Robert Berman

Professor at Chalmers, Mathematical Sciences, Algebra and geometry

Robert Berman works mainly on analytical aspects of complex algebraic and differential geometry. His research focuses on connections between these fields and probability, statistical mechanics and mathematical physics and also arithmetic (Arakelov) geometry, as well as convex geometry and analysis. In broad terms his research concerns, among other things, the problem of describing the emergence of coherent structures in large scale complex systems from a geometric and analytic point of view. His work reveals that similar mathematical tools and structures can be used to understand seemingly unrelated areas, ranging from the geometric structure of the universe to signal processing and metrology, as well as the complexity of algebraic equations.He is (since 2013) a Knut and Alice Wallenberg Academy Fellow (see http://www.wallenbergacademyfellows.se/en/List-of-scientists/BermanRobert/ for a popular account of some of his work).

Source: chalmers.se

Projects

2013–2018

Stochastics for big data and big systems - bridging local and global

Holger Rootzen Applied Mathematics and Statistics
Bernt Wennberg Mathematical Sciences
Rebecka Jörnsten Applied Mathematics and Statistics
Igor Rychlik Applied Mathematics and Statistics
Sergey Zuev Applied Mathematics and Statistics
Johan Jonasson Analysis and Probability Theory
Johan Wästlund Analysis and Probability Theory
Jeffrey Steif Analysis and Probability Theory
Olle Häggström Applied Mathematics and Statistics
Robert Berman Algebra and geometry
Aila Särkkä Applied Mathematics and Statistics
Knut and Alice Wallenberg Foundation

There might be more projects where Robert Berman participates, but you have to be logged in as a Chalmers employee to see them.

Publications

2017

The volume of Kahler-Einstein varieties and convex bodies

Bo Berndtsson, Robert Berman,
Journal für die Reine und Angewandte Mathematik. Vol. 2017 (723), p. 127-152
Scientific journal article - peer reviewed
2016

K-polystability of Q-Fano varieties admitting Kahler-Einstein metrics

Robert Berman,
Inventiones Mathematicae. Vol. 203 (3), p. 973-1025
Scientific journal article - peer reviewed
2014

Kahler-Einstein Metrics on Stable Varieties and log Canonical Pairs

Robert Berman, H. Guenancia,
Geometric and Functional Analysis. Vol. 24 (6), p. 1683-1730
Scientific journal article - peer reviewed
2014

An arithmetic Hilbert-Samuel theorem for singular hermitian line bundles and cusp forms

Robert Berman, G. F. I. Montplet,
Compositio Mathematica. Vol. 150 (10), p. 1703-1728
Scientific journal article - peer reviewed
2014

Symmetrization of Plurisubharmonic and Convex Functions

Robert Berman, Bo Berndtsson,
Indiana University Mathematics Journal. Vol. 63 (2), p. 345-365
Scientific journal article - peer reviewed
2014

Determinantal Point Processes and Fermions on Complex Manifolds: Large Deviations and Bosonization

Robert Berman,
Communications in Mathematical Physics. Vol. 327 (1), p. 1-47
Scientific journal article - peer reviewed
2013

Real Monge-Ampere equations and Kahler-Ricci solitons on toric log Fano varieties

Robert Berman, Bo Berndtsson,
Annales de la faculté des sciences de Toulouse. Vol. 22 (4), p. 649-711
Scientific journal article - peer reviewed
2013

A thermodynamical formalism for Monge-Ampere equations, Moser-Trudinger inequalities and Kahler-Einstein metrics

Robert Berman,
Advances in Mathematics. Vol. 248, p. 1254-1297
Scientific journal article - peer reviewed
2013

RELATIVE KAHLER-RICCI FLOWS AND THEIR QUANTIZATION

Robert Berman,
Analysis & Pde. Vol. 6 (1), p. 131-180
Scientific journal article - peer reviewed
2013

A variational approach to complex Monge-Ampere equations

Robert Berman, Sebastien Boucksom, Viincent Guedj et al
Publications mathématiques. Vol. 117 (1), p. 179-245
Scientific journal article - peer reviewed
2012

Bergman Geodesics

Robert Berman, Julien Keller,
Lecture notes in mathematics. Vol. 2038, p. 283-302
Scientific journal article - peer reviewed
2012

Sharp Asymptotics for Toeplitz Determinants and Convergence Towards the Gaussian Free Field on Riemann Surfaces

