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Celebratio Mathematica

Dmitry Fuchs

My meetings with D. B. Fuchs:
From Tsaghkadzor to Stanford

by Yakov Eliashberg

My first in­ter­ac­tion, which I re­mem­ber, with Dmitry Bor­iso­vich Fuchs was in 1969 at a math­em­at­ic­al school at Tsaghkad­zor, Ar­menia. I was then a stu­dent at Len­in­grad Uni­versity, and this was my first math­em­at­ic­al meet­ing. Dmitry Bor­iso­vich gave a mem­or­able series of lec­tures at the school. In fact, I had seen D.B. much earli­er, in 1963, at a ce­re­mony in Mo­scow, where he was an­noun­cing win­ners of the all-uni­on school math olympi­ad. But this was, of course, a one-dir­ec­tion en­counter.

Dmitry Bor­iso­vich was work­ing for sev­er­al years with my PhD ad­visor Vladi­mir Ab­ramovich Rokh­lin on their book Be­gin­ner’s Course in To­po­logy.1 I re­mem­ber, that at the be­gin­ning of sum­mer in 1972 I came to Ust’-Narva (now Narva-Jões­uu) in Es­to­nia to see V. A. Rokh­lin, who stayed there for the sum­mer. D.B. was liv­ing with the Rokh­lins, as they were work­ing with V.A. on their book (and D.B. was paint­ing in his spare time). I re­mem­ber walk­ing with them for sev­er­al hours while they ar­gued about a title for one of the book’s chapters.

As we be­came friends, Dmitry Bor­iso­vich sev­er­al times in­vited me and my wife Ada to stay with him when we were vis­it­ing Mo­scow from Len­in­grad and Syk­tyvkar. Both of us, Ada and I, en­joyed stay­ing with the Fuchses, meet­ing with his fath­er Bor­is Ab­ramovich and moth­er Eka­ter­ina Ivan­ovna and later with his wife Ira and read­ing at night books from their fant­ast­ic lib­rary.

It was al­ways great to dis­cuss math­em­at­ics with D.B. One of the sub­jects we both were very in­ter­ested in at the time was fo­li­ations, and I learned from him a great deal. In 1978 I came sev­er­al times to Mo­scow to ex­plain to D.B. my proof of Arnold’s fixed point con­jec­ture for sur­faces. D.B. also in­vited his friend An­drei Le­ontovich to par­ti­cip­ate in this three-per­son sem­in­ar.

D.B. spent his first (aca­dem­ic) year in Amer­ica as a vis­it­ing pro­fess­or at Stan­ford. He came with his wife, Ira, and daugh­ters, Katya and Lyalya. For al­most the whole year they did not have a car, and went around every­where on bi­cycles. Some­time close to the end of the year Peter Sarnak, who was leav­ing from Stan­ford to Prin­ceton, left them his big old Amer­ic­an car. They were very happy fi­nally to have great­er free­dom to move around, and drove to the Pa­cific Ocean. Un­for­tu­nately, there are some hills in between Stan­ford and the Ocean. The car didn’t like the hills and blew up. For­tu­nately, nobody was hurt. Some time later they bought a new (small) car, which served them fine, but, in the words of one of my col­leagues, “nicely fit on them”.

Our de­part­ment sec­ret­ary Kar­en very much liked D.B. and was also im­pressed by his size. When a little bit later I brought to the de­part­ment Helmut Hofer, who is also not a small per­son, Kar­en noted: “Yasha likes big math­em­aticians”. After spend­ing a year at Stan­ford, D.B. moved for a per­man­ent po­s­i­tion to UC Dav­is. Dmitry Bor­iso­vich and Ira bought a house there and men­tioned to us that there was a lime tree grow­ing in their garden. A little bit later they cor­rec­ted that: the tree turned out to be a lem­on, not a lime. As time went on, this tree pro­gressed to be­ing an or­ange, and then ended up a grapefruit. Even cit­rus tried to be big­ger near Dmitry Bor­iso­vich Fuchs!

Yakov Eli­ash­berg is the Her­ald L. and Car­oline L. Ritch Pro­fess­or of Math­em­at­ics at Stan­ford Uni­versity. His main work be­longs to sym­plect­ic and con­tact geo­metry and to­po­logy.