Robert Berman
Robert Bermans forskning handlar i stort om analytiska aspekter av komplex algebraisk och differential geometri. Hans forskning är fokuserad på samband mellan dessa områden och sannolikhetsteori, statistisk mekanik och matematisk fysik, samt aritmetisk (Arekelov) geometri, såväl som konvex geometri och analys.
I vida termer berör hans forskning, bland annat, problemet att beskriva hur koherenta strukturer framträder i storskaliga komplexa system, från ett geometriskt och analytiskt perspektiv. Hans arbeten visar att liknande matematiska verktyg och strukturer kan användas för att förstå tillsynes orelaterade områden; från den geometriska strukturen hos universum till signalbehandling och metrologi, så väl som komplexiteten i algebraiska ekvationer.
Han är Wallenberg Scholar sedan 201, läs .
Visar 65 publikationer
On K-stability, height bounds and the Manin-Peyre conjecture
Sharp bounds on the height of K-semistable Fano varieties I, the toric case
The spherical ensemble and quasi-Monte-Carlo designs
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
PROPAGATION OF CHAOS FOR A CLASS OF FIRST ORDER MODELS WITH SINGULAR MEAN FIELD INTERACTIONS
From Monge–Ampère equations to envelopes and geodesic rays in the zero temperature limit
Determinantal point processes and fermions on polarized complex manifolds: bulk universality
From the kÄhler-ricci flow to moving free boundaries and shocks
Propagation of chaos, wasserstein gradient flows and toric Kähler-Einstein metrics
On Large Deviations for Gibbs Measures, Mean Energy and Gamma-Convergence
Kahler-Einstein metrics, canonical random point processes and birational geometry
SAMPLING OF REAL MULTIVARIATE POLYNOMIALS AND PLURIPOTENTIAL THEORY
Convexity of the extended K-energy and the large time behavior of the weak Calabi flow
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
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
An arithmetic Hilbert-Samuel theorem for singular hermitian line bundles and cusp forms
Kähler–Einstein Metrics on Stable Varieties and log Canonical Pairs
Symmetrization of Plurisubharmonic and Convex Functions
Determinantal Point Processes and Fermions on Complex Manifolds: Large Deviations and Bosonization
Real Monge-Ampere equations and Kahler-Ricci solitons on toric log Fano varieties
RELATIVE KAHLER-RICCI FLOWS AND THEIR QUANTIZATION
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
Equidistribution of Fekete points on complex manifolds
Large deviations and entropy for determinantal point processes 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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Visar 4 forskningsprojekt
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)