Marco Matassa

Marco Matassa
Oslo Metropolitan University · Department of Computer Science

PhD

About

27
Publications
701
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258
Citations
Introduction
I am an associate professor at OsloMet – Oslo Metropolitan University in Norway.
Additional affiliations
September 2018 - present
Oslo Metropolitan University
Position
  • Professor (Associate)
October 2017 - August 2018
Vrije Universiteit Brussel
Position
  • PostDoc Position
October 2016 - October 2017
Université Clermont Auvergne
Position
  • PostDoc Position
Education
October 2008 - September 2010
Sapienza University of Rome
Field of study
  • Physics
September 2005 - October 2008
Sapienza University of Rome
Field of study
  • Physics

Publications

Publications (27)
Article
We introduce analogues of the Fubini-Study metrics and the corresponding Levi-Civita connections on quantum projective spaces. We define the quantum metrics as two-tensors, symmetric in the appropriate sense, in terms of the differential calculi introduced by Heckenberger and Kolb. We define connections on these calculi and show that they are torsi...
Preprint
Full-text available
We study the quantum Riemannian geometry of quantum projective spaces of any dimension. In particular we compute the Riemann and Ricci tensors, using previously introduced quantum metrics and quantum Levi-Civita connections. We show that the Riemann tensor is a bimodule map and derive various consequences of this fact. We prove that the Ricci tenso...
Preprint
Full-text available
We introduce analogues of the Fubini-Study metrics and the corresponding Levi-Civita connections on quantum projective spaces, following the approach of Beggs and Majid. We define the quantum metrics as two-tensors, symmetric in the appropriate sense, in terms of the differential calculi introduced by Heckenberger and Kolb. We define connections on...
Article
Let U be a connected, simply connected compact Lie group with complexification G. Let u and g be the associated Lie algebras. Let Γ be the Dynkin diagram of g with underlying set I, and let Uq(u) be the associated quantized universal enveloping ⁎-algebra of u for some 0<q distinct from 1. Let Oq(U) be the coquasitriangular quantized function Hopf ⁎...
Preprint
We study the twisted Hochschild homology of quantum flag manifolds, the twist being the modular automorphism of the Haar state. We prove that every quantum flag manifold admits a non-trivial class in degree two, with an explicit representative defined in terms of a certain projection. The corresponding classical two-form, via the Hochschild-Kostant...
Article
Full-text available
We show that the Dolbeault–Dirac operator on the quantum Lagrangian Grassmannian of rank two, an example of a quantum irreducible flag manifold, satisfies an appropriate version of the Parthasarathy formula. We use this result to complete the proof that the candidate spectral triple for this space, as defined by Krähmer, is a spectral triple.
Article
We prove that all quantum irreducible flag manifolds admit Kähler structures, as defined by Ó Buachalla. In order to show this result, we also prove that the differential calculi defined by Heckenberger and Kolb are differential ∗-calculi in a natural way.
Preprint
We prove that all quantum irreducible flag manifolds admit K\"ahler structures, as defined by \'O Buachalla. In order to show this result, we also prove that the differential calculi defined by Heckenberger and Kolb are differential *-calculi in a natural way.
Article
Full-text available
We classify PBW-deformations of quadratic-constant type of certain quantizations of exterior algebras. These correspond to the fundamental modules of quantum slN\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{...
Preprint
We show that the Dolbeault--Dirac operator on the quantum Lagrangian Grassmannian of rank two, an example of a quantum irreducible flag manifold, satisfies an appropriate version of the Parthasarathy formula. We use this result to complete the proof that the candidate spectral triple for this space, as defined by Kr\"ahmer, is a spectral triple.
Preprint
Let $U$ be a connected, simply connected compact Lie group with complexification $G$. Let $\mathfrak{u}$ and $\mathfrak{g}$ be the associated Lie algebras. Let $\Gamma$ be the Dynkin diagram of $\mathfrak{g}$ with underlying set $I$, and let $U_q(\mathfrak{u})$ be the associated quantized universal enveloping $*$-algebra of $\mathfrak{u}$ for some...
Article
Full-text available
We consider Dolbeault-Dirac operators on quantized irreducible flag manifolds as defined by Kr\"ahmer and Tucker-Simmons. We show that, in general, these operators do not satisfy a formula of Parthasarathy-type. This is a consequence of two results that we prove here: we always have quadratic commutation relations for the relevant quantum root vect...
Article
We investigate the regularity condition for twisted spectral triples. This condition is equivalent to the existence of an appropriate pseudodifferential calculus compatible with the spectral triple. A natural approach to obtain such a calculus is to start with a twisted algebra of abstract differential operators, in the spirit of Higson. Under an a...
