Hirzebruch, Friedrich
Overview
Works:  135 works in 640 publications in 7 languages and 7,274 library holdings 

Genres:  Conference papers and proceedings Biography History 
Roles:  Author, Editor, Honoree, Other, Author of introduction, Dedicatee, Interviewee, Contributor 
Classifications:  QA564, 510 
Publication Timeline
.
Most widely held works about
Friedrich Hirzebruch
 The founders of index theory : reminiscences of and about Sir Michael Atiyah, Raoul Bott, Friedrich Hirzebruch, and I.M. Singer( Book )
 Gesammelte Abhandlungen = Collected papers by Friedrich Hirzebruch( Book )
Most widely held works by
Friedrich Hirzebruch
Topological methods in algebraic geometry by
Friedrich Hirzebruch(
Book
)
59 editions published between 1966 and 1996 in 3 languages and held by 901 WorldCat member libraries worldwide
59 editions published between 1966 and 1996 in 3 languages and held by 901 WorldCat member libraries worldwide
Prospects in mathematics by
Friedrich Hirzebruch(
Book
)
17 editions published between 1971 and 2010 in English and held by 513 WorldCat member libraries worldwide
Prospects in Mathematics, a symposium, was held in Princeton on March 1618, 1970 on the occasion of the dedication of the university's new Fine Hall. Invited addresses were delivered by F.E.P. Hirzebruch, L. Hormander, J. Milnor, J.P. Serre, and I.M. Singer. The lecturers undertook to describe some current trends in mathematics in the prespective of the recent past and in terms of some of the expectations for the future. Among subjects discussed were algebraic groups, quadratic forms, topological aspects of global analysis, variants of the index theorem, and partial differential equations. This volume presents the written texts of those lectures. (Author)
17 editions published between 1971 and 2010 in English and held by 513 WorldCat member libraries worldwide
Prospects in Mathematics, a symposium, was held in Princeton on March 1618, 1970 on the occasion of the dedication of the university's new Fine Hall. Invited addresses were delivered by F.E.P. Hirzebruch, L. Hormander, J. Milnor, J.P. Serre, and I.M. Singer. The lecturers undertook to describe some current trends in mathematics in the prespective of the recent past and in terms of some of the expectations for the future. Among subjects discussed were algebraic groups, quadratic forms, topological aspects of global analysis, variants of the index theorem, and partial differential equations. This volume presents the written texts of those lectures. (Author)
Neue topologische Methoden in der algebraischen Geometrie by
Friedrich Hirzebruch(
Book
)
23 editions published between 1955 and 1962 in German and Undetermined and held by 428 WorldCat member libraries worldwide
23 editions published between 1955 and 1962 in German and Undetermined and held by 428 WorldCat member libraries worldwide
Differentiable manifolds and quadratic forms by
Friedrich Hirzebruch(
Book
)
23 editions published between 1962 and 1992 in English and held by 407 WorldCat member libraries worldwide
23 editions published between 1962 and 1992 in English and held by 407 WorldCat member libraries worldwide
O(n)Mannigfaltigkeiten, exotische Sphären und Singularitäten by
Friedrich Hirzebruch(
Book
)
30 editions published between 1968 and 2007 in 5 languages and held by 403 WorldCat member libraries worldwide
30 editions published between 1968 and 2007 in 5 languages and held by 403 WorldCat member libraries worldwide
Arbeitstagung Bonn, 1984 : proceedings of the meeting held by the MaxPlanckInstitut für Mathematik, Bonn, June 1522, 1984 by
1984, Bonn) Mathematische Arbeitstagung (25(
Book
)
30 editions published between 1984 and 1985 in 4 languages and held by 401 WorldCat member libraries worldwide
30 editions published between 1984 and 1985 in 4 languages and held by 401 WorldCat member libraries worldwide
Lattices and codes : a course partially based on lectures by F. Hirzebruch by
Wolfgang Ebeling(
Book
)
8 editions published between 1994 and 2013 in English and held by 337 WorldCat member libraries worldwide
