jim cogdell and dihua jiang, coordinating editors · steve’s gift for mathematics and his...
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Remembering Steve RallisJim Cogdell and Dihua Jiang, Coordinating Editors
Steve Rallis
Steve Rallis was born inBennington, Vermont,in 1942. He was an un-dergraduate at Harvard,receiving his BA in 1964.From there he movedto MIT where he was astudent of Bert Kostant,receiving his Ph.D. in1968. His early workwas on invariant the-ory. After graduatingfrom MIT, Rallis spenttwo years at the IAS in
Princeton and two years at SUNY StonyBrook,followed by a number of visiting positions at Stras-bourg, Texas, Notre Dame, and Princeton. Alongthe way, the primary focus of Steve’s researchshifted to the theory of automorphic forms andrepresentation theory, but always keeping invari-ant theory as one of his powerful techniques. In1970 Steve married Michele Kaufmann, who hadreceived her Ph.D. in astronomy from Harvard inthe same year that Steve graduated from MIT. In1977 he became a visiting assistant professor atOhio State University. He became a tenure-trackassistant professor the following year and movedup through the ranks, staying at OSU throughoutthe rest of his career. But he always kept a busytraveling schedule, making regular visits to bothStrasbourg and Israel, where he had active col-laborations for many years. He became professoremeritus at OSU in 2008 and passed away in 2012.
The primary focus of Steve’s research wasautomorphic forms, automorphic representations,
Jim Cogdell is professor of mathematics at Ohio State Uni-versity. His email address is [email protected].
Dihua Jiang is professor of mathematics at University ofMinnesota. His email address is [email protected].
DOI: http://dx.doi.org/10.1090/noti964
and their L-functions. His work was very originaland has left a lasting impact on number theoryand representation theory.
Michael HarrisSteve Rallis used to apologize before explaining hisnew ideas. It was one of his most endearing habits,and it was always a cue to pay close attention.Number theorists have been especially attentiveto his work of the 1980s and 1990s in connectionwith what is called the Rallis inner product formula,which calculates the inner product of a pair oftheta functions as a special value or residue of aLanglands L-function. As developed and refined inan extended series of papers with Piatetski-Shapiro,this formula provides an effective classification ofpoles of L-functions of classical groups. Combinedwith Shimura’s explicit local calculations (whichinexplicably fail to refer to Rallis’s work), Rallis’sformula provides the most natural starting pointfor the study of p-adic L-functions of classicalgroups; a striking application is the proof bySkinner and Urban of the Iwasawa-Greenberg mainconjecture for elliptic modular forms. Kudla and hiscollaborators have adapted the formula to analyzethe central derivatives of L-functions in the settingof a vast program, combining representation theorywith Arakelov theory, to generalize the Gross-Zagierformula.
Number theory has yet to absorb all the lessonsof Rallis’s more recent work, but the process isbeginning. His series of papers with Ginzburg andSoudry provided the basis for the results of Jiangand Soudry on the local Langlands correspondencefor generic representations. His papers on therelative trace formula, mostly with Jacquet, havebeen of crucial importance in recent work of Wei
Michael Harris is professor of mathematics at Uni-versité Paris-Diderot Paris 7. His email address [email protected].
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Zhang and others on the global and arithmeticGross-Prasad conjectures. �
Steve was always a collaborative mathematician.Of the ninety-four citations listed on MathSciNet, allbut seven are joint papers. Among his seventeencollaborators were Gerard Schiffmann, with whomhe collaborated off and on for forty years, as well asHervé Jacquet and part of his “Israeli team” DavidGinzburg and David Soudry.
Gerard Schiffmann“Hi, Gerard. What’s up? I found this paper; it mightbe useful for us!” This was a typical start of a dayworking with Steve. Never short of ideas, alwaysenthusiastic, very tenacious—once convinced thatsomething should work, he would never give upuntil he succeeded.
I first met Steve in Princeton. Both of us werespending the academic year 1969–1970 at the IAS.We started to work on the oscillator representation.It took us several years, two of which Steve spentin Strasbourg. It was perhaps at that time thathe adopted his amazing work schedule: six orseven days a week from early in the morningto late in the evening! Steve went back to theStates and eventually settled in Columbus. Alsothat year in Princeton I met Michele for the firsttime, just a few months before their wedding.Later during their stay in Strasbourg my wifeand I had many occasions to visit with them.Early in their relationship Michele recognizedSteve’s gift for mathematics and his devotion toresearch. Remarkably, throughout Steve’s careershe managed to maintain her career in astronomywhile facilitating his life in mathematical research.
