Friedrich Hirzebruch

Friedrich Ernst Peter Hirzebruch, Friedrich EP Hirzebruch, ( born October 17, 1927 in Hamm, † 27, 2012 in Bonn ) was a German mathematician.

He is known both for his pioneering work in modern algebraic geometry using topological methods, as well as a science organizer, who has made ​​an outstanding contribution in a leading position to the international integration of the German mathematicians after the Second World War.

Life

Hirzebruch studied from 1945 to 1950 Mathematics, Physics and Mathematical Logic at the Westfälische Wilhelms-Universität in Münster and at the Swiss Federal Institute of Technology Zurich. It was 1950 when Heinrich Behnke and Heinz Hopf rer with the paper "On four-dimensional Riemann surfaces of ambiguous analytic functions of two complex variables, " Dr.. nat. doctorate. At first he was a research assistant at the Mathematical Institute of the University of Erlangen. From 1952 to 1954 he worked at the Institute for Advanced Study in Princeton, where he worked with Kunihiko Kodaira particularly, and with Donald Spencer, Raoul Bott and Armand Borel. There he achieved international attention by the set of Hirzebruch - Riemann -Roch ( and as a preparation to his signature set ). In 1955 he qualified as a professor of mathematics at Münster.

Following an assistant professor at Princeton University, USA, in the years 1955/1956 he was appointed to a professorship at the Rheinische Friedrich- Wilhelms- University of Bonn, where he taught until his retirement in 1993. He was a visiting professor at the University of California, Berkeley, Harvard University, University of Pennsylvania, Mathematical Sciences Research Institute (Berkeley ), the College de France (Paris), Institut des Hautes Etudes Scientifiques ( Bures- sur -Yvette ), University of Oxford, University of Amsterdam, Kabul University, Chinese Academy of Sciences, Beijing, Kyoto University, Instituto de Matematica Pura e Aplicada in Rio de Janeiro.

He is a founding director of the Max Planck Institute for Mathematics in Bonn, which emerged in 1980 out of the 1969 he founded Collaborative Research Center Theoretical Mathematics at the University of Bonn. He headed the Institute in 1981 until 1995. Moreover, he was president of the German Mathematical Society 1961/1962 and 1990, President of the European Mathematical Society ( EMS) from 1990 to 1994 and Chairman of the Scientific Council of the International Banach Center for Mathematics 1993 to 2002.

Friedrich Hirzebruch been married since 1952 and had three children.

Work

Hirzebruch research concentrated on the fields of algebraic geometry, topology, number theory and singularity theory. His work appeared in New topological methods in algebraic geometry, 1956-1995 in several editions and translated into English, Japanese and Russian, is a standard work. With the eponymous set of Hirzebruch - Riemann -Roch, which ushered in one of the most important developments of modern mathematics, he laid the foundation in 1954 for his international reputation. The theorem is the arithmetic gender ( defined as the alternating sum of the dimensions of the cohomology of the sheaf of sections of a unitary vector bundle ) with the Todd class the same. It has been proven in the 1950s by Hirzebruch with Kobordismentheorie (which he exchanged with René Thom ). He proved to his first signature set ( Princeton, 1953) in preparation. Today we use the Atiyah-Singer index theorem, the unified this whole area. With Armand Borel he gave with his generalization of the Riemann - Roch theorem, a new interpretation of Weyl character formulas for Lie groups. In the 1960s he founded with Michael Atiyah the topological K-theory, a cohomology theory with vector bundles ( in the book Ebbinghaus, inter alia, "numbers", he gives an example of their application to the classification of division algebras ). In the 1970s he examined, inter alia, algebraic surfaces such as the Hilbert module surfaces. Another area were particularly in the 1960s, the topology of singularities ( exotic spheres, etc.), an area in which his student Egbert Brieskorn achieved significant results in the 1960s.

An upside of Hirzebruch 1954 issue of the topology of algebraic varieties was solved in 2009 by Dieter Kotschick.

Friedrich Hirzebruch created the " Math Workshop ", which brings together the international elite mathematicians at the University of Bonn since 1957. On the first working session in 1957 were Alexander Grothendieck, Michael Atiyah, Hans Grauert, Nicolaas Kuiper and Jacques Tits. The collaborative research center set up by him "Theoretical mathematics " gained international reputation. Special recognition he deserved because of the structure of the Max Planck Institute for Mathematics in Bonn.

