Related papers: Displacement techniques in bounded cohomology
We present an improved version of commutator methods for unitary operators under a weak regularity condition. Once applied to a unitary operator, the method typically leads to the absence of singularly continuous spectrum and to the local…
The purpose of this paper is applying minimality of hyperplane arrangements to local system cohomology groups. It is well known that twisted cohomology groups with coefficients in a generic rank one local system vanish except in the top…
Following an old suggestion of M. Kontsevich, and inspired by recent work of A. Beilinson and B. Bhatt, we introduce a new version of periodic cyclic homology for DG agebras and DG categories. We call it co-periodic cyclic homology. It is…
We study the cohomology of symbolic dynamical systems called homshifts: they are the nearest-neighbour $\mathbb{Z}^d$ shifts of finite type whose adjacency rules are the same in every direction. Building on the work of Klaus Schmidt…
We give a new proof of the slope classicality theorem in classical and higher Coleman theory for modular curves at arbitrary level using the completed cohomology classes attached to overconvergent modular forms. The latter give an embedding…
Atomistic simulations provide the most detailed picture of grain boundary (GB) migration currently available. Nevertheless, extracting unit mechanisms from atomistic simulation data is difficult because of the zoo of competing,…
As a guide to constitutive specification, driving forces for dislocation velocity and nucleation rates are derived for a field theory of dislocation mechanics. A condition of closure for the theory in the form of a boundary condition for…
We study the notion of semistability for principal bundles over curves with possibly disconnected reductive structure group. We establish a new characterization of the behavior of semistability under change of group, novel even in the…
The use of homological and homotopical devices, such as Tor and Andr\'e-Quillen homology, have found substantial use in characterizing commutative algebras. The primary category setting has been differentially graded algebras and modules,…
We investigate the convergence properties of a perturbation method proposed some time ago and reveal some of it most interesting features. Anharmonic oscillators in the strong--coupling limit prove to be appropriate illustrative examples…
We study half-space linear kinetic equations with general boundary conditions that consist of both given incoming data and various type of reflections, extending our previous work [LLS14] on half-space equations with incoming boundary…
Symmetric cohomology of groups, defined by M. Staic in [2], is similar to the way one defines the cyclic cohomology for algebras. We show that there is a well-defined restriction, conjugation and transfer map in symmetric cohomology, which…
In connection with the Fuglede conjecture, we study the existence of commuting self-adjoint extensions of the partial differential operators on arbitrary, possibly disconnected domains in $\br^d$, the associated unitary group, the spectral…
Generalising the definition to commuting $d$-tuples of operators, a number of authors have considered structural properties of $m$-isometric, $n$-symmetric and $(m,n)$-isosymmetric commuting $d$-tuples in the recent past. This note is an…
The present paper contains new geometric theorems in mixed characteristic case. We derive a bunch of cohomological consequences using these geometric theorems. Among them an isotropy result for quadratic spaces, a purity result for…
Let u be a local homomorphism of noetherian local rings forming part of a commutative square vf=gu. We give some conditions on the square which imply that u is formally smooth. This result encapsulates a variety of (apparently unrelated)…
We analyse higher order background independence conditions arising from multiple commutators of background deformations in quantum closed string field theory. The conditions are shown to amount to a vanishing theorem for $\Delta_S$…
Using approximations, we give several characterizations of separability of bimodules. We also discuss how separability properties can be used to transfer some representation theoretic properties from one ring to another one: contravariant…
We consider the propagation of a flame front in a solid periodic medium. The model is governed by a free boundary system in which the front's velocity depends on the temperature via a kinetic rate which may degenerate. We show the existence…
This is my dissertation. Its research object is a symmetric group of permutations acting on a finite set. The density of permutations with a given cycle structure pattern is explored when the group order tends to infinity. New and sharper…