43 citations · 92 across the 34 of their papers we have counts for
54 papers
Metric Spectral Geometry of -Crossed Products beyond Equicontinuity
Frederic Latremoliere
We construct linearly twisted spectral triples on -crossed products , starting from a spectral triple and…
How to approximate the flat spectral triple of a quantum torus by fuzzy tori : a twisted tale
Frederic Latremoliere
We prove that the classical and the quantum flat torus can be rigorously approximated at a differential level by finite-dimensional fuzzy tori within the framework of the spectral…
Spectral continuity of almost commutative manifolds for the topology on Riemannian metrics
Frederic Latremoliere
Almost commutative models provide a framework for Connes' work on the standard model of particle physics. These models are constructed as products of a the canonical spectral tripl…
The quantum Gromov-Hausdorff Hypertopology on the class of pointed Proper Quantum Metric Spaces
Frederic Latremoliere
We introduce a hypertopology, induced by an inframetric up to full quantum isometry, on the class of pointed proper quantum metric spaces, which are separable, possibly non-unital,…
Continuity for the spectral propinquity of the Dirac operators associated with an analytic path of Riemannian metrics
Carla Farsi, Frederic Latremoliere
We prove that a polynomial path of Riemannian metrics on a closed spin manifold induces a continuous field in the spectral propinquity of metric spectral triples.
Collapse in Noncommutative Geometry and Spectral Continuity
Carla Farsi, Frederic Latremoliere
If two compact quantum metric spaces are close in the metric sense, then how similar are they, as noncommutative spaces? In the classical realm of Riemannian geometry, informally,…
Spectral Triples on noncommutative solenoids from the standard spectral triples on quantum tori
Carla Farsi, Frederic Latremoliere, Judith Packer
We address the natural question: as noncommutative solenoids are inductive limits of quantum tori, do the standard spectral triples on quantum tori converge to some spectral triple…
Domains of quantum metrics on AF algebras
Konrad Aguilar, Katrine von Bornemann Hjelmborg, Frederic Latremoliere
Given a compact quantum metric space (A, L), we prove that the domain of L coincides with A if and only if A is finite dimensional. We then show how one can explicitly build many q…
Isometry groups of inductive limits of metric spectral triples and Gromov-Hausdorff convergence
Jacopo Bassi, Roberto Conti, Carla Farsi +1
In this paper we study the groups of isometries and the set of bi-Lipschitz automorphisms of spectral triples from a metric viewpoint, in the propinquity framework of Latremoliere.…
The strongly Leibniz property and the Gromov--Hausdorff propinquity
Konrad Aguilar, Stephan Ramon Garcia, Elena Kim +1
We construct a new version of the dual Gromov--Hausdorff propinquity that is sensitive to the strongly Leibniz property. In particular, this new distance is complete on the class o…
Convergence of inductive sequences of spectral triples for the spectral propinquity
Carla Farsi, Frederic Latremoliere, Judith Packer
In the context of metric geometry, we introduce a new necessary and sufficient condition for the convergence of an inductive sequence of quantum compact metric spaces for the Gromo…
Estimating the Jacobian matrix of an unknown multivariate function from sample values by means of a neural network
Frédéric Latrémolière, Sadananda Narayanappa, Petr Vojtěchovský
We describe, implement and test a novel method for training neural networks to estimate the Jacobian matrix of an unknown multivariate function . The training set is constru…
Continuity of the Spectrum of Dirac Operators of Spectral Triples for the Spectral Propinquity
Frederic Latremoliere
The spectral propinquity is a distance, up to unitary equivalence, on the class of metric spectral triples. We prove in this paper that if a sequence of metric spectral triples con…
Convergence of Spectral Triples on Fuzzy Tori to Spectral Triples on Quantum Tori
Frederic Latremoliere
Fuzzy tori are finite dimensional C*-algebras endowed with an appropriate notion of noncommutative geometry inherited from an ergodic action of a finite closed subgroup of the toru…
Metric Approximations of Spectral Triples on the Sierpiński Gasket and other fractal curves
Therese-Marie Landry, Michel L. Lapidus, Frederic Latremoliere
Noncommutative geometry provides a framework, via the construction of spectral triples, for the study of the geometry of certain classes of fractals. Many fractals are constructed…
Bunce-Deddens algebras as quantum Gromov-Hausorff distance limits of circle algebras
Konrad Aguilar, Frederic Latremoliere, Timothy Rainone
We show that Bunce-Deddens algebras, which are AT-algebras, are also limits of circle algebras for Rieffel's quantum Gromov-Hausdorff distance, and moreover, form a continuous fami…
A survey of the Preservation of Symmetries by the Dual Gromov-Hausdorff Propinquity
Frederic Latremoliere
We survey the symmetry preserving properties for the dual propinquity, under natural non-degeneracy and equicontinuity conditions. These properties are best formulated using the no…
The Gromov-Hausdorff propinquity for metric Spectral Triples
Frederic Latremoliere
We define a metric on the class of metric spectral triples, which is null exactly between spectral triples with unitary equivalent Dirac operators and *-isomorphic underlying C*-al…
The Dual Modular Gromov-Hausdorff Propinquity and Completeness
Frederic Latremoliere
The dual modular propinquity is a complete metric, up to full modular quantum isometry, on the class metrical quantum vector bundles, i.e. of Hilbert modules endowed with a type of…
Convergence of Cauchy Sequences for the covariant Gromov-Hausdorff propinquity
Frederic Latremoliere
The covariant Gromov-Hausdorff propinquity is a distance on Lipschitz dynamical systems over quantum compact metric spaces, up to equivariant full quantum isometry. It is built fro…
The Covariant Gromov-Hausdorff Propinquity
Frederic Latremoliere
We extend the Gromov-Hausdorff propinquity to a metric on Lipschitz dynamical systems, which are given by strongly continuous actions of proper monoids on quantum compact metric sp…
Convergence of Heisenberg Modules over Quantum 2-tori for the Modular Gromov-Hausdorff Propinquity
Frederic Latremoliere
The modular Gromov-Hausdorff propinquity is a distance on classes of modules endowed with quantum metric information, in the form of a metric form of a connection and a left Hilber…
Actions of Categories by Lipschitz morphisms on limits for the Gromov-Hausdorff Propinquity
Frederic Latremoliere
We prove a compactness result for classes of actions of many small categories on quantum compact metric spaces by Lipschitz linear maps, for the topology of the covariant Gromov-Ha…
Some applications of conditional expectations to convergence for the quantum Gromov-Hausdorff propinquity
Konrad Aguilar, Frederic Latremoliere
We prove that all the compact metric spaces are in the closure of the class of full matrix algebras for the quantum Gromov-Hausdorff propinquity. We also show that given an action…