Related papers: On Harder-Narasimhan strata in flag manifolds

We study the geometry of flag manifolds under different embeddings into a product of Grassmannians. We show that differential geometric objects and operations -- tangent vector, metric, normal vector, exponential map, geodesic, parallel…

Let ${\cal L}$ be a variation of Hodge structures on the complement $X^{*}$ of a normal crossing divisor (NCD) $ Y$ in a smooth analytic variety $X$ and let $ j: X^{*} = X - Y \to X $ denotes the open embedding. The purpose of this paper is…

This note provides a deeper understanding of the main results obtained in the author's 2007 DPDE paper \cite{Xiao}.

We prove the composition and $L^2$-boundedness theorems for the Nagel-Ricci-Stein flag kernels related to the natural gradation of homogeneous groups.

Given a grid diagram for a knot or link K in $S^3$, we construct a filtered spectrum whose homology is the knot Floer homology of K. We conjecture that the filtered homotopy type of the spectrum is an invariant of K. Our construction does…

Here, I derive an Ising Hamiltonian for $N$ coupled fibre-based Optical Parametric Oscillators (OPOs). For this, I use the Lugiato-Lefever equation. The derivation of the Hamiltonian does not pretend to be mathematically correct, although…

We compute the Harder-Narasimhan Filtration of the normal bundle $N_{C/\mathbb{P}^{g-1}}$ where $C$ is a general tetragonal canonical curve of genus $g$.

Let $M=G/K$ be a generalized flag manifold, that is the adjoint orbit of a compact semisimple Lie group $G$. We use the variational approach to find invariant Einstein metrics for all flag manifolds with two isotropy summands. We also…

In this paper, we investigate the use of compactly supported divergence-free wavelets for the representation of the Navier-Stokes solution. After reminding the theoretical construction of divergence-free wavelet vectors, we present in…

We introduce several families of filtrations on the space of vector bundles over a smooth projective variety. These filtrations are defined using the large k asymptotics of the kernel of the Dolbeault Dirac operator on a bundle twisted by…

Following ideas of Nori, Biswas, ..., we show that given an integer r>0, a noetherian scheme X, and an effective Cartier divisor D on it, the parabolic vector bundles on (X,D) with weights multiples of 1/r (in the sense of…

We extend previous results on boundedness of sets of coherent sheaves on a compact K\"ahler manifold to the relative and not necessarily smooth case. This enlarged context allows us to prove properness properties of the relative Douady…

We introduce a de Rham-Hodge framework induced by a vector field on a compact, oriented smooth manifold. By utilizing a vector field induced isomorphism on differential forms, we define a vector field induced Hodge $L^2$-inner product,…

This paper concerns an inverse elastic scattering problem which is to determine the location and the shape of a rigid obstacle from the phased or phaseless far-field data for a single incident plane wave. By introducing the Helmholtz…

We construct a filtered mapping cone formula that computes the knot Floer complex of the $(n,1)$--cable of the knot meridian in any rational surgery, generalizing Truong's result about the $(n,1)$--cable of the knot meridian in large…

The isomorphism number of an $F$-crystal $(M, \phi)$ over an algebraically closed field of positive characteristic is the smallest non-negative integer $n_M$ such that the $n_M$-th level truncation of $(M, \phi)$ determines the isomorphism…

Smooth vector fields on $\mathbb{R}^n$ can be decomposed into the sum of a gradient vector field and divergence-free (solenoidal) vector field under suitable hypotheses. This is called the Helmholtz-Hodge decomposition (HHD), which has been…

We study a certain type of wild harmonic bundles in relation with a Toda equation. We explain how to obtain a classification of the real valued solutions of the Toda equation in terms of their parabolic weights, from the viewpoint of the…

In this paper we present a fully ab initio Hartree-Fock approach aimed at calculating the static structure factor of crystalline insulators at arbitrary values of momentum transfer. In particular, we outline the computation of the…

A linear stability analysis of the free surface of a horizontally unbounded ferrofluid layer of arbitrary depth subjected to vertical vibrations and a horizontal magnetic field is performed. A nonmonotonic dependence of the stability…