Celebratio Mathematica

Robion C. Kirby

Rob Kirby comes to UC Berkeley

by Martin Scharlemann

I was Rob Kirby’s third Ph.D. stu­dent, and his first stu­dent at Berke­ley. Rob was my fourth pro­spect­ive Ph.D. ad­visor there, and the only one to really help. Here is the story.

In 1969 I entered the UC Berke­ley Ph.D. pro­gram, primar­ily at­trac­ted by Berke­ley’s ex­cel­lent repu­ta­tion in to­po­logy. I was not alone: as­pir­ing to­po­logy stu­dents were pour­ing in­to UCB, many hop­ing to work with such to­po­lo­gic­al lu­minar­ies as Steph­en Smale, Ed Span­i­er, or John Stallings (and that’s just the S’s). Next to Prin­ceton, UC Berke­ley was the world’s cen­ter of cut­ting-edge to­po­logy. Bey­ond its stel­lar reg­u­lar fac­ulty, it also at­trac­ted young hot-shot sum­mer vis­it­ors like the cha­ris­mat­ic Den­nis Sul­li­van.

But when I ar­rived at Berke­ley, I soon found that there were neg­at­ives. The phys­ic­al set­ting for the Math De­part­ment was grim. Evans Hall was not yet com­pleted and the Math­em­at­ics De­part­ment was crammed in­to a small build­ing, one we shared with as­tro­nomers. I was as­signed a desk in a large win­dow­less of­fice with about ten oth­er gradu­ate stu­dents. (A par­tic­u­larly messy desk be­longed to a guy named Bill Thur­ston.) The lib­rary was small and hard to use, but I sup­pose it worked OK for the truly fo­cused. See­ing one stu­dent check out maybe half a dozen is­sues of The Journ­al of Dif­fer­en­tial Geo­metry, while re­turn­ing a like num­ber, I thought, “Who is that guy?” (An­swer: Shing-Tung Yau.)

There was, fam­ously, polit­ic­al tur­moil in the streets. This was both ex­cit­ing and scary, but al­ways in­con­veni­ent. My first Hal­loween even­ing I was blocked from go­ing home by the Oak­land Tac­tic­al Squad (aka The Blue Mean­ies), who were clear­ing Tele­graph Av­en­ue of ri­oters. My first naïve re­ac­tion: “Where did those guys get such great Hal­loween cos­tumes!?” Classes were can­celed for much of the year be­cause of mil­it­ants’ threats. And al­ways, al­ways the mil­it­ary draft and the Vi­et­nam War hung like rap­tors over­head, wait­ing for stu­dents to stumble.

As I worked to­ward passing quals, a fur­ther worry nagged: it was go­ing to be really hard to find a dis­ser­ta­tion su­per­visor, es­pe­cially in to­po­logy. There were lots of eager stu­dents, while many of the fam­ous fac­ulty to­po­lo­gists had moved on to oth­er sub­jects. (Steph­en Smale, for one ex­ample, was do­ing eco­nom­ics.) And so it was that by my third year I had ap­proached three dif­fer­ent fac­ulty mem­bers; none would help with my dis­ser­ta­tion.

At that point Rob Kirby ar­rived, hired away from UCLA after his found­a­tion­al work on the tri­an­gu­la­tion of man­i­folds. His first day on cam­pus, I camped out­side his of­fice, wait­ing for him to have a free mo­ment. When he did, I in­tro­duced my­self and im­me­di­ately asked him if he would su­per­vise my dis­ser­ta­tion. He was of course sur­prised, but said something that I took to be pos­it­ive like, “I’ll sug­gest some things to read.” And so we began. I was de­lighted at how will­ing he was to take me on. Or so I hoped, since I couldn’t really be sure that he had in fact agreed.

What Rob en­cour­aged me to read was Browder’s new book [e1] on simply-con­nec­ted high-di­men­sion­al sur­gery, and the few pa­pers that then ex­is­ted on 4-man­i­folds. (This was a time, be­fore Don­ald­son, Freed­man, and the Kirby cal­cu­lus, when one could learn all that was known about 4-man­i­folds in a mat­ter of weeks.) Browder’s ac­count of sur­gery was beau­ti­ful math­em­at­ics, and Rob mostly let me learn it on my own. We’d meet in an ad hoc way — when I had something to talk about I’d drop by; oth­er­wise I’d just keep read­ing. He had no teach­ing du­ties dur­ing his early months at Berke­ley, and also had no oth­er stu­dents to work with — a lucky time for me. With his first (ad­vanced gradu­ate) class, I fi­nally met my fu­ture com­rades: There were per­haps 40 stu­dents in the classroom when Rob walked in to be­gin his Berke­ley teach­ing. He looked stunned at the num­ber, and his first act was to write the name of the class on the board, ex­pect­ing there was a mis­take and that many would leave. When nobody did, he laughed and said, “I hope you’re not all look­ing for a thes­is ad­visor!”

Quite a few of the stu­dents were, and soon Rob had per­haps 10 ad­visees. He thus began a dra­mat­ic change in the cul­ture of UCB to­po­logy. In­stead of try­ing to avoid po­ten­tial stu­dents, as many over­whelmed fac­ulty did, Rob wel­comed them, even­tu­ally or­gan­iz­ing a sem­in­ar in which stu­dents mostly talked to each oth­er. Not all prospered from his lais­sez-faire ap­proach, but many did, as a list of his early stu­dents shows. Even­tu­ally ad­ded to the mix were Rob’s coau­thor Larry Sieben­mann and also Sieben­mann’s French stu­dents. They would come in the sum­mers, of­fer­ing sem­inars of such length that oc­ca­sion­ally most of the Anglo­phones would leave, and the lan­guage would switch to French.

