Celebratio Mathematica

Yvonne Choquet-Bruhat

Homage to Professeur Yvonne Choquet-Bruhat
on the occasion of her 100th birthday

by Abhay Ashtekar

It is a pleas­ure and great hon­or to par­ti­cip­ate in this cel­eb­ra­tion of Mme Cho­quet’s 100th birth­day. She has been an in­spir­ing fig­ure for me since I stud­ied her early work on Ein­stein’s equa­tions as a Ph.D. stu­dent of Bob Ge­roch’s al­most 50 years ago. Already then she was a le­gend as an early pi­on­eer ex­plor­ing these equa­tions us­ing rig­or­ous meth­ods from geo­met­ric ana­lys­is. In­deed, pa­pers she wrote already in the 1950s are such tower­ing land­marks that they con­tin­ue to be im­port­ant, and cited even today! My ad­mir­a­tion for her work grew over the sub­sequent years as I came to know more about her deep con­tri­bu­tions, not only to gen­er­al re­lativ­ity but also to the glob­al ex­ist­ence and unique­ness of solu­tions to gauge the­or­ies. I then had the priv­ilege of be­ing her col­league at the Jussieu cam­pus in the eighties, as a Pro­fes­seur at Par­is VI.1 Our paths did not cross reg­u­larly. But her warm wel­come in Par­is, and sci­entif­ic dis­cus­sions at sem­inars and “Journées Re­lativ­istes”,2 were among the high­lights of my aca­dem­ic life in France. The Par­is aca­dem­ic scene was not easy for me to nav­ig­ate and I am grate­ful to have had a guide in Mme Cho­quet dur­ing those years.

In the sub­sequent 20 years or so years my own re­search was fo­cused more on quantum grav­ity and even my con­tri­bu­tions to clas­sic­al gen­er­al re­lativ­ity have been more at the in­ter­face of geo­metry and phys­ics rather than geo­metry and ana­lys­is. Non­ethe­less, I al­ways found Mme Cho­quet’s work in­spir­ing. Her book, Ana­lys­is, Man­i­folds and Phys­ics, has been on the most used book-shelf in my of­fice since the late 70s! When she was awar­ded the Dan­nie Heine­man Prize by the Amer­ic­an Phys­ic­al So­ci­ety in 2003, I wrote to her ex­press­ing my sen­ti­ments on hear­ing the news: Most prizes hon­or the re­cip­i­ents, but on rare oc­ca­sions it is the re­cip­i­ents who make the prize more pres­ti­gi­ous. I feel that the Heine­man prize be­came much more sig­ni­fic­ant after 2003! In more re­cent years, I had the priv­ilege of in­ter­act­ing with Mme Cho­quet in per­son at a KITP work­shop in Santa Bar­bara, a Mar­cel Gross­mann Meet­ing in Rome and at the cel­eb­ra­tion of the 100th an­niversary of Gen­er­al Re­lativ­ity in Ber­lin. On the Santa Bar­bara cam­pus, we all watched with great ad­mir­a­tion as she rode her bi­cycle in a cheer­ful, care­free man­ner. She had not changed over all those years — there was the same kind­ness ra­di­at­ing from her, the same math­em­at­ic­al rig­or, and the same sim­pli­city in her de­mean­or, provid­ing us with a role mod­el on how to live a pro­duct­ive and ful­filling life with in­ner serenity.

And then, over the last couple of years, I came to read of her life as a stu­dent in oc­cu­pied France.3 In 1944, when Yvonne’s fath­er, Georges Bruhat — a phys­i­cist and the Deputy Dir­ect­or of the Par­is École Nor­male Supérieure — re­fused to co­oper­ate with the Gestapo, they ar­res­ted Berthe Hubert Bruhat — Yvonne’s moth­er — and threatened to kill her the fol­low­ing day. And Yvonne pleaded with the Gestapo to al­low her to take her moth­er’s place. When I read this, my heart melted and there were tears in my eyes. This was a whole new di­men­sion of Mme Cho­quet that I knew noth­ing about. To have made such deep con­tri­bu­tions to math­em­at­ics and to have at­tained the in­ner serenity in spite of en­dur­ing such trau­mat­ic events early on, made my already enorm­ous ad­mir­a­tion and re­spect grow a thou­sand fold. What a re­mark­able life you have led, Mme Cho­quet! I feel for­tu­nate to have known you in per­son.

Abhay Ashtekar is the Evan Pugh Pro­fess­or of Phys­ics and holds the Eberly Chair at The Pennsylvania State Uni­versity. He foun­ded the In­sti­tute for Grav­it­a­tion and the Cos­mos in 1993 and served as its Dir­ect­or un­til 2021.