was a Japanese mathematician. He was a leading member of the

Japan Japan ( ja, 日本, or , and formally , ''Nihonkoku'') is an island country in East Asia. It is situated in the northwest Pacific Ocean, and is bordered on the west by the Sea of Japan, while extending from the Sea of Okhotsk in the north ...

ese school of

homotopy theory In mathematics, homotopy theory is a systematic study of situations in which maps can come with homotopies between them. It originated as a topic in algebraic topology but nowadays is studied as an independent discipline. Besides algebraic topolog ...

, following in the tradition of

Hiroshi Toda is a Japanese mathematician, who specializes in stable and unstable homotopy theory. He started publishing in 1952. Many of his early papers are concerned with the study of Whitehead products and their behaviour under suspension and more general ...

. Nishida received his

Ph.D. A Doctor of Philosophy (PhD, Ph.D., or DPhil; Latin: or ') is the most common degree at the highest academic level awarded following a course of study. PhDs are awarded for programs across the whole breadth of academic fields. Because it is ...

from

Kyoto University , mottoeng = Freedom of academic culture , established = , type = National university, Public (National) , endowment = ¥ 316 billion (2.4 1000000000 (number), billion USD) , faculty = 3,480 (Teaching Staff) , administrative_staff ...

in 1973, after spending the 1971–72 academic year at the

University of Manchester , mottoeng = Knowledge, Wisdom, Humanity , established = 2004 – University of Manchester Predecessor institutions: 1956 – UMIST (as university college; university 1994) 1904 – Victoria University of Manchester 1880 – Victoria Univer ...

England England is a country that is part of the United Kingdom. It shares land borders with Wales to its west and Scotland to its north. The Irish Sea lies northwest and the Celtic Sea to the southwest. It is separated from continental Europe b ...

. He then became a professor at Kyoto University in 1990. His proof in 1973 of Michael Barratt's conjecture (that positive-degree elements in the

stable homotopy In mathematics, stable homotopy theory is the part of homotopy theory (and thus algebraic topology) concerned with all structure and phenomena that remain after sufficiently many applications of the suspension functor. A founding result was the F ...

ring of spheres are

nilpotent In mathematics, an element x of a ring R is called nilpotent if there exists some positive integer n, called the index (or sometimes the degree), such that x^n=0. The term was introduced by Benjamin Peirce in the context of his work on the class ...

) was a major breakthrough: following

Frank Adams John Frank Adams (5 November 1930 – 7 January 1989) was a British mathematician, one of the major contributors to homotopy theory. Life He was born in Woolwich, a suburb in south-east London, and attended Bedford School. He began researc ...

solution Solution may refer to: * Solution (chemistry), a mixture where one substance is dissolved in another * Solution (equation), in mathematics ** Numerical solution, in numerical analysis, approximate solutions within specified error bounds * Soluti ...

of the

Hopf invariant In mathematics, in particular in algebraic topology, the Hopf invariant is a homotopy invariant of certain maps between n-spheres. __TOC__ Motivation In 1931 Heinz Hopf used Clifford parallels to construct the '' Hopf map'' :\eta\colon S^3 \to S ...

one problem, it marked the beginning of a new global understanding of algebraic topology. His contributions to the field were celebrated in 2003 at the NishidaFest in Kinosaki, followed by a satellite conference at the

Nagoya Institute of Technology The , abbreviated to Nitech (or in Japanese to 名工大, ''Meikōdai''), is a public highest-level educational institution of science and technology located in Nagoya, Japan. Nitech was founded in 1905 as ''Nagoya Higher Technical School'', then ...

; the proceedings were published in ''

Geometry and Topology In mathematics, geometry and topology is an umbrella term for the historically distinct disciplines of geometry and topology, as general frameworks allow both disciplines to be manipulated uniformly, most visibly in local to global theorems in Ri ...

'''s monograph series. In 2000 he was the leading organizer for a concentration year at the Japan–US Mathematics Institute at

Johns Hopkins University Johns Hopkins University (Johns Hopkins, Hopkins, or JHU) is a private university, private research university in Baltimore, Maryland. Founded in 1876, Johns Hopkins is the oldest research university in the United States and in the western hem ...

. Nishida's earliest work grew out of the study of infinite

loop space In topology, a branch of mathematics, the loop space Ω''X'' of a pointed topological space ''X'' is the space of (based) loops in ''X'', i.e. continuous pointed maps from the pointed circle ''S''1 to ''X'', equipped with the compact-open topology ...

s; his first paper (in 1968, on what came eventually to be known as the Nishida relations) accounts for interactions between Steenrod operations and Kudo–Araki (Dyer–Lashof) operations. Some of his later work concerns a circle of ideas surrounding the Segal conjecture, transfer homomorphisms, and stable splittings of

classifying space In mathematics, specifically in homotopy theory, a classifying space ''BG'' of a topological group ''G'' is the quotient of a weakly contractible space ''EG'' (i.e. a topological space all of whose homotopy groups are trivial) by a proper free acti ...

s of groups. The ideas in this series of papers have by now grown into a rich subfield of homotopy theory; it continues today in (for example) the theory of ''p''-compact groups.

References

* G. Nishida, The nilpotency of elements of the stable homotopy groups of spheres. J. Math. Soc. Jpn. 25 (1973) 707–732 * Michael J. Hopkins, Global methods in homotopy theory, in Homotopy theory (Durham, 1985), 73-96, London Math. Soc. Lecture Notes 117, Cambridge Univ. Press, Cambridge, 1987 * V. Voevodsky, A nilpotence theorem for cycles algebraically equivalent to zero. Internat. Math. Res. Notices 4 (1995) 187–198 * Proceedings of the International Meeting and its Satellite Conference on Homotopy Theory, dedicated to Goro Nishida, held in Kinosaki, July 28–August 1 and August 4–8, 2003. Geometry & Topology Monographs, 10. Geometry & Topology Publications, Coventry, 2007 * G. Nishida Stable homotopy type of classifying spaces of finite groups. Algebraic and topological theories (Kinosaki, 1984) 391–404, Kinokuniya, Tokyo, 1986

External links

The nilpotency of elements of the stable homotopy groups of spheres by Goro NISHIDA (Received Feb. 16, 1973)Modular forms and the double transfer for ''BT''² by Goro NISHIDA (Received October 8, 1990) / J-Stage
{{DEFAULTSORT:Nishhida, Goro 1943 births 2014 deaths 20th-century Japanese mathematicians 21st-century Japanese mathematicians Kyoto University alumni Alumni of the University of Manchester Topologists Kyoto University faculty