6 papers
Quantitative Stability and Numerical Resolution of the Moment Measure Problem
Guillaume Bonnet, Yanir A. Rubinstein
The moment measure problem consists in finding a convex function whose moment measure, i.e., the pushforward by of the measure with density , i…
Symmetry notions for toric Fanos
Chenzi Jin, Yanir A. Rubinstein, Yang Zhang
We survey various notions of symmetry for toric varieties. These notions range from algebraic geometric, complex geometric, representation theoretic, combinatorial, convex geometri…
Stability thresholds for big classes
Chenzi Jin, Yanir A. Rubinstein, Gang Tian
In 1987, the -invariant theorem gave a fundamental criterion for existence of Kahler-Einstein metrics on smooth Fano manifolds. In 2012, Odaka-Sano extended the framework to $\…
Asymptotics of discrete Okounkov bodies and thresholds
Chenzi Jin, Yanir A. Rubinstein, Gang Tian
This article initiates the study of discrete Okounkov bodies and higher-dimensional Weierstrass gap phenomena, with applications to asymptotic analysis of stability and global log…
Asymptotics of quantized barycenters of lattice polytopes with applications to algebraic geometry
Chenzi Jin, Yanir A. Rubinstein
This article addresses a combinatorial problem with applications to algebraic geometry. To a convex lattice polytope and each of its integer dilations one may associate th…
Convex meets complex
Yanir A. Rubinstein
Convex geometry and complex geometry have long had fascinating interactions. This survey offers a tour of a few.