In this article we discuss the role of stability functions in geometric invariant theory and apply stability function techniques to various types of asymptotic problems in the Kahler geometry of GIT quotients. We discuss several particular classes of examples, namely, toric varieties, spherical varieties and the symplectic version of quiver varieties.National Science Foundation (U.S.) (Grant DMS-0408993
Let (M,ω) be a Kähler manifold and let K be a compact group that acts on M in a Hamiltonian fashion....
We study the Yang{Mills ow on a holomorphic vector bundle E over a compact Kahler manifold X. We con...
K–polystability is, on the one hand, conjecturally equivalent to the existence of certain canonical ...
We consider the problem of classifying linear systems of hypersurfaces (of a fixed degree) in some p...
We study the conditions under which a fibration of toric varieties, fibered over a flag variety, adm...
On a Weierstrass elliptic surface, we describe the action of the relative Fourier-Mukai transform on...
We study partition functions of random Bergman metrics, with the actions defined by a class of geome...
We give an introduction to moduli stacks of gauged maps satisfying a stability conditition introduce...
In this note, we prove that on polarized toric manifolds the relative K-stability with respect to Do...
In this thesis, we study convergence results of certain non-linear geometric flows on vector bundles...
We show two stability results for a closed Riemannian manifold whose Ricci curvature is small in the...
Let $G$ be a connected, complex reductive Lie group and $X$ a $\mathbb Q$-Fano $G$-spherical variety...
We give a detailed statement of a KAM theorem about the conservation of partially hyperbolic tori on...
The goal of this paper is to look at strong theorems relating thedifferential geometry of vector bun...
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1998.Includes bibliogr...
Let (M,ω) be a Kähler manifold and let K be a compact group that acts on M in a Hamiltonian fashion....
We study the Yang{Mills ow on a holomorphic vector bundle E over a compact Kahler manifold X. We con...
K–polystability is, on the one hand, conjecturally equivalent to the existence of certain canonical ...
We consider the problem of classifying linear systems of hypersurfaces (of a fixed degree) in some p...
We study the conditions under which a fibration of toric varieties, fibered over a flag variety, adm...
On a Weierstrass elliptic surface, we describe the action of the relative Fourier-Mukai transform on...
We study partition functions of random Bergman metrics, with the actions defined by a class of geome...
We give an introduction to moduli stacks of gauged maps satisfying a stability conditition introduce...
In this note, we prove that on polarized toric manifolds the relative K-stability with respect to Do...
In this thesis, we study convergence results of certain non-linear geometric flows on vector bundles...
We show two stability results for a closed Riemannian manifold whose Ricci curvature is small in the...
Let $G$ be a connected, complex reductive Lie group and $X$ a $\mathbb Q$-Fano $G$-spherical variety...
We give a detailed statement of a KAM theorem about the conservation of partially hyperbolic tori on...
The goal of this paper is to look at strong theorems relating thedifferential geometry of vector bun...
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1998.Includes bibliogr...
Let (M,ω) be a Kähler manifold and let K be a compact group that acts on M in a Hamiltonian fashion....
We study the Yang{Mills ow on a holomorphic vector bundle E over a compact Kahler manifold X. We con...
K–polystability is, on the one hand, conjecturally equivalent to the existence of certain canonical ...