Related papers: Subelliptic sharp G\r{a}rding inequality on compac…

We develop the classification of weakly symmetric pseudo--riemannian manifolds $G/H$ where $G$ is a semisimple Lie group and $H$ is a reductive subgroup. We derive the classification from the cases where $G$ is compact, and then we discuss…

Given some vector fields on a smooth manifold satisfying H\"ormander's condition, we define a bi-graded pseudo-differential calculus which contains the classical pseudo-differential calculus and a pseudo-differential calculus adapted to the…

We will present versions of the Rellich-Kondrachov theorem for pseudo-differential operators acting on localizable Hardy spaces. One of the techniques includes boundedness properties for pseudodifferential operators with symbols in the…

We show that the Lusternik-Schnirelmann category of a simple, simply connected, compact Lie group G is bounded above by the sum of the relative categories of certain distinguished conjugacy classes in G corresponding to the vertices of the…

In this paper we will outline elements of the global calculus of seudo-differential operators on the group SU(2). This is a part of a more general approach to pseudo-differential operators on compact Lie groups that will appear in the…

We show how to construct a resolution of symplectic orbifolds obtained as quotients of presymplectic manifolds with a torus action. As a corollary, this allows us to desingularise generic symplectic quotients. Given a manifold with a…

Given a smooth manifold $M$ (with or without boundary), in this paper we study the regularisation of traces for the global pseudo-differential calculus in the context of non-harmonic analysis. Indeed, using the global pseudo-differential…

Let $A$ be a positive bounded linear operator on a complex Hilbert space $\mathcal{H}$ and $\mathcal{B}_{A}(\mathcal{H})$ be the subspace of all operators which admit $A$-adjoints operators. In this paper, we establish some inequalities…

We prove the rigidity of presymplectic actions of a compact semisimple Lie algebra on a presymplectic manifold of constant rank in the local and global case. The proof uses an abstract normal form theorem we had stated in a previous work,…

We study the space of conjugacy classes of subgroups of a compact Lie group G whose identity component is a torus, and consider how various invariants of subgroups behave as sheaves over this space. This feeds in to the author's programme…

The methods of spectral geometry are useful for investigating the metric aspects of noncommutative geometry and in these contexts require extensive use of pseudo-differential operators. In a foundational paper, Connes showed that, by direct…

In this paper, we propose a weak version of quotient for the algebraic action of a group on a variety, which we shall call a pseudo-quotient. They arise when we focus on the purely topological properties of good GIT quotients regardless of…

Given a smooth manifold $M$ (with or without boundary), in this paper we establish a global functional calculus (without the standard assumption that the operators are classical pseudo-differential operators) and the G\r{a}rding inequality…

For a positive integer $g$, let $\mathrm{Sp}_{2g}(R)$ denote the group of $2g \times 2g$ symplectic matrices over a ring $R$. Assume $g \ge 2$. For a prime number $\ell$, we give a self-contained proof that any closed subgroup of…

In this paper, we investigate the subelliptic nonlocal Brezis-Nirenberg problem on stratified Lie groups involving critical nonlinearities, namely, \begin{align*} (-\Delta_{\mathbb{G}, p})^s u&= \mu |u|^{p_s^*-2}u+\lambda h(x, u) \quad…

In this work we establish sharp kernel conditions ensuring that the corresponding integral operators belong to Schatten-von Neumann classes. The conditions are given in terms of the spectral properties of operators acting on the kernel. As…

We show that for a hypoelliptic Dirichlet form operator A on a stratified complex Lie group, if the logarithmic Sobolev inequality holds, then a holomorphic projection of A is strongly hypercontractive in the sense of Janson. This extends…

We establish that for any proper action of a Lie group on a manifold the associated equivariant differentiable cohomology groups with coefficients in modules of $\mathcal{C}^\infty$-functions vanish in all degrees except than zero.…

We construct an algebra of pseudodifferential operators on each groupoid in a class that generalizes differentiable groupoids to allow manifolds with corners. We show that this construction encompasses many examples. The subalgebra of…

We present necessary and sufficient conditions to have global hypoellipticity and global solvability for a class of vector fields defined on a product of compact Lie groups. In view of Greenfield's and Wallach's conjecture, about the…