Robert Berman
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 .
Showing 64 publications
The spherical ensemble and quasi-Monte-Carlo designs
Sharp bounds on the height of K-semistable Fano varieties I, the toric case
The probabilistic vs the quantization approach to Kähler–Einstein geometry
CONICAL CALABI-YAU METRICS ON TORIC AFFINE VARIETIES AND CONVEX CONES
Ensemble Equivalence for Mean Field Models and Plurisubharmonicity
Measure Preserving Holomorphic Vector Fields, Invariant Anti-Canonical Divisors and Gibbs Stability
Emergent Sasaki-Einstein geometry and AdS/CFT
A variational approach to the yau-tian-donaldson conjecture
The Sinkhorn algorithm, parabolic optimal transport and geometric Monge–Ampère equations
Regularity of Weak Minimizers of the K-Energy and Applications to Properness and K-Stability
Statistical mechanics of interpolation nodes, pluripotential theory and complex geometry
On the strict convexity of the K-energy
Kähler-Einstein metrics and the Kähler-Ricci flow on log Fano varieties
From Monge–Ampère equations to envelopes and geodesic rays in the zero temperature limit
PROPAGATION OF CHAOS FOR A CLASS OF FIRST ORDER MODELS WITH SINGULAR MEAN FIELD INTERACTIONS
From the kÄhler-ricci flow to moving free boundaries and shocks
Determinantal point processes and fermions on polarized complex manifolds: bulk universality
Propagation of chaos, wasserstein gradient flows and toric Kähler-Einstein metrics
Kahler-Einstein metrics, canonical random point processes and birational geometry
SAMPLING OF REAL MULTIVARIATE POLYNOMIALS AND PLURIPOTENTIAL THEORY
On Large Deviations for Gibbs Measures, Mean Energy and Gamma-Convergence
The volume of Kahler-Einstein varieties and convex bodies
Convexity of the K-energy on the space of Kähler metrics and uniqueness of extremal metrics
Convexity of the extended K-energy and the large time behavior of the weak Calabi flow
On the optimal regularity of weak geodesics in the space of metrics on a polarized manifold
K-polystability of Q-Fano varieties admitting Kahler-Einstein metrics
Kähler–Einstein Metrics on Stable Varieties and log Canonical Pairs
An arithmetic Hilbert-Samuel theorem for singular hermitian line bundles and cusp forms
Symmetrization of Plurisubharmonic and Convex Functions
Determinantal Point Processes and Fermions on Complex Manifolds: Large Deviations and Bosonization
RELATIVE KAHLER-RICCI FLOWS AND THEIR QUANTIZATION
Real Monge-Ampere equations and Kahler-Ricci solitons on toric log Fano varieties
A variational approach to complex Monge-Ampere equations
Regularity of Plurisubharmonic Upper Envelopes in Big Cohomology Classes
Fekete points and convergence towards equilibrium measures on complex manifolds
Kahler-Einstein metrics emerging from free fermions and statistical mechanics
Relative Kahler-Ricci flows and their quantization
Bergman kernels and equilibrium measures for polarized pseudoconcave domains
Analytic torsion, vortices and positive Ricci curvature
Regularity of plurisubharmonic upper envelopes in big cohomology classes
Bergman kernels for weighted polynomials and weighted equilibrium measures of C^n
Bergman kernels and equilibrium measures for line bundles over projective manifolds
A direct approach to Bergman kernel asymptotics for positive line bundles
Large deviations and entropy for determinantal point processes on complex manifolds
Equidistribution of Fekete points on complex manifolds
Growth of balls of holomorphic sections and energy at equilibrium
Convergence of Bergman measures of high powers of a line bundle
Bergman kernels and equilibrium measures for ample line bundles
Asymptotics for Bergman-Hodge kernels for high powers of complex line bundles
Super toeplitz operators on line bundles
Holomorphic Morse inequalities on manifolds with boundary
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Showing 4 research projects
Komplex geometri och statistisk mekanik
Stochastics for big data and big systems - bridging local and global
Kähler-Einstein metrics, random point processes and variational principles (RANDOM-KAHLER)
Complex geometry in equilibrium