Semistability, modular lattices, and iterated logarithms
Representation Theory
2023-03-29 v2 Algebraic Geometry
Classical Analysis and ODEs
Abstract
We provide a complete description of the asymptotics of the gradient flow on the space of metrics on any semistable quiver representation. This involves a recursive construction of approximate solutions and the appearance of iterated logarithms and a limiting filtration of the representation. The filtration turns out to have an algebraic definition which makes sense in any finite length modular lattice. This is part of a larger project by the authors to study iterated logarithms in the asymptotics of gradient flows, both in finite and infinite dimensional settings.
Cite
@article{arxiv.1706.01073,
title = {Semistability, modular lattices, and iterated logarithms},
author = {Fabian Haiden and Ludmil Katzarkov and Maxim Kontsevich and Pranav Pandit},
journal= {arXiv preprint arXiv:1706.01073},
year = {2023}
}
Comments
v2: new introduction, typos corrected