Some­time in all of this I star­ted writ­ing pa­pers: first with Rob and then with Larry Sieben­mann. My first pa­per with Rob was based on a hope of his for a new to­po­lo­gic­al cat­egory called MC­CG [1]. De­tails aren’t im­port­ant: it didn’t work out and my con­tri­bu­tion was mostly to show that it couldn’t. Our fol­low­ing pa­per on the Poin­care ho­mo­logy sphere [2] fit per­fectly in­to my dis­ser­ta­tion re­search, and is the only pa­per I have writ­ten that earned roy­al­ties, via a So­viet trans­la­tion. Not sure Rob ever got his share.

The pa­pers with Sieben­mann [e2], [e3] came about be­cause he and I (un­be­knownst to each oth­er) were try­ing to un­der­stand smooth homeo­morph­isms: homeo­morph­isms between smooth man­i­folds which were only smooth maps in one dir­ec­tion. I had am­a­teur­ish first res­ults; Larry was de­vel­op­ing an en­tire the­ory. When Rob learned of our mu­tu­al in­terest, he thought­fully sug­ges­ted to Larry that he take me on as an ap­pren­tice, and Larry was kind enough to do so. That’s how I learned Larry’s very ef­fect­ive pre-com­puter meth­od of writ­ing pa­pers: a few sen­tences hand-writ­ten on each page, pages piled in massive stacks, then eas­ily re­shuffled as the ar­gu­ment emerged.

By the time I was ready to fin­ish at Berke­ley, I’d already writ­ten a few pa­pers on my own. In part this was a con­sequence of Rob’s ex­cel­lent ad­vice to stay on a fifth year in­stead of fin­ish­ing in four, since in­sti­tu­tions typ­ic­ally start the pub­lic­a­tion clock with the Ph.D. With sev­er­al pa­pers to choose from, I asked Rob my fi­nal year what I should do about my dis­ser­ta­tion: staple the pa­pers to­geth­er, or just choose one. Rob’s mem­or­able ad­vice: “Hmm, I guess I should read it. Why don’t you pick whatever’s shortest?” So I did.

Berke­ley had no re­quire­ment for a thes­is de­fense, so that seemed to be the end of it. Rob thought it might be a good idea, though, for me to talk about the res­ults in his sem­in­ar. Of course I agreed, ex­pect­ing an audi­ence of stu­dents, most of them Rob’s or in­tend­ing to be Rob’s. But when I walked in, there were stu­dents, sure, but also — the lu­minar­ies! Rob had ar­ranged, on the down-low, an ad hoc thes­is de­fense, by en­cour­aging the seni­or to­po­logy fac­ulty to at­tend my talk. This was a shock, but not a bad one; I could there­after add to my men­tal résumé that I once gave a sem­in­ar talk with Ed Span­i­er in the audi­ence. The fac­ulty pres­ence was also math­em­at­ic­ally use­ful: Jack Wag­on­er spot­ted a gap in my ar­gu­ment, but for­tu­nately one that I was able to fill in real time at the board, a fix I later in­cor­por­ated in­to my dis­ser­ta­tion [e4].

There are so many oth­er stor­ies from Berke­ley at that time: can I men­tion that I lived just half a block from the ori­gin­al Peet’s, where buzzy cof­fee re­fills cost just 25¢? That the rent on our three-bed­room Wal­nut Street cot­tage was \$125/month? That a small French res­taur­ant named Chez Pan­isse opened around the corner, but surely couldn’t last long — who in Berke­ley would pay \$6 dol­lars for din­ner? That my fu­ture wife’s apart­ment shared a wall with what would be­come a Sym­bionese Lib­er­a­tion Army arms dump? I’ll forgo these stor­ies, want­ing to fo­cus here on how Rob Kirby made such a dif­fer­ence both to the en­vir­on­ment of the Berke­ley Math­em­at­ics De­part­ment and to my per­son­al math­em­at­ic­al de­vel­op­ment. But if you are curi­ous, and see me at a con­fer­ence, don’t be shy about ask­ing for more!

Mar­tin Schar­le­mann re­ceived his Ph.D. in math­em­at­ics from UC Berke­ley in 1974. Fol­low­ing a year at the In­sti­tute for Ad­vanced Stud­ies and a year at the Uni­versity of Geor­gia, he moved to UC Santa Bar­bara, where he is now a Dis­tin­guished Pro­fess­or Emer­it­us.


[1]R. C. Kirby and M. G. Schar­le­mann: “A curi­ous cat­egory which equals TOP,” pp. 93–​97 in Man­i­folds—Tokyo 1973. Edi­ted by A. Hat­tori. Univ. Tokyo Press (Tokyo), 1975. MR 0372868 Zbl 0315.​57003

[2]R. C. Kirby and M. G. Schar­le­mann: “Eight faces of the Poin­caré ho­mo­logy 3-sphere,” pp. 113–​146 in Geo­met­ric to­po­logy (Athens, GA, 1977). Edi­ted by J. C. Cantrell. Aca­dem­ic Press (New York), 1979. MR 537730 Zbl 0469.​57006