Bo Berndtsson
Encyclopedia
Bo Berndtsson is a Swedish
mathematician
. His main contributions concern the theory of several complex variables
and complex geometry
. He gained in 1971 a BA degree from the University of Gothenburg in Sweden and obtained his PhD in 1977 under the direction of Tord Ganelius. Since 1996 he has been a professor at Chalmers University of Technology
in Gothenburg. He has also been a guest professor at UCLA in Los Angeles
, Université de Paris, Université Paul Sabatier
in Toulouse
, UAB
in Barcelona
and IPN
in Mexico City
. Berndtsson has been a member of the Royal Swedish Academy of Sciences
since 2003. In 1995 he was awarded the Göran Gustafsson prize.
in the plane. This formalism led to new results concerning
division and interpolation of holomorphic functions.
In the 1990s Berndtsson started to work with L^2 methods that had been introduced by Lars Hörmander
, Joseph J. Kohn
and others in the 1960s and he modified these methods to obtain uniform estimates for the dbar-equation. At this time he also achieved
results about interpolation and sampling in Hilbert spaces of holomorphic functions
using L^2-estimates.
More recently Berndtsson has worked on global problems on complex manifolds. In a series of papers starting in 2005 he has obtained positivity results for the curvature of holomorphic vector bundles naturally associated to holomorphic fibrations. These vector bundles arise as the zeroth direct images of the adjoint of an ample line bundle
over the fibration. The case of a trivial line bundle was considered in earlier work by Phillip Griffiths
in connection to variations of Hodge structures and by Fujita, Kawamata and Eckart Viehweg
in algebraic geometry
. Berndtsson has also explored applications of these positivity results in Kähler geometry (e.g., to geodesics in the space of Kähler metrics ) and algebraic geometry (e.g., a new proof of the Kawamata subadjunction formula in a collaboration with Mihai Paun).
Sweden
Sweden , officially the Kingdom of Sweden , is a Nordic country on the Scandinavian Peninsula in Northern Europe. Sweden borders with Norway and Finland and is connected to Denmark by a bridge-tunnel across the Öresund....
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....
. His main contributions concern the theory of several complex variables
Several complex variables
The theory of functions of several complex variables is the branch of mathematics dealing with functionson the space Cn of n-tuples of complex numbers...
and complex geometry
Complex geometry
In mathematics, complex geometry is the study of complex manifolds and functions of many complex variables. Application of transcendental methods to algebraic geometry falls in this category, together with more geometric chapters of complex analysis....
. He gained in 1971 a BA degree from the University of Gothenburg in Sweden and obtained his PhD in 1977 under the direction of Tord Ganelius. Since 1996 he has been a professor at Chalmers University of Technology
Chalmers University of Technology
Chalmers University of Technology , is a Swedish university located in Gothenburg that focuses on research and education in technology, natural science and architecture.-History:...
in Gothenburg. He has also been a guest professor at UCLA in Los Angeles
Los Ángeles
Los Ángeles is the capital of the province of Biobío, in the commune of the same name, in Region VIII , in the center-south of Chile. It is located between the Laja and Biobío rivers. The population is 123,445 inhabitants...
, Université de Paris, Université Paul Sabatier
Paul Sabatier University
Paul Sabatier University is a French university, in the Academy of Toulouse.Founded in 1229, the University of Toulouse is one of the oldest in Europe. Today’s Toulouse III was named for Paul Sabatier, winner of the 1912 Nobel prize in chemistry, when it was established on the foundations of the...
in Toulouse
Toulouse
Toulouse is a city in the Haute-Garonne department in southwestern FranceIt lies on the banks of the River Garonne, 590 km away from Paris and half-way between the Atlantic Ocean and the Mediterranean Sea...
, UAB
Autonomous University of Barcelona
The Autonomous University of Barcelona is a public university mostly located in Cerdanyola, near the city of Barcelona in Catalonia, Spain....
in Barcelona
Barcelona
Barcelona is the second largest city in Spain after Madrid, and the capital of Catalonia, with a population of 1,621,537 within its administrative limits on a land area of...
and IPN
National Polytechnic Institute
The National Polytechnic Institute colloquially known as the Polytechnic is one of the largest public universities in Mexico with 153.027 students at the high school, undergraduate and postgraduate levels...
in Mexico City
Mexico City
Mexico City is the Federal District , capital of Mexico and seat of the federal powers of the Mexican Union. It is a federal entity within Mexico which is not part of any one of the 31 Mexican states but belongs to the federation as a whole...
