Related papers: Generalized Hitchin system, Spectral curve and N=1…

We consider spectral sequences in smooth generalized cohomology theories, including differential generalized cohomology theories. The main differential spectral sequences will be of the Atiyah-Hirzebruch (AHSS) type, where we provide a…

In this work we present a new approach on studying dynamical systems. Combining the two ways of expressing the uncertainty, using probabilistic theory and credibility theory, we have research the generalized fractional hybrid equations. We…

We study metric aspects of the universal moduli space of solutions to Hitchin's equations as the complex structure $J$ varies over the Teichm\"uller space $\mathcal{T}$ of a closed surface $\Sigma$. Our approach is gauge theoretical and…

In this paper, we confirm a physical conjecture regarding the parabolic $\mathrm{SO}_{2n}$-Hitchin system, showing that Hitchin map factors through a finite cover of the Hitchin base that is isomorphic to an affine space. We first show that…

In this paper we reinterpret the Poisson structure of the Hitchin-type system in cohomological terms. The principal ingredient of a new interpretation in the case of the Beauville system is the meromorphic cohomology of the spectral curve,…

The aim of this paper is two-fold. First, we define symplectic maps between Hitchin systems related to holomorphic bundles of different degrees. We call these maps the Symplectic Hecke Correspondence (SHC) of the corresponding Higgs…

We present an inverse scattering construction of generalised point interactions (GPI) -- point-like objects with non-trivial scattering behaviour. The construction is developed for single centre $S$-wave GPI models with rational…

Stochastic spectral methods are efficient techniques for uncertainty quantification. Recently they have shown excellent performance in the statistical analysis of integrated circuits. In stochastic spectral methods, one needs to determine a…

In this work, we make new developments in generic cotangent bundle geometries, depending on all phase-space variables. In particular, we will focus on the so-called generalized Hamilton spaces, discussing how the main ingredients of this…

Described is n-level quantum system realized in the n-dimensional ''Hilbert'' space H with the scalar product G taken as a dynamical variable. The most general Lagrangian for the wave function and G is considered. Equations of motion and…

We observe Thurston's asymmetric metric on Teichm\"uller space may be expressed in terms of the H\"older regularity of boundary maps. We then associate $2$-dimensional stratified loci in $\mathbb{RP}^{n-1}$ to $\text{PSL}_n(\mathbb{R})$…

Mukai's space, parametrizing simple sheaves on a K3 surface S whose numerical invariants are those of a line bundle on a curve C in S, is interpreted as a deformation of Hitchin's system on C. This is used to show that the nilpotent cone in…

The immersion of the string world sheet, regarded as a Riemann surface, in $R^3$ and $R^4$ is described by the generalized Gauss map. When the Gauss map is harmonic or equivalently for surfaces of constant mean curvature, we obtain…

A classical example of Mumford gives a generically non-reduced component of the Hilbert scheme of smooth curves in the projective 3-space such that a general element of the component is contained in a smooth cubic hypersurface in the…

For supersymmetric GUT models from heterotic string theory, built from a stable holomorphic SU(n) vector bundle $V$ on a Calabi-Yau threefold $X$, the net amount of chiral matter can be computed by a Chern class computation. Corresponding…

We introduce new times in the monodromy preserving equations. While the usual times related to the moduli of complex structures of Riemann curves such as coordinates of marked points, we consider the moduli of generalized complex structures…

We study smooth SU(2) solutions of the Hitchin equations on R^2, with the determinant of the complex Higgs field being a polynomial of degree n. When n>=3, there are moduli spaces of solutions, in the sense that the natural L^2 metric is…

Stochastic differential equations for processes with values in Hilbert spaces are now largely used in the quantum theory of open systems. In this work we present a class of such equations and discuss their main properties; moreover, we…

A moving parallel frame method is applied to geometric non-stretching curve flows in the Hermitian symmetric space Sp(n)/U(n) to derive new integrable systems with unitary invariance. These systems consist of a bi-Hamiltonian modified…

We present a unified representation-theoretic method to compute the Laplace-Beltrami spectrum on homogeneous principal bundles. For this setting, we introduce a multi-parameter family of metric deformations called generalized canonical…