1. Generalised parabolic Higgs bundles

In [MR3174731] Bhosle constructs moduli spaces of generalized parabolic Hitchin (GPH) pairs on a nonsingular curve $X$, together with a Hitchin map. In the case where $X$ is the normalisation of an integral projective curve $Y$ compares to the moduli space of GPH pairs on $X$ to the moduli space of Hitchin pairs on $Y$. The case considered by Bhosle is when the structure group is $GL_n(\mathbb{C})$.
Problem 1.1.
Construct an analog of generalised parabolic Hitchin pairs, the corresponding moduli spaces, and the Hitchin maps, for other complex algebraic groups $G_{\mathbb{C}}$. (I.e. Define and study “$G_\mathbb{C}$principal generalised parabolic Hitchin pairs”.) 
If we believe that nonabelian Hodge theory (NAHT) should work in a really robust way for Higgs pairs on nodal curves, there should be comparison theorems.
Problem 1.2.
Compare generalised parabolic Higgs bundles on nodal curves a la Bhosle [MR3174731] to the work of (a) Bezrukovnikov and Kapranov (microlocal sheaves) [MR3530166] and (b) CrawleyBoevey [MR3064416] (or [arXiv:1109.2018]). Also, what does NAHT on the normalization descend to on the nodal curve? 
In [MR3291351] Bhosle and Parameswaran define a notion of “strong semistability” for vector bundles on a projective variety, and show that the category of such objects on a projective curve $Y$ forms a neutral Tannakian category – i.e. the category is equivalent to representations of some group $\mathcal{G}_Y$ (the “holonomy group scheme”).
Problem 1.3.
Give a geometric description of the holonomy group scheme.
Cite this as: AimPL: Singular geometry and Higgs bundles in string theory, available at http://aimpl.org/singularhiggs.