In 1958 he gave a plenary lecture at the International Congress of Mathematicians in Edinburgh ( complex manifolds ).

His doctoral include, inter alia, Don Zagier, Egbert Brieskorn, Klaus Jänich, Detlef Gromoll, Klaus Lamotke, Winfried Scharlau, Matthias Kreck and Lothar Göttsche.

Many of his books, essays and lectures are characterized by a special pedagogical skill.

Honors and Awards

Hirzebruch received numerous national and international awards and honorary doctorates from the Universities of Warwick ( 1980), Göttingen (1982 ), Oxford ( 1984), Wuppertal (1987 ), Notre Dame ( 1989), Trinity College, Dublin (1992 ), Athens ( 1993), Potsdam (1995 ), Constance (1999) and Augsburg ( 2007). He was a member of the German Academy of Natural Scientists Leopoldina in Halle, the North Rhine- Westphalian Academy of Sciences and Arts in Dusseldorf, the Academy of Sciences and Literature in Mainz, the Heidelberg Academy of Sciences, the Academy of Sciences in Göttingen, the Saxon Academy of Sciences and the Berlin- Brandenburg Academy of Sciences, the Academies of Science in the Netherlands, Ukraine, Russia, France, Great Britain, Poland, the USA and Ireland and of the Academia Europaea. He was also an honorary member of the Austrian Academy of Sciences and the American Academy of Arts and Sciences.

1962 and 1990 he was president of the German Mathematical Society.

Writings (selection )

• Collected Essays, 2 volumes, Springer Verlag 1987
• New topological methods in algebraic geometry, Springer-Verlag 1956, 1962 English: . Topological Methods in Algebraic Geometry. Springer -Verlag 1978, ISBN 3,540,035,257th
• With Günter Scheja: Sheaves and cohomology theory. Aschendorff 1957.
• Karl Heinz Mayer: manifolds, exotic spheres and singularities. Springer -Verlag 1968, ISBN 978-3-540-04227-3.
• Winfried Scharlau with: Introduction to Functional Analysis. Oxford University Press 1971, ISBN 3860254294th
• About the quaternionalen projective spaces. C. H. Beck 1968, ISBN 376964378X.
• Peter Hilton, Reinhold Remmert: Miscellanea mathematica. Springer 1991, ISBN 3540541748th
• With Heinz -Dieter Ebbinghaus, Hans Hermes include: numbers. Springer -Verlag, Berlin, 3rd edition 1993, ISBN 3540556540th
• With Gottfried Barthel, Thomas Höfer: Just configurations and Algebraic Surfaces. Vieweg 1997, ISBN 3,528,089,075th
• With Gerd Fischer, Winfried Scharlau (Editor): A Century of Mathematics from 1890 to 1990. Festschrift for the anniversary of the DMV. Vieweg 1997, ISBN 3,528,063,262th
• Ciro Ciliberto, Rick Miranda, Mina Teicher: Applications of Algebraic Geometry to Coding Theory, Physics and Computation. Springer -Verlag 2001, ISBN 978-1402000041.
• S. Koh, W. Neumann: Differentiable manifolds and quadratic forms. 1971, ISBN 978-0824713096.
• Don Zagier: The Atiyah -Singer Theorem and Elementary Number Theory. Publish or Perish, 1974, ISBN 978-0914098126.
• Gerard van der Geer: Lectures on Hilbert modular surfaces. Montreal, 1981, ISBN 978-2760605626.
• Thomas Berger, Rainer Jung: Manifolds and modular forms. Vieweg 1992, ISBN 3,528,064,145th
• Learning complex analysis in Münster- Paris, Zurich and Princeton from 1945 to 1953, DMV Releases 1998, No.2

Based on lectures given by Hirzebruch:

• Wolfgang Ebeling: Lattices and Codes. A Course Partially Based on Lectures by F. Hirzebruch. Vieweg, Braunschweig others 2002, ISBN 3-528-16497-2.

Some online accessible essays:

• Hirzebruch, van de Ven, " Hilbert modular surfaces and the classification of algebraic surfaces", Inv.Math.23, 1974, 1-29
• Hirzebruch, Atiyah " Kohomologieoperationen and characteristic classes ", Math.Zeitschrift, 77, 1961, 149-187
• Matthias Kreck On the concept of genus in topology and complex analysis, Notices AMS, 2009, No.6, pdf