. Berndtsson has been a member of the Royal Swedish Academy of Sciences
Royal Swedish Academy of Sciences
The Royal Swedish Academy of Sciences or Kungliga Vetenskapsakademien is one of the Royal Academies of Sweden. The Academy is an independent, non-governmental scientific organization which acts to promote the sciences, primarily the natural sciences and mathematics.The Academy was founded on 2...
since 2003. In 1995 he was awarded the Göran Gustafsson prize.
Mathematical work
Berndtsson's first results concern zero sets of holomorphic functions, and in 1981 he showed that any divisor with finite area in the unit ball in the two-dimensional complex space is defined by a bounded holomorphic function (which is not true in higher dimensions). In the 1980s he also developed (together with Mats Andersson) a formalism to generate weighted integral representation formulas for holomorphic functions and solutions to the so-called dbar-equation, which is a the higher-dimensional generalization of the Cauchy-Riemann equationsCauchy-Riemann equations
In mathematics, the Cauchy–Riemann differential equations in complex analysis, named after Augustin Cauchy and Bernhard Riemann, consist of a system of two partial differential equations which must be satisfied if we know that a complex function is complex differentiable...
in the plane. This formalism led to new results concerning
division and interpolation of holomorphic functions.
In the 1990s Berndtsson started to work with L^2 methods that had been introduced by Lars Hörmander
Lars Hörmander
Lars Valter Hörmander is a Swedish mathematician who has been called "the foremost contributor to the modern theory of linear partial differential equations". He was awarded the Fields Medal in 1962, and the Wolf Prize in 1988...
, Joseph J. Kohn
Joseph J. Kohn
Joseph John Kohn is a Professor Emeritus of mathematics at Princeton University, where he does research on partial differential operators and function theory.-Life and work:...
and others in the 1960s and he modified these methods to obtain uniform estimates for the dbar-equation. At this time he also achieved
results about interpolation and sampling in Hilbert spaces of holomorphic functions
using L^2-estimates.
More recently Berndtsson has worked on global problems on complex manifolds. In a series of papers starting in 2005 he has obtained positivity results for the curvature of holomorphic vector bundles naturally associated to holomorphic fibrations. These vector bundles arise as the zeroth direct images of the adjoint of an ample line bundle
Ample line bundle
In algebraic geometry, a very ample line bundle is one with enough global sections to set up an embedding of its base variety or manifold M into projective space. An ample line bundle is one such that some positive power is very ample...
over the fibration. The case of a trivial line bundle was considered in earlier work by Phillip Griffiths
Phillip Griffiths
Phillip Griffiths is an American mathematician, known for his work in the field of geometry, and in particular for the complex manifold approach to algebraic geometry. He was a major developer in particular of the theory of variation of Hodge structure in Hodge theory and moduli theory.He received...
in connection to variations of Hodge structures and by Fujita, Kawamata and Eckart Viehweg
Eckart Viehweg
Eckart Viehweg was a German mathematician. He was a professor of algebraic geometry at the University of Duisburg-Essen.In 2003 he won the Gottfried Wilhelm Leibniz Prize with his wife, Hélène Esnault....
in 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...
. Berndtsson has also explored applications of these positivity results in Kähler geometry (e.g., to geodesics in the space of Kähler metrics ) and algebraic geometry (e.g., a new proof of the Kawamata subadjunction formula in a collaboration with Mihai Paun).
Further activities
Bo Berndtsson was a singer in the Swedish prog rock group Love Explosion that was founded in the late sixties.External links
- http://www.chalmers.se/sections/forskning/professorer/beskrivningar/bo-berndtsson Bo Berndtsson at Chalmers University of Technology
- http://genealogy.math.ndsu.nodak.edu/id.php?id=34758 Mathematics Genealogy Project
- http://www.progg.se/band.asp?ID=20 Love explosion