102 citations · 601 across the 49 of their papers we have counts for
60 papers
On K-stability, height bounds and the Manin-Peyre conjecture
Robert J. Berman
This note discusses some intriguing connections between height bounds on complex K-semistable Fano varieties X and Peyre's conjectural formula for the density of rational points on…
Kähler-Einstein metrics and Archimedean zeta functions
Robert J. Berman
While the existence of a unique Kähler-Einstein metric on a canonically polarized manifold X was established by Aubin and Yau already in the 70s there are only a few explicit formu…
The probabilistic vs the quantization approach to Kähler-Einstein geometry
Robert J. Berman
In the probabilistic construction of Kähler-Einstein metrics on a complex projective algebraic manifold X - involving random point processes on X - a key role is played by the part…
Emergent complex geometry
Robert J. Berman
This is a double exposure of the probabilistic construction of Kahler-Einstein metrics on a complex projective algebraic variety X - where the Kahler-Einstein metric emerges from a…
Ensemble equivalence for mean field models and plurisubharmonicity
Robert J. Berman
We show that entropy is globally concave with respect to energy for a rich class of mean field interactions, including regularizations of the the point-vortex model in the plane, p…
Emergent Sasaki-Einstein geometry and AdS/CFT
Robert J. Berman, Tristan C. Collins, Daniel Persson
We consider supergravity in five-dimensional Anti-De Sitter space with minimal supersymmetry, encoded by a Sasaki-Einstein metric on a five-dimensional compact manifold $…