I met Steve again in 1987. He had invited meto Columbus, the first of a long series of visits.Mathematically, he had matured and within a fewyears he had become a leading expert in his field,due in part to his collaboration with Piatetski-Shapiro. Feeling less pressure, he relaxed andenjoyed more of the social life of the university. Hedid his best to play the absent-minded professor,hardly visible among the piles of papers in hisoffice, but I remember many discussions withhim on topics outside mathematics. He remainedhighly focused on his work but was very perceptiveof everything around him. He had a sharp mind,sometimes a sharp tongue, but above all he was avery generous person with his collaborators andhis students.
The last years were sad. Until the end, he triedto go on with his work, but he was less and lessable to do so. The last thing we did, in 2011, was
Gerard Schiffmann is professor of mathematics atthe Université de Strasbourg. His email address [email protected].
to rewrite a short note of his which complementedone of his old papers. I wish I could still hear himsay, “Hi, Gerard. Let’s start a new project. What areyou up to….” �
Hervé JacquetI wrote a few papers with Steve Rallis. Since Stevehad many collaborators at the same time, this wassomewhat of a challenge because, at times, one hadto struggle to get his attention. At a conference, forinstance, one had to wait patiently in line to get achance to talk to Steve. Moreover, it was difficult tokeep track of the ongoing work of Steve with othermathematicians (work which could be relevant tomy work with Steve). On the other hand, once onecould get Steve’s attention, working with him wasa pleasure. I still have lengthy unpublished notesfrom our collaborations.
Steve’s erudition was astonishing. Rather thanlooking up a reference in the mathematical litera-ture, it was much easier to call Steve on the phoneto find out the facts.
Of the papers we wrote together the mostinteresting ones are also the most tentative. Thereare papers where we conjecture or simply suggestnew relative trace formulas. Steve’s erudition wasof paramount importance in formulating theseconjectures. �
David Ginzburg andDavid Soudry“Hey, the first team is here!” We still hear Steve’svoice, greeting us happily, each time the threeof us met. Indeed, we were a team, and Stevewas our captain. Steve used to come to Tel Avivand visit Piatetski-Shapiro, already in the early1980s. Each one of us was a graduate studentin those days. Steve had a keen interest in ourwork, listened to questions, gave his advice, andshared his vast knowledge and his personal ideasgenerously. Steve became our mentor, and as theyears went by, we teamed up and worked together,visiting each other frequently. Working with Stevewas a great experience for us, still very vivid in ourminds: Steve’s great passion for mathematics, hisenthusiasm and devotion; times of breakthrough,moments of frustration; meeting together the nextmorning and sharing our separate thoughts of thenight before; taking a break and getting coffeeor ice cream, playing pool, or bowling. Togetherwith Steve, we did our best mathematical work.
Hervé Jacquet is professor of mathematics at Columbia Uni-versity. His email address is [email protected].
David Ginzburg is professor of mathematics at Tel Aviv Uni-versity. His email address is [email protected].
David Soudry is professor of mathematics at Tel AvivUniversity. His email address is [email protected].
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Rallis and his coworkers.
We feel very privileged to have known Steve, tohave learned from him and worked with him.Working with Steve was accompanied by manyconversations about life, personal memories andexperiences, dreams, hopes, and fears; history,politics, literature, art, films, and so much more.He was a true friend. Steve will always live in ourminds: Steve the great mathematician and Steveour great beloved friend. �
Steve was known as an excellent postdoc mentor.This is probably because when he brought post-docs to OSU, he expected to collaborate with themand treated them the same way he treated his col-laborators, as equal partners in their endeavors.He was eager to share ideas and engage mathe-matically with them. All of his postdocs left OSUas stronger mathematicians than when they ar-rived, and they continued to collaborate with Stevelong after they left. Among his postdocs were DavidGinzburg, above, and Erez Lapid.
Erez LapidSteve Rallis was a devoted mathematician, full ofideas and very generous in sharing them. I’ve knownSteve from his frequent visits to Israel in the 1990sto work with his close collaborators David Ginzburgand David Soudry. Typically, he would come inDecember to avoid the long, idle winter vacation inthe U.S. I became closer to him as a postdoc at theOhio State University during the years 1999–2002.This was the most productive period of my career,and I couldn’t have asked for a more supportive,dedicated mentor. The “harmonic analysis andautomorphic representations” seminar (known asthe “HAAR seminar”) that Steve organized became
Erez Lapid is professor of mathematics at the HebrewUniversity of Jerusalem and Weizmann Institute of Science.His email address is [email protected].
a hub of activity and attracted speakers from allover the U.S. and beyond on a regular basis. Itbecame one of Steve’s trademarks as is reflected byhis email address: [email protected] was a top priority for Steve. Hepursued it tirelessly and was extremely effectivein multitasking. At the same time, Steve lovedhis daily routine and never seemed in a hurry.Steve cared a lot about the development of hiscurrent and former postdocs and took a keeninterest in their mathematical upbringing. He willbe remembered as a great mathematician wholargely shaped the field of automorphic forms. �
Steve never had that many students. In his entirecareer at OSU he had five students total, beginningwith Dihua Jiang, who later became a collaborator.Steve was a pretty demanding advisor, probablybecause he also treated his students as if they werecollaborators. This could be quite daunting in thebeginning, but if one survived, the experience wasquite rewarding. Among Steve’s later students wasAmeya Pitale.
