Related papers: An introduction to spectral data for Higgs bundles
This paper presents an extended version of lecture notes for an introductory course on Berkovich analytic spaces that I gave in 2010 at Summer School "Berkovich spaces" at Institut de Mathmatiques de Jussieu.
This article determines the spectral data, in the integrable systems sense, for all weakly conformally immersed Hamiltonian stationary Lagrangian in $\R^4$. This enables us to describe their moduli space and the locus of branch points of…
We give a complete, self-contained computation of the spectral data parametrising Higgs bundles in the generic fibres of the $\mathrm{SO}_{2n+1}$-Hitchin fibration where the Higgs fields are $L$-twisted endomorphisms. Although the spectral…
We prove a closed formula counting semistable twisted Higgs bundles of fixed rank and degree over a smooth projective curve defined over a finite field. We also prove a formula for the Donaldson-Thomas invariants of the moduli spaces of…
We present an overview of some recent applications of Higgs bundles and the Hitchin fibration.
This is an expository article on the recent developments of Hodge theory on moduli spaces of smooth projective varieties with semi-ample canonical line bundles.
Lecture notes from a minicourse given at the ICTP in May 2002.
These are expanded notes of a course on basics of quantum field theory for mathematicians given by the author at MIT.
We count invariants of the moduli spaces of twisted Higgs bundles on a smooth projective curve.
This article is a summary of four introductory lectures on ``Neutrino Experiments,'' given at the 2006 TASI summer school. The purposes were to sketch out the present questions in neutrino physics and to discuss the experimental challenges…
In this paper, we study Hermitian-Yang-Mills connections (HYM) on a smooth Hermitian vector bundle over compact K\"{a}hler manifold. We calculate the virtual dimension of the moduli space of HYM connections and provide an analytic proof…
Given an holomorphic Higgs bundle on a compact Riemann surface of genus greater than one, we construct a DQ-module supported by the spectral curve associated to this bundle. Then, we relate quantum curves arising in various situations…
In this paper we continue our study on the moduli spaces of flat G-bundles, for any semi-simple Lie group G, over a Riemann surface by using heat kernel and Reidemeister torsion. Formulas for intersection numbers on the moduli spaces over a…
This is an introduction to the basic elements needed for the measurements and interpretation of data in the millimeter and sub-mm wavelength range. A more complete version will be published in the proceedings of the Saas Fee Winter School…
We introduce the moduli space of quasi-parabolic $SL(2,\mathbb{C})$-Higgs bundles over a compact Riemann surface $\Sigma$ and consider a natural involution, studying its fixed point locus when $\Sigma$ is $\mathbb{C} \mathbb{P}^1$ and…
These notes include introductory material on the notion of splitting fields for modules over a k-algebra where k is a field.
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 topics arising from this theory, especially some recent…
We study moduli spaces of parabolic Higgs bundles on a curve and their dependence on the choice of weights. We describe the chamber structure on the space of weights and show that, when a wall is crossed, the moduli space undergoes an…
Lecture notes written for a one-semester course in mathematical relativity aimed at mathematics and physics students. Not meant as an introduction to general relativity, but rather as a complementary, more advanced text.
This is an informal set of lecture notes on moduli spaces of curves based on a set of lectures given at the ICTP last summer. It begins at an elementary level and discusses the genus 1 case in detail. The notes then give an informal…