Related papers: From $S^1$-fixed points to $\mathcal{W}$-algebra r…

We explore the cohomological structure for the (possibly singular) moduli of $\mathrm{SL}_n$-Higgs bundles for arbitrary degree on a genus g curve with respect to an effective divisor of degree >2g-2. We prove a support theorem for the…

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 carried out on a smooth Riemann surface. We start from an…

Holomorphic principal G-bundles over a complex manifold M can be studied using non-abelian cohomology groups H^1(M,G). On the other hand, if M=\Sigma is a closed Riemann surface, there is a correspondence between holomorphic principal…

Let $G$ be a compact group, let $\mathcal{B}$ be a unital C$^*$-algebra, and let $(\mathcal{A},G,\alpha)$ be a free C$^*$-dynamical system, in the sense of Ellwood, with fixed point algebra $\mathcal{B}$. We prove that…

We consider a manifold X obtained by a Kahler reduction of C^n, and we define its hyperkahler analogue M as a hyperkahler reduction of T^*C^n = H^n by the same group. In the case where the group is abelian and X is a smooth toric variety, M…

Given an $n$-tuple of positive real numbers $\alpha$ we consider the hyperpolygon space $X(\alpha)$, the hyperk\"{a}hler quotient analogue to the K\"ahler moduli space of polygons in $\mathbb{R}^3$. We prove the existence of an isomorphism…

Let $X$ be a compact connected Riemann surface and $D$ an effective divisor on $X$. Let ${\mathcal N}_H(r,d)$ denote the moduli space of $D$-twisted stable Higgs bundles (a special class of Hitchin pairs) on $X$ of rank $r$ and degree $d$.…

We show that the "eigenbundle" (localization bundle) of certain Hilbert modules over bounded symmetric domains of rank r is a "singular" vector bundle (linearly fibrered complex analytic space) which decomposes as a stratified sum of…

An overview about C*-algebra bundles with a Z-grading is presented, with particular emphasis on classification questions. In particular, we discuss the role of the representable KK(X ; -, -)-bifunctor introduced by Kasparov. As an…

This paper consists in a very brief English summary of the results appearing in French in two previous articles. We omit the proofs and focus on explaining our approach and theorems. This paper is not intended to be published. Questions are…

We prove a gluing theorem for solutions of Hitchin's self-duality equations with logarithmic singularities on a rank-2 vector bundle over a noded Riemann surface representing a boundary point of Teichm\"uller moduli space.

We consider models of chaotic inflation driven by the real parts of a conjugate pair of Higgs superfields involved in the spontaneous breaking of a grand unification symmetry at a scale assuming its Supersymmetric value. Employing Kaehler…

The Standard Model of particle physics is standardly formulated in terms of principal fibre bundles and their associated representations -- what may be called a symmetry-first approach. This paper develops an alternative geometry-first…

On a compact connected Riemann surface $C$ of genus at least $2$, we construct Lagrangian correspondences between moduli spaces of rank-$n$ Higgs bundles (respectively, holomorphic connections) and the Hilbert schemes of points on $T^\ast…

To each irreducible infinite dimensional representation $(\pi,\cH)$ of a $C^*$-algebra $\cA$, we associate a collection of irreducible norm-continuous unitary representations $\pi_{\lambda}^\cA$ of its unitary group $\U(\cA)$, whose…

The moduli space of Higgs bundles has two stratifications. The Bialynicki-Birula stratification comes from the action of the non-zero complex numbers by multiplication on the Higgs field, and the Shatz stratification arises from the…

M-theory geometric engineering on manifolds of special holonomy yields a rich class of novel field theories. In this paper, we construct new 3d $\mathcal{N}=2^{\ast}$ and $\mathcal{N}=4^{\ast}$ gauge theories, realized as mass-deformations…

We equip the multi-pullback $C^*$-algebra $C(S^5_H)$ of a noncommutative-deformation of the 5-sphere with a free $U(1)$-action, and show that its fixed-point subalgebra is isomorphic with the $C^*$-algebra of the multi-pullback quantum…

Let F be a field, let G be its absolute Galois group, and let R(G, k) be the representation ring of G over a suitable field k. In this preprint we construct a ring homomorphism from the mod 2 Milnor K-theory k_*(F) to the graded ring gr…

We consider a four-dimensional globally hyperbolic spacetime $(M,g)$ conformal to Minkowski spacetime, together with a massless, conformally coupled scalar field. Using a bulk-to-boundary correspondence, one can establish the existence of…