Related papers: An introduction to spectral data for Higgs bundles
This is an expanded version of the lectures given at the Trieste Summer School 1992 on Low-dimensional Quantum Field Theories for Condensed Matter Physicists.
In the paper a Riemannian structure on the tangent bundle is defined by using a statistical structure $(g,\nabla)$ on the base manifold. Expressions for various curvatures of the structure are derived. Some rigidity results of the structure…
In this paper the moduli space of Higgs pairs over a fixed smooth projective curve with extra formal data is defined and it is endowed with a scheme structure. We introduce a relative version of the Krichever map using a fibration of Sato…
We consider the moduli space of polystable $L$-twisted $G$-Higgs bundles over a compact Riemann surface $X$, where $G$ is a real reductive Lie group, and $L$ is a holomorphic line bundle over $X$. Evaluating the Higgs field at a basis of…
This is an updated survey on the inverse spectral problem written for the Notices of the ICCM. It rapidly reviews some of the material in the previous survey of the same title (arXiv:math/0402356) and then discusses some relatively new…
Given a smooth complex projective variety $M$ and a smooth closed curve $X \subset M$ such that the homomorphism of fundamental groups $\pi_1(X) \rightarrow \pi_1(M)$ is surjective, we study the restriction map of Higgs bundles, namely from…
We present a survey on the moduli spaces of rank 2 quadric bundles over a compact Riemann surface X. These are objects which generalise orthogonal bundles and which naturally occur through the study of the connected components of the moduli…
This is an expanded version of the notes by the second author of the lectures on Hitchin systems and their quantization given by the first author at the Beijing Summer Workshop in Mathematics and Mathematical Physics ``Integrable Systems…
Lecture-notes: introducing and discussing basic kp concepts related to bands interaction at an elementary level to beginners
This article provides a (semi-)popular introduction to the phenomenology of neutrino masses.
The moduli space of stable bundles of rank 2 and degree 1 on a Riemann surface has rational cohomology generated by the so-called universal classes. The work of Baranovsky, King-Newstead, Siebert-Tian and Zagier provided a complete set of…
These are notes from a lecture course on symmetric spaces by the second author given at the University of Pittsburgh in the fall of 2010.
Geometric structures on manifolds became popular when Thurston used them in his work on the geometrization conjecture. They were studied by many people and they play an important role in higher Teichm\"uller theory. Geometric structures on…
These lecture notes are based on a course given at Institut de Physique Th\'eorique of CEA/Saclay in January/February 2013.
Informal collection of lecture notes introducing quantum mechanics in phase space and basic Gaussian quantum mechanics.
We update our analysis of the Higgs sector masses in Minimal Supersymmetry and in the Two-Higgs Doublet Model to the final ATLAS and CMS data from the 2011-2012 LHC run.
These lecture notes review the theoretical background to the Higgs boson, provide an introduction to its phenomenology, and describe the experimental tests that lead us to think that "beyond any reasonable doubt, it is a Higgs boson".…
We study the hypersymplectic geometry of the moduli space of solutions to Hitchin's harmonic map equations on a $G$-bundle. This is the split-signature analogue of Hitchin's Higgs bundle moduli space. Due to the lack of definiteness, this…
The first lecture describes the conflicts between the combined standard model (minimal electroweak and solar) predictions and the results of solar neutrino experiments. The second lecture discusses the possibilities for detecting with solar…
The goal of these lecture notes is to introduce the developing research area of gravitational-wave phenomenology. In more concrete terms, they are meant to provide an overview of gravitational-wave sources and an introduction to the…