Robert Berman

Full Professor at 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 2019, a Wallenberg Scholar, see .

Source: chalmers.se
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Showing 64 publications

2024

The spherical ensemble and quasi-Monte-Carlo designs

Robert Berman
Constructive Approximation. Vol. 59 (2), p. 457-483
Journal article
2024

Sharp bounds on the height of K-semistable Fano varieties I, the toric case

Rolf Andreasson, Robert Berman
Compositio Mathematica. Vol. 160 (10)
Journal article
2024

The probabilistic vs the quantization approach to Kähler–Einstein geometry

Robert Berman
Mathematische Annalen. Vol. 388 (4), p. 4383-4404
Journal article
2023

CONICAL CALABI-YAU METRICS ON TORIC AFFINE VARIETIES AND CONVEX CONES

Robert Berman
Journal of Differential Geometry. Vol. 125 (2), p. 345-377
Journal article
2022

Ensemble Equivalence for Mean Field Models and Plurisubharmonicity

Robert Berman
Archive for Rational Mechanics and Analysis. Vol. 246 (2-3), p. 771-822
Journal article
2022

Measure Preserving Holomorphic Vector Fields, Invariant Anti-Canonical Divisors and Gibbs Stability

Robert Berman
Analysis Mathematica. Vol. 48 (2), p. 347-375
Journal article
2022

Emergent Sasaki-Einstein geometry and AdS/CFT

Robert Berman, Tristan C. Collins, Daniel Persson
Nature Communications. Vol. 13 (1)
Journal article
2021

A variational approach to the yau-tian-donaldson conjecture

Robert Berman, Sebastien Boucksom, Mattias Jonsson
Journal of the American Mathematical Society. Vol. 34 (3), p. 605-652
Journal article
2021

Priors leading to well-behaved Coulomb and Riesz gases versus zeroth-order phase transitions - a potential-theoretic characterization

Robert Berman
Electronic Journal of Probability. Vol. 26 ( 145), p. 1-49
Journal article
2021

Convergence Rates for Discretized Monge–Ampère Equations and Quantitative Stability of Optimal Transport

Robert Berman
Foundations of Computational Mathematics. Vol. 21 (4), p. 1099-1140
Journal article
2020

The Sinkhorn algorithm, parabolic optimal transport and geometric Monge–Ampère equations

Robert Berman
Numerische Mathematik. Vol. 145 (4), p. 771-836
Journal article
2020

Regularity of Weak Minimizers of the K-Energy and Applications to Properness and K-Stability

Robert Berman, T. Darvas, Hoang Chinh Lu
Annales Scientifiques de lEcole Normale Superieure. Vol. 53 (2), p. 267-289
Journal article
2019

Statistical mechanics of interpolation nodes, pluripotential theory and complex geometry

Robert Berman
Annales Polonici Mathematici. Vol. 123 (1), p. 71-153
Journal article
2019

Kähler-Einstein metrics and the Kähler-Ricci flow on log Fano varieties

Robert Berman, Sebastien Boucksom, Philippe Eyssidieux et al
Journal für die Reine und Angewandte Mathematik. Vol. 2019 (751), p. 27-89
Journal article
2019

On the strict convexity of the K-energy

Robert Berman
Pure and Applied Mathematics Quarterly. Vol. 15 (4), p. 983-999
Journal article
2019

From Monge–Ampère equations to envelopes and geodesic rays in the zero temperature limit

Robert Berman
Mathematische Zeitschrift. Vol. 291 (1-2), p. 365-394
Journal article
2019

PROPAGATION OF CHAOS FOR A CLASS OF FIRST ORDER MODELS WITH SINGULAR MEAN FIELD INTERACTIONS

Magnus Önnheim, Robert Berman
SIAM Journal on Mathematical Analysis. Vol. 51 (1), p. 159-196
Journal article
2018

From the kÄhler-ricci flow to moving free boundaries and shocks

Robert Berman, Hoang Chinh Lu
Journal de l'Ecole Polytechnique - Mathematiques. Vol. 5, p. 549-563
Journal article
2018

Propagation of chaos, wasserstein gradient flows and toric Kähler-Einstein metrics

Robert Berman, Magnus Önnheim
Analysis and PDE. Vol. 11 (6), p. 1343-1380
Journal article
2018

Determinantal point processes and fermions on polarized complex manifolds: bulk universality

Robert Berman
Springer Proceedings in Mathematics and Statistics. Vol. 269, p. 341-393
Paper in proceeding
2018

Kahler-Einstein metrics, canonical random point processes and birational geometry

Robert Berman
Proceedings of Symposia in Pure Mathematics. Vol. 97 (1), p. 29-73
Paper in proceeding
2018

SAMPLING OF REAL MULTIVARIATE POLYNOMIALS AND PLURIPOTENTIAL THEORY

Robert Berman, Joaquim Ortega-Cerda
American Journal of Mathematics. Vol. 140 (3), p. 789-820
Journal article
2018

On Large Deviations for Gibbs Measures, Mean Energy and Gamma-Convergence

Robert Berman
Constructive Approximation. Vol. 48 (1), p. 3-30
Journal article
2017

