In memoriam: Jonathan Rogawski
Professor of Mathematics, 1955 – 2011

Jonathan Rogawski
Professor Jonathan Rogawski passed away on September 27, 2011, after a long battle with cancer. Rogawski was a key figure in the dynamic and central field of automorphic forms. He was 56 and had been ill for nearly a decade.

Rogawski was raised in the Brentwood district of Los Angeles and attended the Palisades public high school. He began his higher education at Yale University from which he received simultaneous BS and MS degrees in 1976. He did his PhD research at Princeton University and received his mathematics PhD in 1980 from that school. His thesis advisor was Robert P. Langlands, author of the visionary Langlands Program which asserts the existence of remarkable connections between the fields of infinite dimensional representation theory, algebraic geometry, number theory and automorphic forms. After his PhD, Rogawski held positions at the SFB at the University of Bonn (1980 – 1981), Yale University (1981 – 1983), the Institute for Advanced Study (1983 – 1984), and the University of Chicago (1984 – 1986). He came to UCLA as associate professor in 1986 and advanced to full professor in 1989.

From the start of his career, Rogawski had a very strong awareness of the revolutionary potential of the ideas of Langlands. His early papers established him as a gifted researcher at the forefront of what was quickly becoming a new field. As the first representative of this new wave at UCLA, he was key to attracting to the mathematics department other members of the current number theory group. He also initiated a vital interaction with the growing group of number theorists at Caltech. Michael Harris (University of Paris 7), a leading senior mathematician in the field, wrote that it is "largely because of his energy and his vision that Los Angeles became one of the world's leading centers of number theory."

Rogawski's papers from the 1980s are striking in reach. The majority concern topics in representation theory and harmonic analysis. For example, his 1983 paper "Representations of GL(n) and division algebras over a p-adic field" proved the Langlands correspondence in that setting. Another 1985 paper of that period, also among his most cited, proved basic results about the fundamental class of representations which have Iwahori fixed vectors. However, he also worked on the global number theoretic side, giving (also in 1983, with J. Tunnell) an extension to Hilbert modular forms of a celebrated result of Deligne and Serre concerning Galois representations. This was perhaps the first time that a hard problem on a split group of natural interest was solved, via the global Langlands correspondence, by studying the corresponding problem on an inner form. Today, this technique is fundamental.

At the end of his early phase, Rogawski completed his masterful 1990 book Automorphic Representations of Unitary Groups in Three Variables, published in the prestigious Annals of Mathematics Studies. The book, which realized a dream of his student years, established an extremely important family of results, including the stable trace formulae, for these groups. It was the first work to fully develop the stable trace formula beyond SL(2), and it remains today the only case beyond SL(2) which is completely treated. The monograph brought him broad fame in the subject and provided a partial template for later research, still ongoing today, into the general multivariable cases. He supplemented the book by making several fundamental contributions to the 1992 collaborative volume The Zeta Functions of Picard Modular Surfaces in which the zeta functions of the Shimura varieties attached to unitary groups in three variables were studied. These results also set the standard for the field, and even today their analogues have not been fully established in the n-variable case.

In his second decade of research Rogawski built further, pushing the subject in directions unanticipated at the start of his career. For example, in a much-cited 1993 paper, joint with Blasius, he showed how the novel phenomenon of endoscopy, discovered by Langlands, and studied in detail in his monograph on U(3), could be used to give a geometric construction of the important Galois representations attached to Hilbert modular forms. This research was "the main model for the Paris automorphic forms book project" (Michael Harris). That project, now nearing completion, is a complex endeavor of many mathematicians to extend the results of Rogawski's 1992 book, as well as the later collaborative volume, to n-variables.

Another topic where Rogawski made a basic contribution is the connection between the theory of L-packets and the venerable theory of theta functions; the latter area is called the Weil (or oscillator) representation by many workers now. While the trace formula and harmonic analysis can be used to establish a canonical correspondence between characters of different groups, as well as to understand the internal packet structure of the characters of a group, the Weil representation provides a direct correspondence between different representations themselves. Rogawski, with Gelbart and Soudry, initiated this study, obtaining a complete description of L-packets via the Weil representation in the context of the unitary group in three variables. This work, which uses many methods including the trace formula and the regularized Siegel-Weil formula, required developing the theory of the Shimura integral (of Shintani and Piatetski-Shapiro) for U(3), and overall it too is a template for later work. A third theme of this period, extending into the 1990s, is the theory and application of the relative trace formula which was introduced by Jacquet in the mid-1980s. Rogawski's four papers on this topic developed the theory for U(3), eventually proving the local and global genericity conjectures for this family of groups.

