A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Develops infinite-dimensional Kempf-Ness theory for complexification-free groups.
We prove a version of the affine Kempf-Ness theorem for non-algebraic symplectic structures and shifted moment maps, and use it to describe hyperkahler quotients of T*G, where G is a complex reductive group.
Proves non-positivity of Hirzebruch form on stable weights and connects to flat logarithmic connections.
The paper trivializes moment maps for various geometric structures.
We formulate a Calabi-Yau type conjecture in generalized Kähler geometry, focusing on the case of nondegenerate Poisson structure. After defining natural Hamiltonian deformation spaces for generalized Kähler structures generalizing the notion of Kähler class, we conjecture unique solvability of Gualtieri's Calabi-Yau e…
For linear actions of real reductive Lie groups we prove the Kempf-Ness Theorem about closed orbits and the Kirwan-Ness Stratification Theorem of the null cone. Since our completely self-contained proof focuses strongly on geometric and analytic methods, essentially avoiding any deep algebraic result, it applies also t…
This note contains some observations on abelian convexity theorems. Convexity along an orbit is established in a very general setting using Kempf-Ness functions. This is applied to give short proofs of the Atiyah-Guillemin-Sternberg theorem and of abelian convexity for the gradient map in the case of a real analytic su…
The paper studies conditions for graphs connecting level sets of harmonic polynomials.
We study the line bundle mean curvature flow on Kähler surfaces under the hypercritical phase and a certain semipositivity condition. We naturally encounter such a condition when considering the blowup of Kähler surfaces. We show that the flow converges smoothly to a singular solution to the deformed Hermitian-Yang-Mil…
The purpose of this paper is to give a self-contained exposition of the Atiyah-Bott picture for the Yang-Mills equation over Riemann surfaces with an emphasis on the analogy to finite dimensional geometric invariant theory. The main motivation is to provide a careful study of the semistable and unstable orbits: This in…
We give a systematic treatment of the stability theory for action of a real reductive Lie group G on a topological space. More precisely, we introduce an abstract setting for actions of non-compact real reductive Lie groups on topological spaces that admit functions similar to the Kempf-Ness function. The point of this…
We prove that constant scalar curvature Kähler metric "adjacent" to a fixed Kähler class is unique up to isomorphism. This extends the uniqueness theorem of Donaldson and Chen-Tian, and formally fits into the infinite dimensional G.I.T picture described by Donaldson. We prove that the Calabi flow near a cscK metric exi…
Study on octonionic Nahm's equations and their moduli space properties.
Geometric invariant theory introduces stability conditions mirroring abelian category theory.
Study local perturbations of vector bundles with polynomial curvature solutions.
Regularization leads to balancedness in deep linear networks.
Paper addresses optimization on Hadamard manifolds, generalizing gradient flow.
Gradient descent on Hadamard manifolds converges to boundary points, solving optimization problems.