The volume of Kahler-Einstein varieties and convex bodies

Bo Berndtsson, Robert Berman
Journal fur die Reine und Angewandte Mathematik. Vol. 2017 (723), p. 127-152
Journal article
2017

Convexity of the K-energy on the space of Kähler metrics and uniqueness of extremal metrics

Robert Berman, Bo Berndtsson
Journal of the American Mathematical Society. Vol. 30 (4), p. 1165-1196
Journal article
2017

Convexity of the extended K-energy and the large time behavior of the weak Calabi flow

Robert Berman, T. Darvas, Hoang Chinh Lu
Geometry and Topology. Vol. 21 (5), p. 2945-2988
Journal article
2017

On the optimal regularity of weak geodesics in the space of metrics on a polarized manifold

Robert Berman
Trends in Mathematics (9,78332E+12), p. 111-120
Book chapter
2017

Large Deviations for Gibbs Measures with Singular Hamiltonians and Emergence of Kahler-Einstein Metrics

Robert Berman
Communications in Mathematical Physics. Vol. 354 (3), p. 1133-1172
Journal article
2016

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

Robert Berman
Inventiones Mathematicae. Vol. 203 (3), p. 973-1025
Journal article
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
Journal article
2014

Kähler–Einstein Metrics on Stable Varieties and log Canonical Pairs

Robert Berman, Henri Guenancia
Geometric and Functional Analysis. Vol. 24 (6), p. 1683-1730
Journal article
2014

Symmetrization of Plurisubharmonic and Convex Functions

Robert Berman, Bo Berndtsson
Indiana University Mathematics Journal. Vol. 63 (2), p. 345-365
Journal article
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
Journal article
2013

RELATIVE KAHLER-RICCI FLOWS AND THEIR QUANTIZATION

Robert Berman
Analysis and PDE. Vol. 6 (1), p. 131-180
Journal article
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
Journal article
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
Journal article
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
Journal article
2012

Bergman Geodesics

Robert Berman, Julien Keller
Lecture Notes in Mathematics. Vol. 2038, p. 283-302
Review article
2012

Regularity of Plurisubharmonic Upper Envelopes in Big Cohomology Classes

Robert Berman, J. P. Demailly
Progress in Mathematics. Vol. 296, p. 39-66
Book chapter
2012

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

Robert Berman
International Mathematics Research Notices. Vol. 2012 (22), p. 5031-5062
Journal article
2011

Fekete points and convergence towards equilibrium measures on complex manifolds

Robert Berman, Sebastien Boucksom, David Witt Nyström
Acta Mathematica. Vol. 207 (1), p. 1-27
Magazine article
2011

Kahler-Einstein metrics emerging from free fermions and statistical mechanics

Robert Berman
Journal of High Energy Physics. Vol. 2011 (10), p. Art. no. 106-
Journal article
2010

Relative Kahler-Ricci flows and their quantization

Robert Berman
preprint på arxiv.org
Magazine article
2010

Analytic torsion, vortices and positive Ricci curvature

Robert Berman
preprint på arxiv.org
Magazine article
2010

Bergman kernels and equilibrium measures for polarized pseudoconcave domains

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

Regularity of plurisubharmonic upper envelopes in big cohomology classes

Robert Berman, Jean-Pierre Demailly
arxiv.org/abs/0905.1246
Magazine article
2009

Bergman kernels and equilibrium measures for line bundles over projective manifolds

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

A direct approach to Bergman kernel asymptotics for positive line bundles

Bo Berndtsson, Robert Berman, Johannes Sjöstrand
Arkiv för Matematik. Vol. 46 (2), p. 197-217
Journal article
2008

Equidistribution of Fekete points on complex manifolds

Robert Berman, Sebastien Boucksom
www.arxiv.org, artikelnr 0807.0035
Magazine article
2008

Convergence of Bergman measures of high powers of a line bundle

Robert Berman, David Witt Nyström
Preprint
2008

Growth of balls of holomorphic sections and energy at equilibrium

Robert Berman, Sebastien Boucksom
Inventiones Mathematicae. Vol. 181 (2), p. 337-394
Journal article
2007

Bergman kernels and equilibrium measures for ample line bundles

Robert Berman
www.arxiv.org, artikel 0704.1640
Magazine article
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
Journal article
2006

Super toeplitz operators on line bundles

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

Asymptotics of Bergman Kernels

Robert Berman, Bo Berndtsson, Johannes Sjöstrand
Preprint
2005

Holomorphic Morse inequalities on manifolds with boundary

Robert Berman
Annales de lInstitut Fourier. Vol. 55 (4), p. 1055-
Journal article
2002

Bergman kernels and local holomorphic Morse inequalities

Robert Berman
Licentiate thesis

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Showing 4 research projects

2018–2021

Komplex geometri och statistisk mekanik

Robert Berman Algebra and geometry
Swedish Research Council (VR)

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

8 publications exist
2013–2017

Kähler-Einstein metrics, random point processes and variational principles (RANDOM-KAHLER)

Robert Berman Algebra and geometry
European Commission (EC)

2012–2015

Complex geometry in equilibrium

Robert Berman Algebra and geometry
Swedish Research Council (VR)

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