In the last decade, especially after he became ill, Rogawski published less research. Nevertheless, he published two significant papers. The former, with Lapid, obtained new results toward a recent important conjecture of Clozel about the spectral structure of restrictions of representations to subgroups. The latter, with Ramakrishnan, used the relative trace formula for GL(2) in a novel way to prove a result about non-vanishing of L-functions.

Throughout his career, Rogawski truly enjoyed interacting and working with other mathematicians. His numerous collaborators found his speed and organizing ability remarkable. After a productive meeting he would prepare notes that frequently found their way, almost unchanged, into the final manuscript. His mathematics co-authors were Blasius, Friedberg, Gelbart, Glaubermann, Jacquet, Knapp, Kottwitz, Lapid, Lubotzky, Ramakrishnan, Soudry and Tunnell. Many became personal friends. In addition, Rogawski co-authored two papers in mathematical economics, one with Shubik and one with Dubey. For many years, until just before his death, he was the editor in charge of papers in number theory and automorphic forms for the Pacific Journal of Mathematics.

Between 1995 and 2009, eight students received their PhD under Rogawski's supervision. As an adviser he was patient and gentle, but highly effective. He was superb at choosing interesting research problems which were appropriate for the student and which generated interest from other mathematicians when solved. He inspired respect and affection from his students. All his students remain in research and teaching.

Rogawski was a gifted musician who played violin in the Yale Symphony Orchestra, as well as in his high school orchestra. He recalled with pleasure the Vienna stop of a European tour with the Yale Symphony. Rogawski also played classical guitar, and he played chamber music on both instruments with musical colleagues in his younger years. One of the undersigned remembers vividly the 1977 Corvallis conference on the Langlands program where Rogawski, who was one of the youngest participants, played the violin sonatas of Beethoven (especially the Kreutzer, which is difficult) with Don Zagier at the piano, during the evenings. He loved listening to music, and he was delighted when two of his recently finishing research students gave him an iPod as a reverse graduation gift. He used it all the time.

From the beginning of his time at UCLA, Rogawski was committed to teaching calculus. He felt that this was an area where a teacher could have a fundamental early impact on the intellectual development of students. In 2000, the department recognized his teaching with the Sorgenfrey Distinguished Teaching Award. In the late 1990s, he wrote notes for a potential calculus text, believing that there was an open place for a general text that maintained a spirit of rigor within an informal style of presentation. He wanted his text also to communicate some of the beauty of the subject while always making it clear how important a tool calculus is for understanding the world. In 2007, his text Calculus appeared, published by W.H. Freeman. Now in its second edition, it has filled that place and become one of the leading texts in the country, in use at universities, including UCLA, colleges and high schools. It is a testament to his character that he was able to complete such lengthy complex tasks, essentially commencing what for many would be a new career, while under treatment for life-threatening illness.

Jon Rogawski was a gentle, kind, and deeply religious family man. He was also a wonderful colleague who took joy in his work, in others, and in life. He became a true master of what he studied or reflected upon. While he had a sure hand when working with other people, he was never doctrinaire, even when he knew the right answer or held a definite view. Discussion with him always had a sense of discovery and possibility. Several of the undersigned spent many happy luncheon hours with him, which were delightful because of the wide-ranging nature of topics discussed, and the light shed on them by Rogawski's penetrating mind. Rogawski was a rare personality, without egotism, and informed by balance and equanimity. Although very busy and careful with his time, he was generously available for students and colleagues who needed help, even when their ideas were unclear. Rogawski loved new ideas and was endlessly curious about the world. He wanted profoundly to understand how things work, from economics and finance to particle physics. Even in his last days, he was interested in recent results in physics and astronomy.

Rogawski is survived by his wife Julie, his three daughters Rivkah, Dvora, and Hannah, and his son Akiva. His mother Elise and his brother Michael also survive him.

Jon Rogawski will be much missed by his family, friends and colleagues.

Don Blasius, UCLA Mathematics
Haruzo Hida, UCLA Mathematics
Dinakar Ramakrishnan, Caltech Mathematics
Veeravalli Varadarajan, UCLA Mathematics