Article
Full-text available
We study the twisted Hochschild homology of quantum full flag manifolds, with the twist being the modular automorphism of the Haar state. We show that non-trivial 2-cycles can be constructed from appropriate invariant projections. The main result is that $HH_2^\theta(\mathbb{C}_q[G / T])$ is infinite-dimensional when $\mathrm{rank}(\mathfrak{g}) >...
Article
We prove a result for the commutator of quantum root vectors corresponding to cominuscole parabolics. Specifically we show that, given two quantum root vectors, belonging respectively to the quantized nilradical and the quantized opposite nilradical, their commutator belongs to the quantized Levi factor. This generalizes the classical result for Li...
Article
Full-text available
In recent years Planck-scale modifications of the dispersion relation have been attracting increasing interest also from the viewpoint of possible applications in astrophysics and cosmology, where spacetime curvature cannot be neglected. Nonetheless the interplay between Planck-scale effects and spacetime curvature is still poorly understood, parti...
Article
We consider Dolbeault-Dirac operators on quantum projective spaces, following Krahmer and Tucker-Simmons. The main result is an explicit formula for their squares, which can be expressed essentially in terms of some central elements. This computation is completely algebraic. These operators can also be made to act on the corresponding Hilbert space...
Article
We prove an analogue of Weyl's law for quantized irreducible generalized flag manifolds. By this we mean defining a zeta function, similarly to the classical setting, and showing that it satisfies the following two properties: as a functional on the quantized algebra it is proportional to the Haar state; its first singularity coincides with the cla...
Article
We show that the family of spectral triples for quantum projective spaces introduced by D'Andrea and Dbrowski, which have spectral dimension equal to zero, can be reconsidered as modular spectral triples by taking into account the action of the element K2por its inverse. The spectral dimension computed in this sense coincides with the dimension of...
Article
Full-text available
We study a notion of non-commutative integration, in the spirit of modular spectral triples, for the quantum group $SU_{q}(2)$. In particular we define the non-commutative integral as the residue at the spectral dimension of a zeta function, which is constructed using a Dirac operator and a weight. We consider the Dirac operator introduced by Kaad...
Article
Full-text available
We extend the construction of a spectral triple for k-Minkowski space, previously given for the two-dimensional case, to the general n-dimensional case. This takes into account the modular group naturally arising from the symmetries of the geometry, and requires the use of notions that have been recently developed in the frameworks of twisted and m...
Article
Full-text available
We present a spectral triple for $\kappa$-Minkowski space in two dimensions. Starting from an algebra naturally associated to this space, a Hilbert space is built using a weight which is invariant under the $\kappa$-Poincar\'e algebra. The weight satisfies a KMS condition and its associated modular operator plays an important role in the constructi...
Article
Full-text available
The interest of part of the quantum-gravity community in the possibility of Planck-scale-deformed Lorentz symmetry is also fueled by the opportunities for testing the relevant scenarios with analyses, from a signal-propagation perspective, of observations of bursts of particles from cosmological distances. In this respect the fact that so far the i...
Article
Full-text available
We report a general analysis of worldlines for theories with deformed relativistic symmetries and momentum dependence of the speed of photons. Our formalization is faithful to Einstein's program, with spacetime points viewed as an abstraction of physical events. The emerging picture imposes the renunciation of the idealization of absolutely coincid...
Article
Full-text available
Observations of gamma-ray bursts are being used to test for a momentum dependence of the speed of photons, partly motivated by preliminary results reported in analyses of some quantum-spacetime scenarios. The relationship between time of arrival, momentum of the photon and redshift of the source which is used for these purposes assumes a "breakdown...
Article
We here advocate a perspective on recent research investigating possible Planck-scale deformations of relativistic symmetries, which is centered on Einstein's characterization of spacetime points, given exclusively in terms of physical events. We provide the first ever explicit construction of worldlines governed by a Planck-scale deformation of Po...

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