Related papers: Formes de Whitney et primitives relatives de forme…

The objective of this article is to prove the necessity statement in Crawley-Boevey's conjectural solution to the (tame) Deligne-Simpson problem. We use the nonabelian Hodge correspondence, variation of parabolic weights and results of…

By using variational techniques we provide new existence results for Yamabe-type equations with subcritical perturbations set on a compact $d$-dimensional ($d\geq 3$) Riemannian manifold without boundary. As a direct consequence of our main…

This paper is a continuation of our previous works where we study maps from $X_0(N)$, $N \ge 1$, into $\mathbb P^2$ constructed via modular forms of the same weight and criteria that such a map is birational (see [12]). In the present paper…

Let $\g$ be any simple Lie algebra over $\mathbb{C}$. Recall that there exists an embedding of $\mathfrak{sl}_2$ into $\g$, called a principal TDS, passing through a principal nilpotent element of $\g$ and uniquely determined up to…

Let $V$ be a symmetric space over a connected reductive Lie algebra $G$, with Lie algebra $\mathfrak{g}$ and discriminant $\delta\in \mathbb{C}[V]$. A fundamental object is the invariant holonomic system $\mathcal{G} =\mathcal{D}(V)\Big/…

In bounding the homology of a manifold, Forman's Discrete Morse theory recovers the full precision of classical Morse theory: Given a PL triangulation of a manifold that admits a Morse function with c_i critical points of index i, we show…

The three dimensional primitive equations with full viscosity are considered in a horizontally periodic box $\Omega$, which are subject to either the homogeneous Neumann or Dirichlet conditions on the upper and bottom parts of the boundary.…

We establish some conditional uniqueness of weak solutions to the viscous primitive equations, and as an application, we prove the global existence and uniqueness of weak solutions, with the initial data taken as small $L^\infty$…

A distinguished family of completely prime primitive ideals in the universal enveloping algebra of a reductive Lie algebra ${\mathfrak g}$ over ${\mathbb C}$ are those ideals constructed from one-dimensional representations of finite…

We introduce a categorical analogue of Saito's notion of primitive forms. Let $W$ denote the potential $\frac{1}{n+1} x^{n+1}$. For the category $MF(W)$ of matrix factorizations of $W$ we prove that there exists a unique, up to non-zero…

Given a smooth morphism of schemes $X\rightarrow T$, denote by $\mathcal D_{X/T}^{\mathsf{cr}}$ the sheaf of rings of fiberwise crystalline differential operators on $X$ relative to $T$ and by $\Omega^\bullet_{X/T}$ the de Rham sheaf of…

In this paper, we improve the global existence result in [9] slightly. More precisely, the global existence of strong solutions to the primitive equations with only horizontal viscosity and diffusivity is obtained under the assumption of…

For an arbitrary subset $E\subset\mathbb{R}^n,$ we introduce and study the three vanishing subspaces of the H\"older space $\dot{C}^{0,\omega}(E)$ consisting of those functions for which the ratio $|f(x)-f(y)|/\omega(|x-y|)$ vanishes, when…

For any prism $(A, d)$, we construct an analogue of Fontaine's map $W_r(A/d) \to A/d\phi(d)\cdots\phi^{r-1}(d)$. Subsequently, we define a canonical map from de Rham-Witt forms to prismatic cohomology in the perfect case and prove that it…

Saito theory associates to a quasihomogeneous isolated singularity the structure of a Dubrovin--Frobenius manifold. This structure is not unique, depending on the special choice of a primitive form or, equivalently, a good basis. We study…

In this paper we develop a formalism for working with twisted realizations of vertex and conformal algebras. As an example, we study realizations of conformal algebras by twisted formal power series. The main application of our technique is…

The $\theta$-vacua of a gauge theory admit an equivalent formulation as vacua of a massless Chern-Simons $3$-form, which originate from the topological susceptibility of the vacuum. This formulation provides a framework in which the…

Let $r \geq 2$ be an integer, $q$ a prime power and $\mathbb{F}_{q}$ the finite field with $q$ elements. Consider the problem of showing existence of primitive elements in a subset $\mathcal{A} \subseteq \mathbb{F}_{q^r}$. We prove a sieve…

We prove that if $G$ is the graph of a connected triangulated $(d-1)$-manifold, for $d\geq 3$, then $G$ is generically globally rigid in $\mathbb R^d$ if and only if it is $(d+1)$-connected and, if $d=3$, $G$ is not planar. The special case…

This is the second in a series of papers dedicated to studying w-knots, and more generally, w-knotted objects (w-braids, w-tangles, etc.). These are classes of knotted objects that are wider but weaker than their "usual" counterparts. To…