Ameya PitaleI was very fortunate to have Steve as my thesisadvisor. He was very generous with his time andideas. I recall one summer when I used to meetwith Steve and Cary Rader every day for a couple ofhours. This was before I had obtained any resultstowards my thesis, and it was very frustrating tome when every angle of approach seemed to fail. Istill remember Steve’s comment that I was actuallylearning to be a mathematics researcher—you getto a good idea only after hitting a million deadends, and the key is to keep working. This advicehas stayed with me since then and has indeedhelped to shape me into the mathematician that Iam today. �
Steve was a definite presence in the OSU mathe-matics department. He would come in every morn-ing and start making his rounds. He would checkin with the staff, visit with his colleagues, talk withhis visitors and his post-docs, meet with his students(usually in the lounge with others present), and stillmanage to teach his classes. He seemed to be ev-erywhere, except his office; there was no point intrying to call him during the day. But he came backto the department after dinner to work and keptthe same schedule on the weekends; then you hada better chance of finding him in his office working,but still ready to talk mathematics. His work ethicwas an inspiration to all.
Steve could also be a polarizing presence in thedepartment. Steve was deeply committed to the OSU
Ameya Pitale is professor of mathematics at the Universityof Oklahoma. His email address is [email protected].
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mathematics department and had definite ideasabout the direction that the OSU department shouldtake in terms of hiring and growth…and he had noqualms about sharing these. Two of his long-timecolleagues in the department were Paul Ponomarevand Bob Stanton.
Paul Ponomarev andBob StantonHistorical sources depict Socrates as a “gadfly”who strolled the agora and challenged the “wise”men with simple questions—of course, eventually,it cost him his life. In our department Steve was anincarnation of his ethnic ancestor. The agora—allthe floors of the department, most importantlythe chairman’s suite; the “wise” men—colleagueswho sounded off authoritatively. It was our goodfortune to have Steve come by our offices threeto five times a day, but few of our chairs wereenlightened enough to appreciate his several dailyvisits to them. Was he more than a “gadfly”?During his time with us he was a positive force inthe department, a presence that could never beignored. He tried to stop bad appointments butwas not always successful, and he championedexcellent appointments; he ridiculed, perhapsnot always within collegial bounds, misguidedpolicies advocated by certain “leaders” in the OSUdepartment. He left his mark on the department,but with time any mark wears off, and his leadershiphas been sorely missed since the onset of his illness.
His presence in the department gave it avisibility not seen since, whether it be throughthe conferences he helped organize at OSU, thespeakers he brought to the HAAR seminar, thecollaborators and postdocs who came for longvisits—from Israel, the United States, Europe, andAsia.
He was also a friend—faithful when in needand with a ready amusing story when glum. Inreturn, we had ample opportunity to respond inkind. We used to kid him about his purportedresemblance to Jerry Garcia until the day on HighStreet when visitors to the university stoppedus to ask for Jerry’s autograph. Until the end,we could tease him about his classes: the worldexpert on automorphic forms who became theprime expositor of real analysis to mathematicseducation majors, acquiring the reputation amongthem as the “teddy bear” of the department. Wecan’t kid him anymore, but we will never stoptelling stories about him. �
Paul Ponomarev is professor of mathematics at OhioState University. His email address is [email protected].
Bob Stanton is professor of mathematics at OhioState University. His email address is [email protected].
The Association for Women in Mathematics (AWM) is a professional society whose goal is to encourage women and girls to pursue careers in the mathematical sciences, and to promote equal opportunity and equal treatment of women in the mathematical sciences.AWM sponsors a wide variety of activities for women at all levels, from middle school to university faculty. AWM programs include research conferences and workshops, lecture series and prizes, travel grants, an essay contest, and day-long workshops for middle and high school girls.
AWM is currently accepting nominations for two awards (deadline April 30): • The Gweneth Humphreys Award for Mentorship of Undergraduate Women in Mathematics • The Louise Hay Award for Contributions to Mathematics Education
In preparation for our fall election, we also strongly encourage nominations for the following AWM officers: • President • Clerk • Four Members-at-Large
Please send your suggestions to [email protected]
Are you interested in helping more girls discover a love of mathematics? Would you like to see more women build successful careers in the field? Join AWM now and get involved!
http://awm-math.org
April 2013 Notices of the AMS 469