Tribute to Heisuke Hironaka

As Heisuke Hironaka recounts in his account published in “Le Petit Mémorial” – a collection, marking the 40th anniversary of IHES, of testimonies from people who knew the Institute in its early days –, he was the first foreign visitor, having been invited by Alexander Grothendieck, whose lectures on ‘schemes’ he had attended at Harvard in 1958; In December 1959, he therefore went to the headquarters of the Fondation Thiers, on Square Bugeaud near the Porte Dauphine in Paris, where the Institute was then located; it had only two permanent professors at the time, Alexander Grothendieck and Jean Dieudonné. This visit also followed a recommendation from his thesis supervisor at Harvard, Oscar Zariski.

As he himself says, he returned there frequently, notably for an extended stay in 1967–1968 which, as Bernard Teissier recounts in his account, marked the beginning of regular contact with a community of French mathematicians who were inspired by his lectures, thereby establishing a new mathematical movement in France that continues to this day.

In 1970, Heisuke Hironaka met up again with Jean Dieudonné in Nice, then Dean of the University and organiser of the International Congress of Mathematicians, during which he received the Fields Medal for his theorem on the resolution of singularities.

As soon as he established the Japan Association for Mathematical Sciences (JAMS), one of his initiatives was to fund visits by young Japanese mathematicians to IHES. It was following discussions with him that the idea of a ‘Japan Fund at IHES’ took shape, an initiative broader in scope than the support provided by JAMS, and consistent with the private sponsorship efforts that the Institute had begun to develop as early as 1998.

Following a series of events organised in Tokyo with his active support to set up this fund, the opportunity arose to take advantage of a procedure established by Keidanren, the Japanese equivalent of MEDEF. Political contacts were essential to this end: those provided by André Lévy-Lang at BNP Paribas Japan, via its director Yusuke Yasuda and his adviser Toru Yosano, and those provided by Raymond Barre, former chairman of the IHES Board of Directors, thanks to his connections with former Prime Minister Yasuhiro Nakasone. These efforts came to fruition in 2007, thanks to the support of Fumio Cho, the then Chairman of Toyota Motor Company, who was influential within Keidanren. Hironaka’s national stature was, of course, decisive for the credibility of the initiative, as it enabled mobilising leading figures and gaining their commitment.

Hironaka played a prominent role in 2006 during a conference on singularities held at the Institute, supported by the Hayashibara Foundation as part of the Year of Asia at IHES. On that occasion, he gave a truly remarkable lecture at the Maison du Japon à Paris. Until the end of my term as director in 2013, I subsequently met him regularly during my visits to Japan.

Beyond his work as a mathematician at the very highest level of the discipline, Hironaka’s commitment to supporting initiatives in education at all levels and to international cooperation remained constant throughout his life, as other accounts highlight. The positive regard he maintained for IHES throughout all these years made him one of the most loyal allies the Institute has ever had. We are infinitely indebted to him, and the memory of his work must be cherished.

Jean-Pierre Bourguignon
Nicolaas Kuiper Honorary Professor, and former Director of IHES