Related papers: Local trace formulae for commuting Hamiltonians in…

The obstruction to the local-global principle for a hermitian lattice (L, H) can be quantified by computing the mass of (L, H). The mass formula expresses the mass of (L, H) as a product of local factors, called the local densities of (L,…

We consider the homogenization of a singularly perturbed self-adjoint fourth order elliptic equation with locally periodic coefficients, stated in a bounded domain. We impose Dirichlet boundary conditions on the boundary of the domain. The…

In this paper we use the gradient flow equation introduced in [10] to construct a Morse complex for the Hamiltonian action $\mathbb A_H$ on a mixed regularity space of loops in the cotangent bundle $T^*M$ of a closed manifold $M$.…

We prove trace identities for commutators of operators, which are used to derive sum rules and sharp universal bounds for the eigenvalues of periodic Schroedinger operators and Schroedinger operators on immersed manifolds. In particular, we…

In this paper we study in detail the localized wave functions defined in Phys. Rev. Lett. {\bf 76}, 1613 (1994), in connection with the scarring effect of unstable periodic orbits in highly chaotic Hamiltonian system. These functions appear…

In this paper we provide a review of asymptotic results of Toeplitz operators and their applications in TQFT. To do this we review the differential geometric construction of the Hitchin connection on a prequantizable compact symplectic…

Given a sequence of Hermitian holomorphic line bundles $(L_k,h_k)$ over a complex manifold $M$ which may not be compact, we generalize the scaling method in arXiv:2310.08048 to study the asymptotic behavior of the Bergman kernels and…

In this paper we study the asymptotic behavior of second-order uniformly elliptic operators on weighted Riemannian manifolds. They naturally emerge when studying spectral properties of the Laplace-Beltrami operator on families of manifolds…

For a compact locally symmetric space X, we establish a version of the Selberg trace fromula for a non-unitary representation of the fundamental group of X. On the spectral side appears the spectrum of the "flat Laplacian", acting in the…

In this paper, we study the dynamical aspects of the \emph{Hamiltonian homeomorphism group} $Hameo(M,\omega)$ which was introduced by M\"uller and the author. We introduce the notion of autonomous continuous Hamiltonian flows and extend the…

Starting from a local action for mimetic gravity that includes higher derivatives of a scalar field $\phi$, we derive a gauge-fixed canonical action of the theory in the ADM canonical formalism in the time gauge $\phi=t$. This reduced…

We consider a relativistic extended object described by a reparametrization invariant local action that depends on the extrinsic curvature of the worldvolume swept out by the object as it evolves. We provide a Hamiltonian formulation of the…

We introduce the notion of measurable bounded cohomology for measured groupoids, extending continuous bounded cohomology of locally compact groups. We show that the measurable bounded cohomology of the semidirect groupoid associated to a…

This paper is devoted to semi-classical aspects of symplectic reduction. Consider a compact prequantizable Kahler manifold M with a Hamiltonian torus action. Guillemin and Sternberg introduced an isomorphism between the invariant part of…

We apply the ADM approach to obtain a Hamiltonian description of the Einstein-Hilbert action. In doing so we add four new ingredients: (i) We eliminate the diffeomorphism constraints. (ii) We replace the densities $\sqrt g$ by a function…

The Lefschetz formula for the action of a Hecke correspondence on the weighted cohomology of a locally symmetric space is derived. It is also proven that each Hecke correspondence on the reductive Borel-Serre compactification of the locally…

Let $H_0$ be a periodic operator on $\R^+$(or periodic Jacobi operator on $\N$). It is known that the absolutely continuous spectrum of $H_0$ is consisted of spectral bands $\cup[\alpha_l,\beta_l]$. Under the assumption that $\limsup_{x\to…

We consider a semiclassical asymptotics of local trace for the 3D-Schroedinger operator with self-generated magnetic field in the case when electric potential has one or several Coulomb-like singularities; it is given by Weyl expression…

Symmetries and their anomalies are powerful tools to understand quantum matter. In this work, for quantum spin chains, we define twisted locality-preserving automorphisms and their Gross-Nesme-Vogts-Werner indices, which provide a unified…

A Hamiltonian operator $\hat H$ is constructed with the property that if the eigenfunctions obey a suitable boundary condition, then the associated eigenvalues correspond to the nontrivial zeros of the Riemann zeta function. The classical…