The aim of this paper is two-fold. Firstly, we prove Toda's-independence conjecture for
Gopakumar–Vafa invariants of arbitrary local curves. Secondly, following Davison's work, we …

A log Calabi-Yau surface with maximal boundary, or Looijenga pair, is a pair $(Y, D) $ with $
Y $ a smooth rational projective complex surface and $ D= D_1+\dots+ D_l\in|-K_Y| $ an …

arXiv:1909.10543v1 [math.DG] 23 Sep 2019 Page 1 Higgs bundles – Recent applications
Laura P. Schaposnik ∗ September 25, 2019 Introduction This note is dedicated to introducing …

We provide a general method for constructing moduli stacks whose points are diagrams of
vector bundles over a fixed base, indexed by a fixed simplicial set--that is, quiver bundles of …

This paper is a survey aimed on the introduction of non-Abelian Hodge theory that gives the
correspondence between flat bundles and Higgs bundles. We will also introduce some …

We introduce the notion of generalized hyperpolygon, which arises as a representation, in
the sense of Nakajima, of a comet-shaped quiver. We identify these representations with …

Prior works relating meromorphic Higgs bundles to topological recursion, in particular those
of Dumitrescu-Mulase, have considered non-singular models that allow the recursion to be …

In view of the recent proofs of the P= W conjecture, the present paper reviews and relates
the latest results in the field, with a view on how P= W phenomena appear in multiple areas …

We construct a family of S n modules indexed by c∈{1,…, n} with the property that upon
restriction to S n− 1 they recover the classical parking function representation of Haiman …

We explore very stable and wobbly bundles, twisted in a particular sense by a line bundle,
over complex algebraic curves of genus $1 $. We verify that twisted stable bundles on an …