Celebratio Mathematica

Alberto Pedro Calderón

A tribute to Alberto Pedro Calderón

by Carlos E. Kenig

I was one of Al­berto Calderón’s gradu­ate stu­dents at the Uni­versity of Chica­go from 1975 to 1978. This was a peri­od of in­tense math­em­at­ic­al activ­ity. Dur­ing the 1976 Christ­mas break Calderón ob­tained his re­mark­able res­ult on the bounded­ness of the Cauchy in­teg­ral for Lipschitz curves with small con­stant. (The gen­er­al case was ob­tained by Coi­f­manMcIn­toshMey­er in 1981.) As soon as classes star­ted in the winter quarter, I went to see Calderón in his of­fice, where he was ex­plain­ing his proof to Bill Beck­ner. There was real ex­cite­ment in the air, which even I, a mere gradu­ate stu­dent, could feel. Soon after, the an­nu­al meet­ing of the AMS took place in St. Louis in the midst of a ter­ri­fy­ing cold spell and a ter­rible winter storm. In con­nec­tion with the AMS meet­ing there was a con­fer­ence in har­mon­ic ana­lys­is at Wash­ing­ton Uni­versity, the very first con­fer­ence I at­ten­ded. At this con­fer­ence Calderón ex­plained his proof with his usu­al el­eg­ance. One could also sense his pleas­ure in hav­ing fi­nally made a dent in this prob­lem, which he had thought about for so long. This work opened up en­tire new vis­tas of re­search, which are still be­ing ex­plored.

Shortly after our re­turn from St. Louis, I asked Calderón for a thes­is prob­lem. His re­sponse was this: Find a prob­lem your­self, and let’s dis­cuss it af­ter­wards. For­tu­nately for me, the re­cent work on the Cauchy in­teg­ral had opened up many new pos­sib­il­it­ies. I chose to ex­plore the the­ory of Hardy spaces on Lipschitz do­mains and went on to ob­tain my de­gree in 1978. Calderón was a math­em­atician of deep and ori­gin­al in­sights and also of great gen­er­os­ity with both his ideas and his time. I count my­self as ex­tremely for­tu­nate to have been his stu­dent, es­pe­cially at such a highly sig­ni­fic­ant mo­ment — an ex­per­i­ence that greatly in­flu­enced much of my en­su­ing re­search.