Related papers: The Schwartz space of a smooth semi-algebraic stac…

Sampling theory has traditionally drawn tools from functional and complex analysis. Past successes, such as the Shannon-Nyquist theorem and recent advances in frame theory, have relied heavily on the application of geometry and analysis.…

We define and develop a framework to understand functional integrals as countable families of Banach-valued Haar integrals on locally compact topological groups. The definition forgoes the goal of constructing a genuine measure on an…

In this work we characterize the subsets of ${\mathbb R}^n$ that are images of Nash maps $f:{\mathbb R}^m\to{\mathbb R}^n$. We prove Shiota's conjecture and show that a subset ${\mathcal S}\subset{\mathbb R}^n$ is the image of a Nash map…

A topological description of various generalized function algebras over corresponding basic locally convex algebras is given. The framework consists of algebras of sequences with appropriate ultra(pseudo)metrics defined by sequences of…

A Reeb space is defined as the space of all the connected components of inverse images of a smooth map, which is a fundamental tool in studying smooth manifolds using generic smooth maps whose codimensions are not positive such as Morse…

We construct a weak categorification of the quantum toroidal algebra action on the Grothendieck group of moduli space of stable (or framed) sheaves over an algebraic surface, which is constructed by Schiffmann-Vasserot and Negu\c{t}. The…

Let G be a semi-simple Lie group and Q a parabilic subgroup of its complexification G^\mathbb C, then Z:=G^\mathbb C/Q is a compact complex homogeneous manifold. Moreover, G as well as K^\mathbb C, the complexification of the maximal…

This paper studies ways to represent an ordered topological vector space as a space of continuous functions, extending the classical representation theorems of Kadison and Schaefer. Particular emphasis is put on the class of semisimple…

A general theory of matrix-spherical functions for dual Hopf algebras and right coideal subalgebras is developed. We establish their existence and define their orthogonality relations. When specialized to Kolb and Letzter's quantum…

The configuration space of $n$ marked points on the complex plane is considered. We investigate a decomposition of this space by so-called Gauss-skizze i.e. a class of graphs being forests, introduced by Gauss. It is proved that this…

Let $\mathcal{X}$ be a tame proper Deligne-Mumford stack of the form $[M/G]$ where $M$ is a scheme and $G$ is an algebraic group. We prove that the stack $\mathcal{K}_{g,n}(\mathcal{X},d)$ of twisted stable maps is a quotient stack and can…

We define the spherical Hecke algebra H for an almost split Kac-Moody group G over a local non-archimedean field. We use the hovel I associated to this situation, which is the analogue of the Bruhat-Tits building for a reductive group. The…

In this paper we prove the existence of an algebraic model for quasi-coherent sheaves on certain non-connective geometric stacks arising in stable homotopy theory and spectral algebraic geometry using the machinery of adapted homology…

On a connected, oriented, smooth Riemannian manifold without boundary we consider a real scalar field whose dynamics is ruled by $E$, a second order elliptic partial differential operator of metric type. Using the functional formalism and…

We consider zero sets of entire functions belonging to the Schwartz algebra. This algebra is defined as the Fourier-Laplace transform image of the space of all distributions compactly supported on the real line. We study the conditions…

An $F$-zip over a scheme $S$ over a finite field is a certain object of semi-linear algebra consisting of a locally free module with a descending filtration and an ascending filtration and a $\Frob_q$-twisted isomorphism between the…

It is generally known that linear (free) field theories are one of the few QFT that are exactly soluble. In the Schroedinger functional description of a scalar field on flat Minkowski spacetime and for flat embeddings, it is known that the…

It is shown that every holomorphic map $f$ from a Runge domain $\Omega$ of an affine algebraic variety $S$ into a projective algebraic manifold $X$ is a uniform limit of Nash algebraic maps $f_\nu$ defined over an exhausting sequence of…

Nash and Tognoli show that smooth closed manifolds can be the zero sets of some real polynomial maps and non-singular. The canonical projections of spheres naturally embedded in the $1$-dimensional higher Euclidean spaces and some natural…

To a smooth and proper morphism $\mathcal{X}\to U$ with quasicompact semiseparated target we associate a sheaf in the \'etale topology, which takes an affine $U$-scheme $V$ to the set of $V$-linear semiorthogonal decompositions (of fixed…