The purpose of coding theory is the design of efficient systems for the transmission of information. The mathematical treatment leads to certain finite structures: the errorcorrecting codes. Surprisingly problems which are interesting for the design of codes turn out to be closely related to problems studied partly earlier and independently in pure mathematics. This book is about an example of such a connection: the relation between codes and lattices. Lattices are studied in number theory and in the geometry of numbers. Many problems about codes have their counterpart in problems about lattices and sphere packings. We give a detailed introduction to these relations including recent results of G. van der Geer and F. Hirzebruch. Let us explain the history of this book. In [LPS82] J.S. Leon, V. Pless, and N.J.A. Sloane considered the Lee weight enumerators of selfdual codes over the prime field of characteristic 5. They wrote in the introduction to their paper: "The weight enumerator of anyone of the codes ... is strongly constrained: it must be invariant under a threedimensional representation of the icosahedral group. These invariants were already known to Felix Klein, and the consequences for coding theory were discovered by Gleason and Pierce (and independently by the third author) ... (It is worth mentioning that precisely the same invariants have recently been studied by Hirzebruch in connection with cusps of the Hilbert modular surface associated with Q(J5)
8 editions published between 1994 and 2013 in English and held by 337 WorldCat member libraries worldwide
The purpose of coding theory is the design of efficient systems for the transmission of information. The mathematical treatment leads to certain finite structures: the errorcorrecting codes. Surprisingly problems which are interesting for the design of codes turn out to be closely related to problems studied partly earlier and independently in pure mathematics. This book is about an example of such a connection: the relation between codes and lattices. Lattices are studied in number theory and in the geometry of numbers. Many problems about codes have their counterpart in problems about lattices and sphere packings. We give a detailed introduction to these relations including recent results of G. van der Geer and F. Hirzebruch. Let us explain the history of this book. In [LPS82] J.S. Leon, V. Pless, and N.J.A. Sloane considered the Lee weight enumerators of selfdual codes over the prime field of characteristic 5. They wrote in the introduction to their paper: "The weight enumerator of anyone of the codes ... is strongly constrained: it must be invariant under a threedimensional representation of the icosahedral group. These invariants were already known to Felix Klein, and the consequences for coding theory were discovered by Gleason and Pierce (and independently by the third author) ... (It is worth mentioning that precisely the same invariants have recently been studied by Hirzebruch in connection with cusps of the Hilbert modular surface associated with Q(J5)
Lectures on Hilbert modular surfaces by
Friedrich Hirzebruch(
Book
)
27 editions published between 1972 and 1981 in 3 languages and held by 321 WorldCat member libraries worldwide
27 editions published between 1972 and 1981 in 3 languages and held by 321 WorldCat member libraries worldwide
The AtiyahSinger theorem and elementary number theory by
Friedrich Hirzebruch(
Book
)
15 editions published between 1974 and 1983 in English and held by 319 WorldCat member libraries worldwide
15 editions published between 1974 and 1983 in English and held by 319 WorldCat member libraries worldwide
Miscellanea mathematica by
Michael Francis Atiyah(
Book
)
12 editions published in 1991 in English and held by 286 WorldCat member libraries worldwide
Mathematics has a certain mystique, for it is pure and ex act, yet demands remarkable creativity. This reputation is reinforced by its characteristic abstraction and its own in dividual language, which often disguise its origins in and connections with the physical world. Publishing mathematics, therefore, requires special effort and talent. Heinz Gotze, who has dedicated his life to scientific pu blishing, took up this challenge with his typical enthusi asm. This Festschrift celebrates his invaluable contribu tions to the mathematical community, many of whose leading members he counts among his personal friends. The articles, written by mathematicians from around the world and coming from diverse fields, portray the important role of mathematics in our culture. Here, the reflections of important mathematicians, often focused on the history of mathematics, are collected, in recognition of Heinz Gotze's lifelong support of mathematics
