Related papers: Hecke modifications of Higgs bundles and the exten…
The analytic Langlands correspondence describes the solution to the spectral problem for the quantised Hitchin Hamiltonians. It is related to the S-duality of $\cal{N}=4$ super Yang-Mills theory. We propose a one-parameter deformation of…
This paper is a survey on the role of Higgs bundle theory in the study of higher Teichm\"uller spaces. Recall that the Teichm\"uller space of a compact surface can be identified with a certain connected component of the moduli space of…
This paper deals with moduli spaces of framed principal bundles with connections with irregular singularities over a compact Riemann surface. These spaces have been constructed by Boalch by means of an infinite-dimensional symplectic…
Here we survey several results and conjectures on the cohomology of the total space of the Hitchin system: the moduli space of semi-stable rank n and degree d Higgs bundles on a complex algebraic curve C. The picture emerging is a dynamic…
We formulate and prove a Riemann-Hilbert correspondence between $\hbar$-differential equations and sheaf quantizations, which can be considered as a correspondence between two kinds of quantizations (deformation and sheaf quantization) of…
In these lectures I consider the Hitchin integrable systems and their relations with the self-duality equations and the twisted super-symmetric Yang-Mills theory in four dimension follow Hitchin and Kapustin-Witten. I define the Symplectic…
This thesis contains work which appeared in several papers. Additionally to the results in the papers it contains a detailed introduction and some further proofs and remarks. The dissertation gives a description of the topology and…
We establish a Kobayashi-Hitchin correspondence for the stable Higgs sheaves on a compact Kaehler manifold. Using it, we also obtain a Kobayashi-Hitchin correspondence for the stable Higgs G-sheaves, where G is any complex reductive linear…
This letter describes a completely-integrable system of Yang-Mills-Higgs equations which generalizes the Hitchin equations on a Riemann surface to arbitrary k-dimensional complex manifolds. The system arises as a dimensional reduction of a…
The appearance of the Bethe Ansatz equation for the Nonlinear Schr\"{o}dinger equation in the equivariant integration over the moduli space of Higgs bundles is revisited. We argue that the wave functions of the corresponding two-dimensional…
Given an orthogonal bundle $E$ over a smooth projective curve $X$ we define a Hecke transformation in the moduli space of orthogonal bundles by performing an elementary transformation with respect to a Lagrangian submodule $L \subset…
Clifford Taubes showed that the moduli space of the variational equation of the Yang-Mills-Higgs functional on the plane is non-empty, and its elements correspond to "vortices". Inspired by this result, in this paper, we show that the…
In this paper, we establish the Hitchin--Kobayashi correspondence for the $I_\pm$-holomorphic quiver bundle $\mathcal{E}=(E,\phi)$ over a compact generalized K\"{a}hler manifold $(X, I_+,I_-,g, b)$ such that $g$ is Gauduchon with respect to…
This paper is devoted to the study of the Higgs bundle associated with the universal abelian variety over the good reduction of a Shimura curve of PEL type. Due to the endomorphism structure, the Higgs bundle decomposes into the direct sum…
We present a short review of theories based on warped extra dimensions (motivated by the hierarchy problem of the Standard Model) which can accomodate a Higgs boson in the range suggested by the recent LHC results at 7 TeV. Using the…
In this paper we study the relation between parabolic Higgs bundles and irreducible representations of the fundamental group of punctured Riemann surfaces established by Simpson. We generalize a result of Hitchin, identifying those…
We discuss the relation between Liouville theory and the Hitchin integrable system, which can be seen in two ways as a two step process involving quantization and hyperkaehler rotation. The modular duality of Liouville theory and the…
In this paper, motivated by the recent discovery of a Higgs-like boson at the LHC with a mass m_H\simeq 126 GeV, we review different models where the hierarchy problem is solved by means of a warped extra dimension. In the Randall-Sundrum…
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.
The non-abelian Hodge correspondence identifies complex variations of Hodge structures with certain Higgs bundles. In this work we analyze this relationship, and some of its ramifications, when the variations of Hodge structures are…