and their opinions, including on non-mathematical matters. At times, he could be provocative and say things that were politically incorrect. But he did so in his own special way, entertaining and with a twinkle in his eye. Sharing his company was always a pleasure.

Christian's presence at the department was characterized by constancy, even after his retirement. If not prevented, he nearly always showed up at the "usual time" – which in his case, was mid-to-late afternoon. This is when he would talk to many of his colleagues (those who were still around) and students, and corresponded with his large international network of acquaintances. Despite his late meeting time, he was surprisingly well-informed about what was happening at the department – at least until it began to expand tremendously. While some guests may have been puzzled by his eccentricity at first, any confusion was quickly swept away once they got to know him. And then, they never forgot him.

Christian was unmarried, had no relatives and lived all his life in the same large apartment on Carit Etlars Vej where he was born. The apartment was dark and filled with furniture and other items that seemed to have always been there. Within it, there was a unique collection of rare and precious books. Among the many books are complete collections of first editions by famed Danish authors such as Hans Christian Andersen and Søren Kierkegaard, as well as foreign books and incunables.   The volumes weren't just for decoration. He had read many of them and was delighted to show the most interesting ones to his guests. Christian also owned a rather modest cottage on Vasevej in Holte with a large plot of land. This is where he enjoyed weekends. Like the apartment, it was stocked with furniture and books.

At the beginning of 2020, Christian became seriously ill and was in various hospitals until November 2020, when he returned to his apartment. Here, he was able to get by with home care and his housekeeper. During his illness, a group of visiting friends was formed. These included former colleagues and students, all of whom provided him with company and support. Despite growing health problems, including Parkinson's, Christian was of sound mind until he unexpectedly died in his cottage after a fall.  The day before, he had been at the department for the last time.

Christian lived frugally and leaves a not-inconsiderable fortune, part of which will go towards a scholarship for Danish mathematicians.

Jørn Børling Olsson

Tribute to Christian U. Jensen's research

Christian U. Jensen made many significant and original contributions in many areas of mathematics. 

After studying in Hamburg with Hasse, Christian's first area of research focused on various problems in classical algebraic number theory, especially non-Pellian equations. This resulted in two smaller publications. These studies led him to the study of Prüfer rings and the general Ring and Module theory. In this context, a small but elegant work on the projective dimension of countable connected flat modules can be mentioned; as an often and still cited work. Christian's result was generalized by B. Osofsky, who demonstrated a correlation between the projective dimension of the quotient field of certain polynomial rings and the continuum hypothesis.

Christian continued to work in the field of homological dimension theory and started to investigate the derived functors of inverse limits. This work was summarized in a Springer Lecture Note. Among many other results, he and L. Gruson proved a famous theorem by Gruson and Raynaud (A noetherian; FPD(A) = dim(A)).

Christian concluded his work on the topic by applying model theory to algebras, and in particular, algebras of the finite representation type, where a significant contribution was made to the still unsolved problem:

If any left module is a direct sum of finitely generated left modules, does the same then hold for right modules?

In this context, Christian wrote an often-cited book with H. Lenzing, which is a classic on the subject.

Christian then became preoccupied for many years with various problems within Galois theory, especially Inverse Galois Theory, the study of embedding problems, the realization of groups such as Galois Groups via explicit polynomials, and the theory of so-called generic polynomials. This work was summarized in a book authored with Arne Ledet and Noriko Yui.

For the last few years, Christian returned to Ring and Module Theory. Together with Anders Thorup and myself, Søren Jøndrup, we found great pleasure in examining compact rings. In doing so, a new light was cast on some of Christian's previous achievements.

Christian was an inspiring lecturer, and his notes on homological algebra (Mat 322), 3 AL and 4 AL have been highly appreciated. They deserved to be published as textbooks in English.

Søren Jøndrup, with contributions by Ian Kiming