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We introduce the wave-front set for distributions with respect to Fourier images of weighted translation invariant Banach function spaces. We prove that usual mapping properties for pseudo-differential operators hold in the context of such…

We show how the theory of canonical bases in modified universal enveloping algebras can be used to develop the theory of Chevalley groups over any commutative ring with 1.

Let $\overline{M}=\overline{G}/\overline{H}$ be a homogeneous Riemannian manifold. Given a Lie subgroup $G\subset \overline{G}$ and a reductive decomposition of the homogeneous structure of $\overline{M}$, we analyze a canonical reductive…

Let $\C$ be a sequence of multisets of subspaces of a vector space $\F_q^k$. We describe a practical algorithm which computes a canonical form and the stabilizer of $\C$ under the group action of the general semilinear group. It allows us…

We prove a canonical bundle formula for generically finite morphisms in the setting of generalized pairs (with $\mathbb{R}$-coefficients). This complements Filipazzi's canonical bundle formula for morphisms with connected fibres. It is then…

We develop the wave packet decomposition to study the Schrodinger evolution with rough potential. As an application, we obtain the improved bound on the wave propagation for the generic value of a parameter.

We develop an algorithm for the computation of general Fourier integral operators associated with canonical graphs. The algorithm is based on dyadic parabolic decomposition using wave packets and enables the discrete approximate evaluation…

We prove a conjecture stated in a previous paper by the author about the existence of canonical filtrations for a family of vertex operator algebras in rational levels.

We consider a canonical bundle formula for generically finite proper surjective morphisms and obtain subadjunction formulae for minimal log canonical centers of log canonical pairs. We also treat related topics and applications.

We review some recent results obtained for the time evolution of wave packets for systems of equations of pseudo-differential type, including Schr{\"o}dinger ones, and discuss their application to the approximation of the associated unitary…

We have found a new class of time dependent partial waves which are solutions of time dependent Schr\"odinger equation for three dimensional harmonic oscillator. We also showed the decomposition of coherent states of harmonic oscillator…

Arthur has conjectured the existence of what are now known as Arthur packets of representations of reductive algebraic groups over local and global fields. In the case of classical groups he subsequently gave a definition of these packets,…

In this note we formulate and prove a version of Cartan decomposition for holomorphic loop groups, similar to Cartan decomposition for $p$-adic loop groups, discussed proved by Garland (and later by the authors by geometric mathods). The…

The purpose of this paper is to apply deformation quantization to the study of the coadjoint orbit method in the case of real reductive groups. We first prove some general results on the existence of equivariant deformation quantization of…

Canonical quantization of electromagnetic field is traditionally done using plane waves. It is possible to formulate the quantization using other complete set of basis functions. Wavelets are a special kind of functions which are localized…

Contents 1. Algebraicity criterion: statement 2. Proof of the algebraicity criterion. 3. Pseudoeffectivity and movable classes. 4. Harder-Narasimhan filtrations and pseudo-effectivity. 5. Pseudo-effectivity of relative canonical bundles. 6.…

In this paper, we collect some technical results about weights on C*-algebras which are useful in de theory of locally compact quantum groups in the C*-algebra framework. We discuss the extension of a lower semi-continuous weight to a…

In this paper we apply the formalism of the analytical signal theory to the Schrodinger wavefunction. Making use exclusively of the wave-particle duality and the principle of relativistic covariance, we actually derive the form of the…

We construct canonical semi-orthogonal decompositions for derived categories of smooth projective surfaces. These decompositions are compatible with the operations in the minimal model program, such as blow-ups and conic bundles. Therefore…

For proper surjective holomorphic maps from K"ahler manifolds to analytic spaces, we give a decomposition theorem for the cohomology groups of the canonical bundle twisted by Nakano semi-positive vector bundles by means of the higher direct…