Friedrich Hirzebruch
Encyclopedia
Friedrich Ernst Peter Hirzebruch (born 17 October 1927) is a German
mathematician
, working in the fields of topology
, complex manifold
s and algebraic geometry
, and a leading figure in his generation.
, Westphalia
. He studied at the University of Münster
from 1945–1950, with one year at ETH Zürich
.
He then had a position at Erlangen, followed by the years 1952–54 at the Institute for Advanced Study
in Princeton, New Jersey
. After one year at Princeton University
1955–56, he was made a professor at the University of Bonn
, where he remained, becoming director of the Max-Planck-Institut für Mathematik
in 1981.
More than 300 people participated in the event in ceremony of his 80th birthday at Bonn in 2007.
The Hirzebruch–Riemann–Roch theorem (1954) for complex manifolds was a major advance and quickly became part of the mainstream developments around the classical Riemann–Roch theorem
;
it was also a precursor of the Atiyah–Singer index theorem
.
Hirzebruch's book Neue topologische Methoden in der algebraischen Geometrie (1956) was a basic text for the 'new methods' of sheaf theory, in complex algebraic geometry.
He went on to write the foundational papers on topological K-theory
with Michael Atiyah
, and collaborate with Armand Borel
on the theory of characteristic class
es. In his later work he provided a detailed theory of Hilbert modular surface
s, working with Don Zagier
.
Hirzebruch is a foreign member of numerous academies and societies, including the United States National Academy of Sciences
, the Russian Academy of Sciences
, and the French Academy of Sciences
.
In 1980/81 he delivered the first Sackler Distinguished Lecture
in Israel.
in 1988, a Lobachevsky Medal
in 1989.
The government of Japan awarded him the Order of the Sacred Treasure
in 1996.
Hirzebruch won an Einstein Medal in 1999, and received the Cantor medal
in 2004.
Germans
The Germans are a Germanic ethnic group native to Central Europe. The English term Germans has referred to the German-speaking population of the Holy Roman Empire since the Late Middle Ages....
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
, working in the fields of topology
Topology
Topology is a major area of mathematics concerned with properties that are preserved under continuous deformations of objects, such as deformations that involve stretching, but no tearing or gluing...
, complex manifold
Complex manifold
In differential geometry, a complex manifold is a manifold with an atlas of charts to the open unit disk in Cn, such that the transition maps are holomorphic....
s and algebraic geometry
Algebraic geometry
Algebraic geometry is a branch of mathematics which combines techniques of abstract algebra, especially commutative algebra, with the language and the problems of geometry. It occupies a central place in modern mathematics and has multiple conceptual connections with such diverse fields as complex...
, and a leading figure in his generation.
Life
He was born in HammHamm
Hamm is a city in North Rhine-Westphalia , Germany. It is located in the northeastern part of the Ruhr area. As of December 2003 its population was 180,849. The city is situated between the A1 motorway and A2 motorway...
, Westphalia
Province of Westphalia
The Province of Westphalia was a province of the Kingdom of Prussia and the Free State of Prussia from 1815 to 1946.-History:Napoleon Bonaparte founded the Kingdom of Westphalia, which was a client state of the First French Empire from 1807 to 1813...
. He studied at the University of Münster
University of Münster
The University of Münster is a public university located in the city of Münster, North Rhine-Westphalia in Germany. The WWU is part of the Deutsche Forschungsgemeinschaft, a society of Germany's leading research universities...
from 1945–1950, with one year at ETH Zürich
ETH Zurich
The Swiss Federal Institute of Technology Zurich or ETH Zürich is an engineering, science, technology, mathematics and management university in the City of Zurich, Switzerland....
.
He then had a position at Erlangen, followed by the years 1952–54 at the Institute for Advanced Study
Institute for Advanced Study
The Institute for Advanced Study, located in Princeton, New Jersey, United States, is an independent postgraduate center for theoretical research and intellectual inquiry. It was founded in 1930 by Abraham Flexner...
in Princeton, New Jersey
Princeton, New Jersey
Princeton is a community located in Mercer County, New Jersey, United States. It is best known as the location of Princeton University, which has been sited in the community since 1756...
. After one year at Princeton University
Princeton University
Princeton University is a private research university located in Princeton, New Jersey, United States. The school is one of the eight universities of the Ivy League, and is one of the nine Colonial Colleges founded before the American Revolution....
1955–56, he was made a professor at the University of Bonn
University of Bonn
The University of Bonn is a public research university located in Bonn, Germany. Founded in its present form in 1818, as the linear successor of earlier academic institutions, the University of Bonn is today one of the leading universities in Germany. The University of Bonn offers a large number...
, where he remained, becoming director of the Max-Planck-Institut für Mathematik
Max-Planck-Institut für Mathematik
The Max-Planck-Institut für Mathematik is a mathematical research institute located in Bonn, Germany. It is named in honour of the German physicist Max Planck...
in 1981.
More than 300 people participated in the event in ceremony of his 80th birthday at Bonn in 2007.
