Related papers: The factorization of the Giry monad
Using a family of graded algebra structures on a planar algebra and a family of traces coming from random matrix theory, we obtain a tower of non-commutative probability spaces, naturally associated to a given planar algebra. The associated…
Let $X$ be a Banach space, $\Sigma$ be a $\sigma$-algebra, and $m:\Sigma\to X$ be a (countably additive) vector measure. It is a well known consequence of the Davis-Figiel-Johnson-Pelcz\'{y}nski factorization procedure that there exist a…
Lyubashenko's construction associates representations of mapping class groups Map_{g,n} of Riemann surfaces of any genus g with any number n of holes to a factorizable ribbon category. We consider this construction as applied to the…
We discuss free probability theory and free harmonic analysis from a categorical perspective. In order to do so, we extend first the set of analytic convolutions and operations and then show that the comonadic structure governing free…
In factoring matrices into the product of two matrices operations are typically performed with elements restricted to matrix subspaces. Such modest structural assumptions are realistic, for example, in large scale computations. This paper…
Rational transformations of polynomials are extensively studied in the context of finite fields, especially for the construction of irreducible polynomials. In this paper, we consider the factorization of rational transformations with…
We provide a toolbox of extension, gluing, and assembly techniques for factorization algebras. Using these tools, we fill various gaps in the literature on factorization algebras on stratified manifolds, the main one being that…
Abstract. This article determines relations between two notions concerning monoids: factorability structure, introduced to simplify the bar complex; and quadratic normalisation, introduced to generalise quadratic rewriting systems and…
In [1] a conjecture for the modular transformation of the free fermion generalised Gibbs ensemble (GGE) was given where only the KdV charge associated to the weight four quasi primary field was inserted. In this paper we first generalise…
A new class of modified gravity theories, made possible by subtle features of the canonical formulation of general covariance, naturally allows MOND-like behavior (MOdified Newtonian Dynamics) in effective space-time solutions without…
We show that any theory with second class constraints may be cast into a gauge theory if one makes use of solutions of the constraints expressed in terms of the coordinates of the original phase space. We perform a Lagrangian path integral…
The module category of any artin algebra is filtered by the powers of its radical, thus defining an associated graded category. As an extension of the degree of irreducible morphisms, this text introduces the degree of morphisms in the…
Let X be a smooth complex projective variety, and let Y in X be a smooth very ample hypersurface such that -K_Y is nef. Using the technique of relative Gromov-Witten invariants, we give a new short and geometric proof of (a version of) the…
Let $\varphi\colon\Gamma\to G$ be a homomorphism of groups. We consider factorizations $\Gamma\xrightarrow{f} M\xrightarrow{g} G$ of $\varphi$ such that either $g$ or $f$ are universal normal maps (namely, crossed modules). These two…
We realize the enveloping algebra of the positive part of a symmetrizable Kac-Moody algebra as a convolution algebra of constructible functions on module varieties of some Iwanaga-Gorenstein algebras of dimension 1.
In [GHKK18], Gross-Hacking-Keel-Kontsevich discuss compactifications of cluster varieties from "positive subsets" in the real tropicalization of the mirror. To be more precise, let $\mathfrak{D}$ be the scattering diagram of a cluster…
This paper shows that quantization of $\pi$-finite spaces, as a functor out of a higher category of spans, is equivariant in two ways: Symmetries of a given polarization/Lagrangian always induce coherent symmetries of the quantization. On…
In this paper we give a purely categorical construction of d-fold matrix factorizations of a natural transformation, for any even integer d. This recovers the classical definition of those for regular elements in commutative rings due to…
Codensity monads provide a universal method to generate complex monads from simple functors. Recently, a wide range of important monads in logic, denotational semantics, and probabilistic computation, such as several incarnations of the…
We generalize the free Fermi-gas formulation of certain 3d ${\cal N}=3$ supersymmetric Chern-Simons-matter theories by allowing Fayet-Iliopoulos couplings as well as mass terms for bifundamental matter fields. The resulting partition…