Robert Berman,
International Mathematics Research Notices (22), p. 5031-5062
Scientific journal article - peer reviewed
2012

Regularity of Plurisubharmonic Upper Envelopes in Big Cohomology Classes

Robert Berman, J. P. Demailly,
Perspectives in Analysis, Geometry, and Topology: On the Occasion of the 60th Birthday of Oleg Viro. Marcus Wallenberg Symposium on Perspectives in Analysis, Geometry and Topology. Stockholm, Sweden, May 19-25, 2008 . Vol. 296, p. 39-66
Conference paper - peer reviewed
2011

Sharp asymptotics for Toeplitz determinants, fluctuations and the gaussian free field on a Riemann surface,

Robert Berman,
preprint på arxiv.org
Scientific journal article - non peer reviewed
2011

Kahler-Einstein metrics emerging from free fermions and statistical mechanics

Robert Berman,
Journal of High Energy Physics (10), p. Art. no. 106
Scientific journal article - peer reviewed
2011

Fekete points and convergence towards equilibrium measures on complex manifolds

Robert Berman, Sebastien Boucksom, David Witt Nyström et al
Acta Mathematica. Vol. 207 (1), p. 1-27
Scientific journal article - non peer reviewed
2010

Analytic torsion, vortices and positive Ricci curvature

Robert Berman,
preprint på arxiv.org
Scientific journal article - non peer reviewed
2010

Relative Kahler-Ricci flows and their quantization

Robert Berman,
preprint på arxiv.org
Scientific journal article - non peer reviewed
2010

Growth of balls of holomorphic sections and energy at equilibrium

Robert Berman, S. Boucksom,
Inventiones Mathematicae. Vol. 181 (2), p. 337-394
Scientific journal article - peer reviewed
2010

Bergman kernels and equilibrium measures for polarized pseudoconcave domains

Robert Berman,
International Journal of Mathematics. Vol. 21 (1), p. 77-115
Scientific journal article - peer reviewed
2009

Regularity of plurisubharmonic upper envelopes in big cohomology classes

Robert Berman, Jean-Pierre Demailly,
http://arxiv.org/abs/0905.1246
Scientific journal article - non peer reviewed
2009

Bergman kernels for weighted polynomials and weighted equilibrium measures of C^n

Robert Berman,
Indiana University Mathematics Journal. Vol. 58 (4), p. 1921-1946
Scientific journal article - peer reviewed
2009

Bergman kernels and equilibrium measures for line bundles over projective manifolds

Robert Berman,
American Journal of Mathematics. Vol. 131 (5), p. 1485-1524
Scientific journal article - peer reviewed
2008

Growth of balls of holomorphic sections and energy at equilibrium

Robert Berman, Sebastien Boucksom,
Inventiones Mathematicae. Vol. 181 (2), p. 337-394
Scientific journal article - peer reviewed
2008

Equidistribution of Fekete points on complex manifolds

Robert Berman, Sebastien Boucksom,
www.arxiv.org, artikelnr 0807.0035
Scientific journal article - non peer reviewed
2008

Convergence of Bergman measures of high powers of a line bundle

Robert Berman, David Witt Nyström,
Preprint
2008

A direct approach to Bergman kernel asymptotics for positive line bundles

Bo Berndtsson, Robert Berman, Johannes Sjöstrand et al
Arkiv för Matematik. Vol. 46 (2), p. 197-217
Scientific journal article - peer reviewed
2007

Asymptotics for Bergman-Hodge kernels for high powers of complex line bundles

Robert Berman, Johannes Sjöstrand,
Ann. de la Fac. des Sciences de Toulouse Vol. XIV (2007) no. 4, p. 719--771
Scientific journal article - peer reviewed
2007

Bergman kernels and equilibrium measures for ample line bundles

Robert Berman,
www.arxiv.org, artikel 0704.1640
Scientific journal article - non peer reviewed
2006

Super toeplitz operators on line bundles

Robert Berman,
Journal of Geometric Analysis. Vol. 16 (1), p. 1-22
Scientific journal article - peer reviewed
2005

Holomorphic Morse inequalities on manifolds with boundary

Robert Berman,
Annales De L Institut Fourier. Vol. 55 (4), p. 1055-
Scientific journal article - peer reviewed
2005

Asymptotics of Bergman Kernels

Robert Berman, Bo Berndtsson, Johannes Sjöstrand et al
Preprint
2002

Bergman kernels and local holomorphic Morse inequalities

Robert Berman,
Licentiate thesis