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We explore the geometric implications of introducing a spectral cut-off on Riemannian manifolds.
The spectral function of an elliptic operator
Lars Hörmander · 1968
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The dirac operator on the fuzzy sphere
H. Grosse and P. Prešnajder · 1995
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Universal formula for noncommutative geometry actions: Unification of gravity and the standard model
Ali H Chamseddine and Alain Connes · 1996
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Classification of finite spectral triples
Thomas Krajewski · 1998
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Distances in Finite Spaces from Noncommutative Geometry
B. Iochum, T. Krajewski, and P. Martinetti · 1999
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Fuzzy complex projective spaces and their star-products
A.P. Balachandran, Brian P. Dolan, J. Lee, X. Martin, and Denjoe O’Connor · 2002
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A fuzzy three sphere and fuzzy tori
Brian P Dolan and Denjoe O’Connor · 2003
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Topics in optimal transportation
Cédric Villani · 2003
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Heat kernels and Dirac operators
Nicole Berline, Ezra Getzler, and Michèle Vergne · 2004
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Modern multidimensional scaling: theory and applications
Ingwer Borg and Patrick J. F. Groenen · 2005
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On Spin Structures and Dirac Operators on the Noncommutative Torus
Mario Paschke and Andrzej Sitarz · 2006
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Why the standard model
Ali H Chamseddine and Alain Connes · 2008
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Moduli spaces of dirac operators for finite spectral triples
Branimir Ćaćić · 2011
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On the spectral characterization of manifolds
Alain Connes · 2013
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Elements of noncommutative geometry
José M Gracia-Bondía, Joseph C Várilly, and Héctor Figueroa · 2013
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Geometry and the quantum: Basics
Ali H. Chamseddine, Alain Connes, and Viatcheslav Mukhanov · 2014
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Spectral geometry with a cut-off: topological and metric aspects
Francesco D’Andrea, Fedele Lizzi, and Pierre Martinetti · 2014
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Scaling behaviour in random non-commutative geometries
Lisa Glaser · 2017
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Finite-rank approximations of spectral zeta residues
Abel B. Stern · 2018
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Spectral estimators for finite non-commutative geometries
John W. Barrett, Paul Druce, and Lisa Glaser · 2019
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Finite spectral triples for the fuzzy torus
John W. Barrett and James Gaunt · 2019
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Truncated geometry: Spectral approximation of the torus
T. Berendschot · 2019
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Lisa Glaser and Abel Stern · 2019
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John W. Barrett · 2015
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Quanta of geometry: Noncommutative aspects
Ali H. Chamseddine, Alain Connes, and Viatcheslav Mukhanov · 2015
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Monte carlo simulations of random non-commutative geometries
John W. Barrett and Lisa Glaser · 2016
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Conic optimization via operator splitting and homogeneous self-dual embedding
Brendan O’Donoghue, Eric Chu, Neal Parikh, and Stephen Boyd · 2016
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Measuring finite quantum geometries via quasi-coherent states
Lukas Schneiderbauer and Harold C. Steinacker · 2016
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A python implementation of the pointforge algorithm, with the sphere as an example
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Spectral truncations in noncommutative geometry and operator systems
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Gromov-Hausdorff convergence of state spaces for spectral truncations
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