Celebratio Mathematica

I first heard of Abby Thompson in Spring 1984 in a let­ter from Bill Menasco, then a postdoc at Rut­gers Uni­versity. He wrote that he had been col­lab­or­at­ing with Abby and that she was a strong gradu­ate stu­dent (of Ju­li­us Shaneson) who had be­come in­ter­ested in 3-man­i­folds and knot the­ory, and that they had some nice res­ults.1 It happened that Bob Ed­wards and I were plan­ning on spend­ing the sum­mer in Cam­bridge, UK, and Bill sug­ges­ted we in­vite Abby to come over and give a talk to our small gath­er­ing of to­po­lo­gists (see photo). We did so, and Abby made such a good im­pres­sion that I de­cided to use my last Re­search As­sist­ant­ship from an NSF grant I’d re­ceived to fund Abby’s par­ti­cip­a­tion in the spring semester of the fam­ous to­po­logy year at MSRI in 1984–85.

While at MSRI, Abby met one of my former PhD stu­dents, Marty Schar­le­mann, whom she later fol­lowed to his home in­sti­tu­tion at the Uni­versity of Cali­for­nia at Santa Bar­bara to fin­ish her PhD thes­is (1986). She also met Joel Hass, an­oth­er of my former stu­dents, whom she mar­ried in 1987. They now have three great kids, El­lie (b. 1988), Ben­jamin (b. 1991), and Lucy (b. 1995). I’m proud to say that I gave all three kids their first driv­ing les­son, on a stick shift at that. So, thanks to Bill — and his let­ter — I ac­quired a math­em­at­ic­al “grand­daugh­ter” and “daugh­ter-in-law”.

Abby spent 1987–88 in Berke­ley on a fel­low­ship, and she and Joel showed an in­terest in river kayak­ing. I’d been an avid white­wa­ter kayaker in the late 1970s with Den­nis John­son, so was happy to fur­ther their in­terest by tak­ing them both to the Rich­mond Plunge (aka the Rich­mond Mu­ni­cip­al Na­ta­tori­um in Rich­mond, CA), where we prac­ticed rolling kayaks. After their move to Dav­is in 1988, they fin­ish­ing learn­ing to roll and began run­ning easy rivers. I soon joined them and we began run­ning Class IV rivers,2 some­times with Den­nis and with Bruce Ham­mock, a re­mark­able bio­chem­ist, and later still, by the Hass chil­dren as they each, in turn, be­came old enough to roll a kayak. We had many won­der­ful trips on Cali­for­nia white­wa­ter.

Abby was a brave and de­term­ined kayaker right up un­til she stopped run­ning white­wa­ter (around 2010). One in­cid­ent I re­mem­ber was the S-rap­id on the South Fork of the Amer­ic­an River. It twists, goes through a hole3 and then over a 6-foot drop. Abby got caught in the hole, and turned over as she went over the drop. I was be­low watch­ing and began to worry as Abby didn’t sur­face, but then she sud­denly rolled up. An ob­serv­er on the shore ex­claimed, “Holy cow!” for the delay had been un­usu­ally long. A few seconds un­der­wa­ter in tur­bu­lence can seem like minutes, so most people will bail out and swim if they don’t roll im­me­di­ately. Evid­ently Abby took her time to set up prop­erly and then roll suc­cess­fully. I call that forti­tudin­ous!

Abby is a fine speak­er, and there were quite a few fall semesters when she would lead off my to­po­logy sem­in­ar at Berke­ley. Since our re­search in­terests differed by one in terms of di­men­sions, we did not start to col­lab­or­ate math­em­at­ic­ally un­til this last dec­ade, but since then I have been well tutored in the in­tric­a­cies of 3-di­men­sion­al man­i­folds. She writes well (much bet­ter than I) and is al­ways gen­er­ous with her time and con­tri­bu­tions.

In ad­di­tion to her work on the 3-sphere re­cog­ni­tion prob­lem (for which she won the AMS Sat­ter Prize), I want to men­tion a beau­ti­ful pa­per,4 coau­thored with Joel Hass and Bill Thur­ston, that proves that there are closed 3-man­i­folds with two dif­fer­ent Hee­gaard split­tings of genus \( g \) which re­quire \( g \) sta­bil­iz­a­tions be­fore be­com­ing equi­val­ent. Pri­or to this pa­per’s pub­lic­a­tion, it was con­jec­tured that one sta­bil­iz­a­tion would be enough. Giv­en the right hy­per­bol­ic 3-man­i­fold, the two Hee­gaard split­tings are re­lated in that one is the up­side-down of the oth­er. I, with help, wrote a sketch of their ar­gu­ment here.

While Vice Pres­id­ent of the Amer­ic­an Math­em­at­ic­al So­ci­ety (2019–22), Abby wrote a column op­pos­ing the re­quire­ment to in­clude a di­versity state­ment in job ap­plic­a­tions. She likened this ob­lig­a­tion to the re­quire­ment im­posed in the early 1950s on Uni­versity of Cali­for­nia pro­fess­ors to sign a loy­alty oath. The column cre­ated quite a brouhaha, with vo­cal sup­port from many math­em­aticians and equally vo­cal op­pos­i­tion from oth­ers. Abby was im­me­di­ately fam­ous and was honored with the “Hero of In­tel­lec­tu­al Free­dom” award by the Amer­ic­an Coun­cil of Trust­ees and Alumni (ACTA). The award was presen­ted to her by the late Robert Zi­m­mer, then Pres­id­ent of the Uni­versity of Chica­go. Abby is also a Found­ing Mem­ber of the Aca­dem­ic Com­mit­tee of the Aca­dem­ic Free­dom Al­li­ance.

In 2021 a small group of re­search math­em­aticians, Abby in­cluded, came to­geth­er to found a new or­gan­iz­a­tion to pro­mote math­em­at­ic­al re­search, the As­so­ci­ation for Math­em­at­ic­al Re­search (AMR, amathr.org). Abby is the Sec­ret­ary of this new or­gan­iz­a­tion, and has been in­stru­ment­al in help­ing it get off to a strong start.5