Related papers: Residues and Differential Operators on Schemes
In this dissertation I establish that a broad class of Banach *-algebras of infinite integral operators, defined by the property that the kernels of the elements of the algebras possess subexponential off-diagonal decay, is inverse closed…
We introduce a general axiomatic framework for algebras with triangular decomposition, which allows for a systematic study of the Bernstein-Gelfand-Gelfand Category $\mathcal{O}$. The framework is stated via three relatively simple axioms;…
We introduce a $p$-adic analytic analogue of Backelin and Kremnizer's construction of the quantum flag variety of a semisimple algebraic group, when $q$ is not a root of unity and $| q-1|<1$. We then define a category of $\lambda$-twisted…
BD algebras (Beilinson-Drinfeld algebras) are algebraic structures which are defined similarly to BV algebras (Batalin-Vilkovisky algebras). The equation defining the BD operator has the same structure as the equation for BV algebras, but…
We construct a Batalin-Vilkovisky (BV) algebra on moduli spaces of Riemann surfaces. This algebra is background independent in that it makes no reference to a state space of a conformal field theory. Conformal theories define a homomorphism…
Let us suppose that $\mathbb{Q}_p$ is the field of $p$-adic numbers and $\mathbb{G}$ is a split connected reductive group scheme over $\mathbb{Z}_p$. In this work we will introduce a sheaf of twisted arithmetic differential operators on the…
This paper studies the restriction multiplicities of half-diagram modules for the partition algebra and their geometric interpretations. By specializing the Bowman-De Visscher-Orellana formula [BVC, Theorem 4.3] for restriction…
This paper presents an innovative approach to the study of recurrent sequences by introducing the concept of arithmetic pseudo-operators. Unlike conventional operators, these pseudo-operators are pure complex numbers with specific…
We introduce perfect resolving algebras and study their fundamental properties. These algebras are basic for our theory of differential graded schemes, as they give rise to affine differential graded schemes. We also introduce etale…
The residual finite-dimensionality of a $\mathrm{C}^*$-algebra is known to be encoded in a topological property of its space of representations, stating that finite-dimensional representations should be dense therein. We extend this…
BSS RAMs were introduced to provide a mathematical framework for characterizing algorithms over first-order structures. Non-deterministic BSS RAMs help to model different non-deterministic approaches. Here, we deal with different types of…
We show that 2D periodic operators with local and perpendicular defects form an algebra. We provide an algorithm of finding spectrum for such operators. While the continuous spectral components can be computed by simple algebraic operations…
We exhibit an adjunction between a category of abstract algebras of partial functions that we call difference-restriction algebras and a category of Hausdorff \'etale spaces. Difference-restriction algebras are those algebras isomorphic to…
Differential chains are a proper subspace of de Rham currents given as an inductive limit of Banach spaces endowed with a geometrically defined strong topology. Boundary is a continuous operator, as are operators that dualize to Hodge star,…
We introduce a new formalism of differential operators for a general associative algebra A. It replaces Grothendieck's notion of differential operator on a commutative algebra in such a way that derivations of the commutative algebra are…
R. B. Melrose's b-calculus provides a framework for dealing with problems of partial differential equations that arise in singular or degenerate geometric situations. This article is a somewhat informal short course introducing many of the…
For a finitely-generated vertex operator algebra of central charge c, a locally convex topological completion is constructed. We construct on the completion a structure of an algebra over the operad of the c/2-th power of the determinant…
We construct some inverse-closed algebras of bounded integral operators with operator-valued kernels, acting in spaces of vector-valued functions on locally compact groups. To this end we make systematic use of covariance algebras…
Bayesian structure learning allows inferring Bayesian network structure from data while reasoning about the epistemic uncertainty -- a key element towards enabling active causal discovery and designing interventions in real world systems.…
By analytic deformations of complex structures, we mean perturbations of the Dolbeault operator. By algebraic deformations of complex structures, we mean deformations of holomorphic glueing data. For complex manifolds there is,…