The Hirzebruch–Riemann–Roch theorem (1954) for complex manifolds was a major advance and quickly became part of the mainstream developments around the classical Riemann–Roch theorem
Riemann–Roch theorem
The Riemann–Roch theorem is an important tool in mathematics, specifically in complex analysis and algebraic geometry, for the computation of the dimension of the space of meromorphic functions with prescribed zeroes and allowed poles...
;
it was also a precursor of the Atiyah–Singer index theorem
Atiyah–Singer index theorem
In differential geometry, the Atiyah–Singer index theorem, proved by , states that for an elliptic differential operator on a compact manifold, the analytical index is equal to the topological index...
.
Hirzebruch's book Neue topologische Methoden in der algebraischen Geometrie (1956) was a basic text for the 'new methods' of sheaf theory, in complex algebraic geometry.
He went on to write the foundational papers on topological K-theory
K-theory
In mathematics, K-theory originated as the study of a ring generated by vector bundles over a topological space or scheme. In algebraic topology, it is an extraordinary cohomology theory known as topological K-theory. In algebra and algebraic geometry, it is referred to as algebraic K-theory. It...
with Michael Atiyah
Michael Atiyah
Sir Michael Francis Atiyah, OM, FRS, FRSE is a British mathematician working in geometry.Atiyah grew up in Sudan and Egypt but spent most of his academic life in the United Kingdom at Oxford and Cambridge, and in the United States at the Institute for Advanced Study...
, and collaborate with Armand Borel
Armand Borel
Armand Borel was a Swiss mathematician, born in La Chaux-de-Fonds, and was a permanent professor at the Institute for Advanced Study in Princeton, New Jersey, United States from 1957 to 1993...
on the theory of characteristic class
Characteristic class
In mathematics, a characteristic class is a way of associating to each principal bundle on a topological space X a cohomology class of X. The cohomology class measures the extent to which the bundle is "twisted" — particularly, whether it possesses sections or not...
es. In his later work he provided a detailed theory of Hilbert modular surface
Hilbert modular surface
In mathematics, a Hilbert modular surface is one of the surfaces obtained by taking a quotient of a product of two copies of the upper half-plane by a Hilbert modular group....
s, working with Don Zagier
Don Zagier
Don Bernard Zagier is an American mathematician whose main area of work is number theory. He is currently one of the directors of the Max Planck Institute for Mathematics in Bonn, Germany, and a professor at the Collège de France in Paris, France.He was born in Heidelberg, Germany...
.
Hirzebruch is a foreign member of numerous academies and societies, including the United States National Academy of Sciences
United States National Academy of Sciences
The National Academy of Sciences is a corporation in the United States whose members serve pro bono as "advisers to the nation on science, engineering, and medicine." As a national academy, new members of the organization are elected annually by current members, based on their distinguished and...
, the Russian Academy of Sciences
Russian Academy of Sciences
The Russian Academy of Sciences consists of the national academy of Russia and a network of scientific research institutes from across the Russian Federation as well as auxiliary scientific and social units like libraries, publishers and hospitals....
, and the French Academy of Sciences
French Academy of Sciences
The French Academy of Sciences is a learned society, founded in 1666 by Louis XIV at the suggestion of Jean-Baptiste Colbert, to encourage and protect the spirit of French scientific research...
.
In 1980/81 he delivered the first Sackler Distinguished Lecture
Sackler Distinguished Lectures
The Sackler Distinguished Lectures are en endowed annual lecture series, bringing an outstanding mathematician to Israel every year. The lectures are given Tel Aviv University. They are supported by Raymond R. Sackler The Sackler Distinguished Lectures are en endowed annual lecture series, bringing...
in Israel.
Honors
Amongst many other honors, Hirzebruch was awarded a Wolf Prize in MathematicsWolf Prize in Mathematics
The Wolf Prize in Mathematics is awarded almost annually by the Wolf Foundation in Israel. It is one of the six Wolf Prizes established by the Foundation and awarded since 1978; the others are in Agriculture, Chemistry, Medicine, Physics and Arts...
in 1988, a Lobachevsky Medal
Lobachevsky Medal
The Lobachevsky Prize, awarded by the Russian Academy of Sciences, and the Lobachevsky Medal, awarded by the Kazan State University, are mathematical awards in honor of Nikolai Ivanovich Lobachevsky.-History:...
in 1989.
The government of Japan awarded him the Order of the Sacred Treasure
Order of the Sacred Treasure
The is a Japanese Order, established on January 4, 1888 by Emperor Meiji of Japan as the Order of Meiji. It is awarded in eight classes . It is generally awarded for long and/or meritorious service and considered to be the lowest of the Japanese orders of merit...
in 1996.
Hirzebruch won an Einstein Medal in 1999, and received the Cantor medal
Cantor medal
The Cantor medal of the Deutsche Mathematiker-Vereinigung is named in honor of Georg Cantor. It is awarded at most every second year during the yearly meetings of the society...
in 2004.
See also
- Atiyah–Hirzebruch spectral sequence
- Hirzebruch signature theorem
- Hirzebruch surfaceHirzebruch surfaceIn mathematics, a Hirzebruch surface is a ruled surface over the projective line. They were studied by .-Definition:The Hirzebruch surfaceΣn is the P1 bundle over P1associated to the sheafO+O.\...