Related papers: Bayesian inversion and the Tomita-Takesaki modular…
In this paper, we prove an existence theorem of a local moduli space for geometric structures in a very general setting. Then to show the interest of this result, we apply it to the case of sasakian and Sasaki-Einstein structures.
We extend the results of [CGLS22] to higher weight modular forms and prove a rank $0$ Tamagawa number formula (also known as the Bloch-Kato conjecture) for modular forms at good Eisenstein primes, under some technical assumption on periods.…
This article shows that a large class of posterior measures that are absolutely continuous with respect to a Gaussian prior have strong maximum a posteriori estimators in the sense of Dashti et al. (2013). This result holds in any separable…
The paper gives an operator algebras model for the conditional monotone independence, introduced by T. Hasebe. The construction is used to prove an embedding result for the N. Muraki's monotone product of C*-algebras. Also, the formulas…
We introduce the category of C*-discrete inclusions of C*-algebras $A\subset B$ with a faithful conditional expectation $E:B\twoheadrightarrow A$. This class includes many examples such as finite Watatani index inclusions, and also abundant…
In this paper, we discuss positive maps induced by (irreducibly) covariant linear operators for finite groups. The application of group theory methods allows deriving some new results of a different kind. In particular, a family of…
We introduce the inverse monoid of inner partial automorphisms of a semigroup -- a tool that associates to every semigroup an inverse semigroup. When the semigroup is a group, this inverse semigroup is isomorphic to the group of inner…
This paper proves a reciprocity formula for modular inverses for non-zero integers and demonstrates some applications of the reciprocity formula in calculating or verifying some modular inverses of specific forms, including the modular…
Convex sets of completely positive maps and positive semidefinite kernels are considered in the most general context of modules over $C^*$-algebras and a complete charaterization of their extreme points is obtained. As a byproduct, we…
In \cite{grku1}, Greither and Kurihara proved a theorem about the commutativity of projective limits and Fitting ideals for modules over the classical equivariant Iwasawa algebra $\Lambda_G=\mathbb{Z}_p[G][[T]]$, where $G$ is a finite,…
The study of open quantum systems relies on the notion of unital completely positive semigroups on $C^*$-algebras representing physical systems. The natural generalisation would be to consider the unital completely positive semigroups on…
The application of the Tomita-Takesaki modular theory to the Haag-Kastler net approach in QFT yields external (space-time) symmetries as well as internal ones (internal ``gauge para-groups") and their dual counterparts (the ``super…
A result of the author shows that the behavior of Gowers norms on bounded exponent abelian groups is connected to finite nilspaces. Motivated by this, we investigate the structure of finite nilspaces. As an application we prove inverse…
We introduce strong Morita equivalence for inverse semigroups. This notion encompasses Mark Lawson's concept of enlargement. Strongly Morita equivalent inverse semigroups have Morita equivalent universal groupoids in the sense of Paterson…
We present a unitary approach to the construction of representations and intertwining operators. We apply it to the $C^*$-algebras, groups, Gabor type unitary systems and wavelets. We give an application of our method to the theory of…
The notions of disintegration and Bayesian inversion are fundamental in conditional probability theory. They produce channels, as conditional probabilities, from a joint state, or from an already given channel (in opposite direction). These…
We show that elementary abelian direct factors can be disregarded in the study of the modular isomorphism problem. Moreover, we obtain four new series of abelian invariants of the group base in the modular group algebra of a finite…
We consider the Bayesian approach to linear inverse problems when the underlying operator depends on an unknown parameter. Allowing for finite dimensional as well as infinite dimensional parameters, the theory covers several models with…
The Bayesian perspective on inverse problems has attracted much mathematical attention in recent years. Particular attention has been paid to Bayesian inverse problems (BIPs) in which the parameter to be inferred lies in an…
In this note, we prove that intrinsic characteristic classes of Lie algebroids - which in degree one recover the modular class - behave functorially with respect to arbitrary transverse maps, and in particular are weak Morita invariants. In…