12 editions published in 1991 in English and held by 286 WorldCat member libraries worldwide
Mathematics has a certain mystique, for it is pure and ex act, yet demands remarkable creativity. This reputation is reinforced by its characteristic abstraction and its own in dividual language, which often disguise its origins in and connections with the physical world. Publishing mathematics, therefore, requires special effort and talent. Heinz Gotze, who has dedicated his life to scientific pu blishing, took up this challenge with his typical enthusi asm. This Festschrift celebrates his invaluable contribu tions to the mathematical community, many of whose leading members he counts among his personal friends. The articles, written by mathematicians from around the world and coming from diverse fields, portray the important role of mathematics in our culture. Here, the reflections of important mathematicians, often focused on the history of mathematics, are collected, in recognition of Heinz Gotze's lifelong support of mathematics
Gesammelte Abhandlungen = Collected papers by
Friedrich Hirzebruch(
Book
)
34 editions published between 1987 and 2014 in 5 languages and held by 274 WorldCat member libraries worldwide
34 editions published between 1987 and 2014 in 5 languages and held by 274 WorldCat member libraries worldwide
Manifolds and modular forms by
Friedrich Hirzebruch(
Book
)
21 editions published between 1992 and 1994 in English and German and held by 243 WorldCat member libraries worldwide
During the winter term 1987/88 I gave a course at the University of Bonn under the title "Manifolds and Modular Forms". I wanted to develop the theory of "Elliptic Genera" and to learn it myself on this occasion. This theory due to Ochanine, Landweber, Stong and others was relatively new at the time. The word "genus" is meant in the sense of my book "Neue Topologische Methoden in der Algebraischen Geometrie" published in 1956: A genus is a homomorphism of the Thorn cobordism ring of oriented compact manifolds into the complex numbers. Fundamental examples are the signature and the Agenus. The Agenus equals the arithmetic genus of an algebraic manifold, provided the first Chern class of the manifold vanishes. According to Atiyah and Singer it is the index of the Dirac operator on a compact Riemannian manifold with spin structure. The elliptic genera depend on a parameter. For special values of the parameter one obtains the signature and the Agenus. Indeed, the universal elliptic genus can be regarded as a modular form with respect to the subgroup r (2) of the modular group; the two cusps 0 giving the signature and the Agenus. Witten and other physicists have given motivations for the elliptic genus by theoretical physics using the free loop space of a manifold
21 editions published between 1992 and 1994 in English and German and held by 243 WorldCat member libraries worldwide
During the winter term 1987/88 I gave a course at the University of Bonn under the title "Manifolds and Modular Forms". I wanted to develop the theory of "Elliptic Genera" and to learn it myself on this occasion. This theory due to Ochanine, Landweber, Stong and others was relatively new at the time. The word "genus" is meant in the sense of my book "Neue Topologische Methoden in der Algebraischen Geometrie" published in 1956: A genus is a homomorphism of the Thorn cobordism ring of oriented compact manifolds into the complex numbers. Fundamental examples are the signature and the Agenus. The Agenus equals the arithmetic genus of an algebraic manifold, provided the first Chern class of the manifold vanishes. According to Atiyah and Singer it is the index of the Dirac operator on a compact Riemannian manifold with spin structure. The elliptic genera depend on a parameter. For special values of the parameter one obtains the signature and the Agenus. Indeed, the universal elliptic genus can be regarded as a modular form with respect to the subgroup r (2) of the modular group; the two cusps 0 giving the signature and the Agenus. Witten and other physicists have given motivations for the elliptic genus by theoretical physics using the free loop space of a manifold
Algebraic geometry, Hirzebruch 70 : proceedings of the Algebraic Geometry Conference in honor of F. Hirzebruch's 70th birthday,
May 1116, 1998, Stefan Banach International Mathematical Center Warszawa, Poland by Algebraic Geometry Conference in Honor of F. Hirzebruch's 70th Birthday(
Book
)
