Related papers: On positive definiteness over locally compact quan…

In this paper we set up a general formalism to deal with quantum theories on a Lobatchevski space, i.e. a spatial manifold that is homogeneous, isotropic and has negative curvature. The heart of our approach is the construction of a…

A construction of the noncommutative-geometric counterparts of classical classifying spaces is presented, for general compact matrix quantum structure groups. A quantum analogue of the classical concept of the classifying map is introduced…

We review the notion of simple compact quantum groups and examples, and discuss the problem of construction and classification of simple compact quantum groups. Several new quantum groups constructed by Banica, Curran and Speicher since the…

Hyper-Positive real, matrix-valued, rational functions are associated with absolute stability (the Lurie problem). Here, quantitative subsets of Hyper-positive functions, related through nested inclusions, are introduced. Structurally, this…

We study the Haagerup--Kraus approximation property for locally compact quantum groups, generalising and unifying previous work by Kraus--Ruan and Crann. Along the way we discuss how multipliers of quantum groups interact with the…

The object of the present is a proof of the existence of functorial resolution of tame quotient singularities for quasi-projective varieties over algebraically closed fields.

A causal, non-Hermitian, renormalizable, local, unitary and Lorentz convariant formulation of Quantum Theory (QT) (= Quantum Mechanics (QM) and Quantum Field Theory (QFT)) is developed which is free of formalistic problems we face in the…

The positive definiteness of real quadratic forms with convolution structures plays an important role in stability analysis for time-stepping schemes for nonlocal operators.In this work, we present a novel analysis tool to handle discrete…

We study quantum field theories which have quantum groups as global internal symmetries. We show that in such theories operators are generically non-local, and should be thought as living at the ends of topological lines. We describe the…

In a recent paper [2], Chang et al. have proposed studying "Quantum $\mathbb{F}_{un}$": the $q \mapsto 1$ limit of Modal Quantum Theories over finite fields $\mathbb{F}_q$, motivated by the fact that such limit theories can be naturally…

This paper studies certain aspects of harmonic analysis on nonabelian free groups. We focus on the concept of a positive definite function on the free group and our primary goal is to understand how such functions can be extended from balls…

In this article -that has also the intention to survey some known results in the theory of compact quantum groups using methods different from the standard and with a strong algebraic flavor- we consider compact o-coalgebras and Hopf…

In this paper we extensively investigate the class of conditionally positive definite operators, namely operators generating conditionally positive definite sequences. This class itself contains subnormal operators, $2$- and $3$-isometries…

We consider a constructive modification of quantum-mechanical formalism. Replacement of a general unitary group by unitary representations of finite groups makes it possible to reproduce quantum formalism without loss of its empirical…

Motivated by classical investigation of conjugation invariant positive-definite functions on discrete groups, we study tracial central states on universal C*-algebras associated with compact quantum groups, where centrality is understood in…

Positive definite functions of compact support are widely used for radial basis function approximation as well as for estimation of spatial processes in geostatistics. Several constructions of such functions for ${\mathbb R}^d$ are based…

In this article we study definable functions in tame expansions of algebraically closed valued fields. For a given definable function we have two types of results: of type (I), which hold at a neighborhood of infinity, and of type (II),…

Motivated by quantum thermodynamics we first investigate the notion of strict positivity, that is, linear maps which map positive definite states to something positive definite again. We show that strict positivity is decided by the action…

These are lecture notes supporting a minicourse taught at the Summer School in Total Positivity and Quantum Field Theory at CMSA Harvard in June 2025. We give an introduction to positive geometries and their canonical forms. We present the…

We propose a definition of quantum computable functions as mappings between superpositions of natural numbers to probability distributions of natural numbers. Each function is obtained as a limit of an infinite computation of a quantum…