Heisuke Hironaka | |
|---|---|
 | |
| Born | (1931-04-09)April 9, 1931 (age 93) |
| Nationality | Japanese |
| Alma mater | Kyoto University (BA) Harvard University (PhD) |
| Spouse | Wakako Hironaka (née Kimoto) |
| Awards | Asahi Prize(1967) Fields Medal(1970) Order of Culture(1975) Legion of Honour(2004) |
| Scientific career | |
| Fields | Mathematics |
| Institutions | Brandeis University Harvard University Columbia University Kyoto University |
| Thesis | On the Theory of Birational Blowing-up (1960) |
| Doctoral advisor | Oscar Zariski |
| Doctoral students | José Manuel Aroca Hernández-Ros Charles Barton, III Dave Bayer Bruce Bennett Max Benson Jacob E. Goodman William Haboush Jerome Hoffman Audun Holme Monique Lejeune-Jalabert Takehiko Miyata Loren Olson Mary Schaps Andrew Schwartz Mark Spivakovsky [de] Allen Tannenbaum Bernard Teissier Philip Wagreich Boris Youssin |
Heisuke Hironaka (広中 平祐,Hironaka Heisuke, born April 9, 1931) is a Japanesemathematician who was awarded theFields Medal in 1970 for his contributions toalgebraic geometry.[1]
Hironaka was born on April 9, 1931 inYamaguchi, Japan. He was inspired to study mathematics after a visitingHiroshima University mathematics professor gave a lecture at his junior high school. Hironaka applied to the undergraduate program at Hiroshima University, but was unsuccessful. However, the following year, he was accepted intoKyoto University to study physics, entering in 1949 and receiving his Bachelor of Science and Master of Science from the University in 1954 and 1956. Hironaka initially studied physics, chemistry, and biology, but his third year as an undergraduate, he chose to move to taking courses in mathematics.[2]
The same year, Hironaka was invited to a seminar group led byYasuo Akizuki, who would have a major influence on Hironaka's mathematical development. The group, informally known as the Akizuki School, discussed cutting-edge research developments including theresolution of singularities problem for which Hironaka later received the Fields Medal.[3] Hironaka has described his interest in this problem as having the logic and mystery of "a boy falling in love with a girl."[4] In 1956, Akizuki invited then Harvard professorOscar Zariski to Kyoto University. Hironaka took the opportunity to present his own research to Zariski, who suggested that Hironaka move toHarvard University to continue his studies.[2]
In 1957, Hironaka moved to the United States to attend Harvard University as a doctoral student under the direction of Zariski.[5] Hironaka'salgebra background, developed under Akizuki, allowed him to bring fresh insights into mathematics discussions in Harvard, which placed a greater emphasis on geometric perspectives. In 1958–1959,Alexander Grothendieck visited Harvard University and was another important influence on Hironaka, inviting him to theInstitut des Hautes Études Scientifique (IHES) in Paris.[3]
Returning to Harvard in 1960, Hironaka received hisPhD for his thesisOn the Theory of Birational Blowing-up.[6]
Hironaka was an Associate Professor of Mathematics atBrandeis University from 1960–1963. He taught atColumbia University from 1964–1968 and became a professor of mathematics atHarvard University from 1968 until becomingemeritus in 1992.
Hironaka returned to Japan for a joint professorship at theResearch Institute for Mathematical Sciences andKyoto University from 1975–1983 and was the Institute Director from 1983–1985.[7]
Hironaka was the president ofYamaguchi University from 1996–2002.[8]
In 1960, Hironaka introducedHironaka's example, showing that a deformation ofKähler manifolds need not be Kähler. The example is a 1-parameter family ofsmoothcompactcomplex3-manifolds such that most fibers are Kähler (and even projective), but one fiber is not Kähler. This can be used to show that several other plausible statements holding for smooth varieties of dimension at most 2 fail for smooth varieties of dimension at least 3.[9]
In 1964, Hironaka proved thatsingularities of algebraic varieties admitresolutions incharacteristic zero. Hironaka was able to give a general solution to this problem, proving that anyalgebraic variety can be replaced by (more precisely isbirationally equivalent to) a similar variety that has no singularities.[2]
Hironaka recalled that he felt very close to approaching the solution while studying in Harvard. Then, soon after getting his first teaching position at Brandeis, he realized that if he combined hiscommutative algebra experience from Kyoto, geometry of polynomials from Harvard, and globalization technique from IHES, he had everything he needed to solve the problem.[3]
In 2017 he posted to his personal webpage a manuscript that claims to prove the existence of a resolution of singularities in positive characteristic.[10]
Hironaka received a Fields Medal, the highest honor in mathematics, at theInternational Congress of Mathematicians at Nice in 1970 at 39, just under the 40 year age limit.
List of Awards:
Hironaka has been active in promoting mathematical education, particularly in Japan and South Korea. Hironaka wrote or co-authored 26 books on mathematics and other topics.[4]
In 1980, he started a summer seminar for Japanese high school students, and later created a program for Japanese and American college students. In 1984 he established the Japanese Association for Mathematical Sciences (JAMS) to fund these seminars, serving as executive director.[3] Additional funding was received from corporations and the Japanese government. Harvard emeritus math professorShing-Tung Yau noted that "In the 1980s there were few domestic grant opportunities for foreign travel or exchange [...] today, one can see the fruits of Hironaka’s efforts in the number of former JAMS fellows who have become professors of mathematics across the United States and Japan."[4]
As visiting professor atSeoul National University in 2008–2009, Hironaka mentored undergraduate studentJune Huh, a former high school drop-out and aspiring poet, encouraging his interest in pursuing math for graduate school. Huh won a Fields medal in 2022 for the linkages he found betweenalgebraic geometry andcombinatorics.[15]
Hironaka marriedWakako Kimoto in 1960, a Brandeis Wien International Scholar who entered Japanese politics through her election to the House of Councillors in 1986. They have a son Jo, and daughter Eriko, who is also a mathematician.[2][16]
On his love for mathematics, Hironaka said "I accumulate anything to do with numbers. For instance, I have more than 10,000 photos of flowers and leaves. I like to just count the numbers and compare them. I am so pleased to be a mathematician, because I can see the mathematical interest in things."[3]