13 editions published in 1999 in English and held by 225 WorldCat member libraries worldwide
13 editions published in 1999 in English and held by 225 WorldCat member libraries worldwide
Einführung in die Funktionalanalysis by
Friedrich Hirzebruch(
Book
)
32 editions published between 1971 and 1996 in German and Undetermined and held by 215 WorldCat member libraries worldwide
32 editions published between 1971 and 1996 in German and Undetermined and held by 215 WorldCat member libraries worldwide
Surveys in differential geometry : papers dedicated to Atiyah, Bott, Hirzebruch, and Singer by Conference on Geometry and Topology(
Book
)
11 editions published between 2000 and 2002 in English and held by 181 WorldCat member libraries worldwide
11 editions published between 2000 and 2002 in English and held by 181 WorldCat member libraries worldwide
Geradenkonfigurationen und algebraische Flächen by
Gottfried Barthel(
Book
)
13 editions published between 1987 and 1990 in German and Undetermined and held by 144 WorldCat member libraries worldwide
13 editions published between 1987 and 1990 in German and Undetermined and held by 144 WorldCat member libraries worldwide
Proceedings of the Hirzebruch 65 Conference on Algebraic Geometry : May 27, 1993 by
Hirzebruch 65 Conference on Algebraic Geometry(
Book
)
6 editions published in 1996 in English and held by 87 WorldCat member libraries worldwide
6 editions published in 1996 in English and held by 87 WorldCat member libraries worldwide
Codierungstheorie und ihre Beziehung zu Geometrie und Zahlentheorie. : Primzahlen: Theorie und Anwendung / Don Zagier by
Friedrich Hirzebruch(
Book
)
7 editions published between 1988 and 1989 in German and held by 59 WorldCat member libraries worldwide
7 editions published between 1988 and 1989 in German and held by 59 WorldCat member libraries worldwide
LeopoldinaSymposion Singularitäten singularities : im Schloss Reinhardsbrunn (Thüringen) vom 3. bis 7. Mai 1978 by
LeopoldinaSymposion Singularitäten(
Book
)
13 editions published between 1980 and 1981 in 3 languages and held by 48 WorldCat member libraries worldwide
13 editions published between 1980 and 1981 in 3 languages and held by 48 WorldCat member libraries worldwide
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Related Identities
 Atiyah, Michael Francis 1929 Honoree Author Dedicatee
 Mayer, K. H.
 Schwermer, Joachim Other Editor
 Suter, S. (Silke) 1943 Other Editor
 Koh, S. S.
 Neumann, W. D. (Walter David) 1946
 Ebeling, Wolfgang Author
 Remmert, Reinhold Editor
 Zagier, Don 1951
 Bott, Raoul 19232005 Honoree Dedicatee
Useful Links
Associated Subjects
Algebra Algebraic topology Atiyah, Michael Francis, Bott, Raoul, Coding theory Differentiable manifolds Differential topology Discontinuous groups Einstein manifolds Errorcorrecting codes (Information theory) Finite fields (Algebra) Fixed point theory Forms, Modular Forms, Quadratic Functional analysis Geometry Geometry, Algebraic Geometry, Differential Hilbert modular surfaces Hilbert space Hirzebruch, Friedrich Homology theory Index theory (Mathematics) Lattice theory Lie algebras Manifolds (Mathematics) Mathematicians Mathematics Modular groups Numbers, Prime Number theory Singer, I. M.(Isadore Manuel), Singularities (Mathematics) Sphere Surfaces, Algebraic Topology Wolf Foundation Prizes
Alternative Names
Chircebruch, F.
Chircebruch, F. 19272012
Chircebruch, F. [t]
Friedrich Ernst Peter Hirzebruch.
Friedrich Hirzebruch Duits wiskundige
Friedrich Hirzebruch German mathematician
Friedrich Hirzebruch matemàtic alemany
Friedrich Hirzebruch matematico tedesco
Friedrich Hirzebruch mathématicien allemand
Friedrich Hirzebruch tysk matematikar
Friedrich Hirzebruch tysk matematiker
Hircebruh, F.
Hirzebruch, F.
Hirzebruch, F. 19272012
Hirzebruch, F. (Friedrich)
Hirzebruch, Friedrch E.P. 1927
Hirzebruch, Friedrich.
Hirzebruch, Friedrich E. 19272012
Hirzebruch, Friedrich E. P. 19272012
Hirzebruch, Friedrich Ernst Peter 1927...
Hirzebruch Friedrich Ernst Peter 19272012
Hirzebruch, Fritz
Hirzebruch, Fritz 1927
Hirzebruch, Fritz 19272012
Хирцебрух, Ф..
Хирцебрух, Фридрих
프리드리히 히르체브루흐
フリードリッヒ・ヒルツェブルフ ドイツの数学者
弗里德里希·希策布鲁赫
Languages
English
(243)
German (130)
French (3)
Multiple languages (3)
Italian (1)
Miscellaneous languages (1)
Germanic (1)
German (130)
French (3)
Multiple languages (3)
Italian (1)
Miscellaneous languages (1)
Germanic (1)
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