Celebratio Mathematica

Robion C. Kirby

Tribute to Rob Kirby

by J. Elisenda (Eli) Grigsby

When I first met Rob, I was a first-year grad stu­dent at Berke­ley, and he was teach­ing Berke­ley’s second-semester al­geb­ra­ic to­po­logy course. My dom­in­ant memor­ies of Rob from that time were: (i) he rarely wrote any­thing on the board, and (ii) he seemed genu­inely taken aback whenev­er I called him Pro­fess­or Kirby. I quickly stopped.

The course it­self was a turn­ing point for me. I cred­it his Poin­caré ho­mo­logy sphere home­work prob­lem (pic­ture be­low) for hook­ing me on low-di­men­sion­al to­po­logy. It was such a cool mix of a lot of dif­fer­ent ideas, and it was fun to hear the his­tory: that Poin­caré’s ori­gin­al con­jec­ture was about ho­mo­logy, not ho­mo­topy, and Poin­caré had dis­covered this counter­example to his own ori­gin­al con­jec­ture, which led him to re­vise it.

I was tak­ing a com­mut­at­ive al­gebra class at the same time. Those prob­lem sets felt like work, but Rob’s didn’t. I now see that this was partly about the math and partly about Rob, and that these two facts are con­nec­ted. Math is cre­ated in com­munit­ies, and math­em­at­ic­al com­munit­ies have a tone to them which is set early on and dif­fi­cult-to-budge later.

When it was time to pick an ad­visor, I knew it would be Rob. Some older stu­dents warned me he was very hands-off and didn’t give thes­is prob­lems, but his style turned out to be just right for me. He was al­ways ready to talk math; he asked ques­tions, and was in­ter­ested in what I had to say — un­less it wasn’t in­ter­est­ing, in which case he’d gently tell me so. He was sup­port­ive in an au­then­t­ic, math-centered way. This helped me de­vel­op my own com­pass.

Dur­ing my second year, he gave a top­ics course on Hee­gaard Flo­er ho­mo­logy. This was less than a year after Peter Oz­sváth and Zoltán Szabó pos­ted their first two found­a­tion­al pa­pers, [e2], [e1]. Thanks to Rob, we all got a head start learn­ing a the­ory that now, 20 years later, has be­come re­quired back­ground for many 3.5-di­men­sion­al to­po­lo­gists.

Back then, he and Paul Melvin were also work­ing on find­ing a purely com­bin­at­or­i­al de­scrip­tion of the the­ory (as were many oth­ers, I’d bet), and he was very open about dis­cuss­ing their strategy. Even­tu­ally I star­ted think­ing about the prob­lem too. Oth­er ad­visors might have be­come guarded at this point, or dis­cour­aged me, or warned me off of the prob­lem. But this wasn’t Rob’s style. He was happy to have an­oth­er per­son in­volved, and some of my fond­est and most form­at­ive math­em­at­ic­al mo­ments were those spent dis­cuss­ing holo­morph­ic struc­tures on branched cov­ers of the disk with Rob and Paul in Ban­ff (2003), then Gokova and Bud­apest (2004).

Like all grad stu­dents, I struggled. A lot. Rob’s re­sponse was al­ways something along the lines of: “Don’t work so hard. You have to make sure you’re en­joy­ing the math you’re do­ing. Oth­er­wise, what’s the point?” This was — of course — in­cred­ibly ir­rit­at­ing to hear at the time. Sure. Easy for you to say. You’re a pro­fess­or at Berke­ley. But of course he was right. Math is a mara­thon, not a sprint. En­joy­ing the scenery you’re help­ing to paint is the whole point.

This is all to say that there is a light­ness and ease with which Rob moves through math­em­at­ics and life, and I have ob­served this same grace throughout his circle. It may be hy­per­bol­ic (pun in­ten­ded) of me to say, but I’ll go ahead: I think this grace has touched the whole field of low-di­men­sion­al to­po­logy. I have per­son­ally found this com­munity to be a little bit friend­li­er than oth­ers I’ve in­hab­ited. People are just a bit more likely to cred­it and sup­port each oth­er; to ask ques­tions be­cause they really want to know the an­swer, and not be­cause they want to show how much they already know.

Five years ago, I men­tioned this to my then-part­ner, who was strug­gling with set­ting the right tone at his start-up com­pany, and he wrote to Rob for ad­vice. Rob’s re­sponse:

I think I was lucky to start out […] with a good bunch of stu­dents […], and they of­ten passed on tra­di­tions to the young­er stu­dents.

Also, I oc­ca­sion­ally passed on the com­ment that it was al­ways a good idea to be ex­tra gra­cious in re­fer­ring to oth­er people’s work, or in­clud­ing someone as a coau­thor; that those no­tions paid off hand­somely in a nicer com­munity to work in. My fath­er used to talk about up­ward spir­als, in which you nor­mally re­act to an­oth­er per­son in a slightly (ep­si­lon) nicer way than you might be in­clined to, and then the re­sponse may be slightly nicer and an up­ward spir­al is star­ted. Of course ep­si­lon has to be small, or you be­come a phony.

This is Rob all over. Without any fan­fare, he has quietly nudged us all up­ward.