Let C \mathcal C be a concrete c...

We investigate how to characterize subcategories of abelian categories in terms intrinsic axioms. In particular, we find axioms which generating cogenerating functorially finite subcategories, precluster tilting and cluster categories. As a consequence prove that any d-abelian category is equivalent d-cluster subcategory an category, without assumption on the being projectively generated.

We study infinitesimal deformations of autodual and hyper-holomorphic connections on complex vector bundles hyper-Kähler manifolds arbitrary dimension. In particular, we describe the DG Lie algebra controlling this deformation problem. Moreover, prove associative formality for derived endomorphisms a holomorphic bundle admitting projectively connection.

We study superpositions and direct integrals of quadratic Dirichlet forms. show that each quasi-regular space over a probability admits unique representation as integral irreducible spaces, for the same underlying topology. The holds strongly local metrizable Luzin, Radon measure space, admitting carr\'e du champ operator. In this case, is only projectively unique.

We study the SU(2) WZNW model over a family of elliptic curves. Starting from the formulation developed in [TUY], we derive a system of differential equations which contains the Knizhnik-Zamolodchikov-Bernard equations[Be1][FW]. Our system completely determines the N-point functions and is regarded as a natural elliptic analogue of the system obtained in [TK] for the projective line. We also ca...

Identifying the projective group for patterns by developing the camera model, the projective Fourier transform and its inverse are obtained in analogy with the classical, that is, Euclidean Fourier analysis. Projectively adapted properties are demonstrated in a numerical test. Using the expression of the projective Fourier integral by a standard Fourier integral in the coordinates given by the ...

We introduce a notion of Homological Projective Duality for smooth algebraic varieties in dual projective spaces, a homological extension of the classical projective duality. If algebraic varieties X and Y in dual projective spaces are Homologically Projectively Dual, then we prove that the orthogonal linear sections of X and Y admit semiorthogonal decompositions with an equivalent nontrivial c...