Related papers: Singular equivariant asymptotics and the moment ma…

We study isometric Lie group actions on symmetric spaces admitting a section, i.e. a submanifold which meets all orbits orthogonally at every intersection point. We classify such actions on the compact symmetric spaces with simple isometry…

Given a compact boundaryless Riemannian manifold $Y$ on which a compact Lie group $G$ acts, there is always a metric on $Y$ such that the action is by isometries. Assuming $Y$ is equipped with such a metric, recall that the $G$-invariant…

We discuss several aspects concerning the asymptotic dynamics of dicrete-time semigroups associated with a quantum channel. By using an explicit expression of the asymptotic map, which describes the action of the quantum channel on its…

Let $M$ be a compact Riemannian manifold with smooth boundary, and let $R(\lambda)$ be the Dirichlet-to-Neumann operator at frequency $\lambda$. We obtain a leading asymptotic for the spectral counting function for $\lambda^{-1}R(\lambda)$…

We introduce equivariant Liouville forms and Duistermaat-Heckman distributions for Hamiltonian group actions with group valued moment maps. The theory is illustrated by applications to moduli spaces of flat connections on 2-manifolds.

We study the orbit structure and the geometric quantization of a pair of mutually commuting hamiltonian actions on a symplectic manifold. If the pair of actions fulfils a symplectic Howe condition, we show that there is a canonical…

We study the asymptotic behavior of the heat content on a compact Riemannian manifold with boundary and with singular specific heat and singular initial temperature distributions imposing Robin boundary conditions. Assuming the existence of…

On non-K\"ahler manifolds the notion of harmonic maps is modified to that of Hermitian harmonic maps in order to be compatible with the complex structure. The resulting semilinear elliptic system is {\it not} in divergence form. The case of…

This work deals with the structure of the isometry group of pseudo-Riemannian 2-step nilmanifolds. We study the action by isometries of several groups and we construct examples showing substantial differences with the Riemannain situation;…

We investigate a large class of elliptic differential inclusions on non-compact complete Riemannian manifolds which involves the Laplace-Beltrami operator and a Hardy-type singular term. Depending on the behavior of the nonlinear term and…

We prove an inverse spectral result for $S^1$-invariant metrics on $S^2$ based on the so-called asymptotic equivariant spectrum. This is roughly the spectrum together with large weights of the $S^1$ action on the eigenspaces. Our result…

Let $G\subset \O(n)$ be a compact group of isometries acting on $n$-dimensional Euclidean space $\R^n$, and ${\bf{X}}$ a bounded domain in $\R^n$ which is transformed into itself under the action of $G$. Consider a symmetric, classical…

The (local) invariant symplectic action functional $\A$ is associated to a Hamiltonian action of a compact connected Lie group $\G$ on a symplectic manifold $(M,\omega)$, endowed with a $\G$-invariant Riemannian metric $<\cdot,\cdot>_M$. It…

Starting from Montgomery's conjecture, there has been a substantial interest on the connections of random matrix theory and the theory of L-functions. In particular, moments of characteristic polynomials of random matrices have been…

We study the asymptotic behaviour of the eigenvalues of the Laplace-Beltrami operator on a compact hypersurface in \mathds{R}^{n+1} as it is flattened into a singular double-sided flat hypersurface. We show that the limit spectral problem…

This is an expanded version of the talk I gave at Oberwolfach, MIT and several other universities.

The systematic study of harmonic self-maps on cohomogeneity one manifolds has recently been initiated by P\"uttmann and the second named author in \cite{MR4000241}. In this article we investigate the corresponding Jacobi equation describing…

In this paper we give a survey of elliptic theory for operators associated with diffeomorphisms of smooth manifolds. Such operators appear naturally in analysis, geometry and mathematical physics. We survey classical results as well as…

The monopole map defines an element in an equivariant stable cohomotopy group refining the Seiberg-Witten invariant. This first of two articles presents the details of the definition of the stable cohomotopy invariant and discusses its…

The asymptotic solution for the Painleve-2 equation with small parameter is considered. The solution has algebraic behavior before point $t_*$ and fast oscillating behavior after the point $t_*$. In the transition layer the behavior of the…