98 citations · 341 across the 35 of their papers we have counts for
17 papers · 1 filter
Ideal quantum metrics from fractional Laplacians
Dimitris Michail Gerontogiannis, Bram Mesland
We develop a novel framework for Monge--Kantorovič metrics using Schatten ideals and commutators of fractional Laplacians on Ahlfors regular spaces. Notably, for those metrics we d…
Theta correspondence via group C*-algebras
Magnus Goffeng, Bram Mesland, Mehmet Haluk Sengun
We prove that the well-known explicit construction of the local theta correspondence by Li has a simple interpretation in terms of group C*-algebras. In particular, we deduce that…
Adelic C*-correspondences and parabolic induction
Magnus Goffeng, Bram Mesland, Mehmet Haluk Sengun
In analogy with the construction of representations of adelic groups as restricted products of representations of local groups, we study restricted tensor products of Hilbert C*-mo…
Curvature and Weitzenbock formula for the Podleś quantum sphere
Bram Mesland, Adam Rennie
We prove that there is a unique Levi-Civita connection on the one-forms of the Dabrowski-Sitarz spectral triple for the Podleś sphere . We compute the full curvature ten…
Heat operators and isometry groups of Cuntz-Krieger algebras
Dimitris Michail Gerontogiannis, Magnus Goffeng, Bram Mesland
This paper introduces heat semigroups of topological Markov chains and Cuntz-Krieger algebras by means of spectral noncommutative geometry. Using recent advances on the logarithmic…
Curvature and Weitzenbock formula for spectral triples
Bram Mesland, Adam Rennie
Using the Levi-Civita connection on the noncommutative differential one-forms of a spectral triple $(\B,\H,\D)$, we define the full Riemann curvature tensor, the Ricci curvature te…
Classifying the Dynamics of Architected Materials by Groupoid Methods
Bram Mesland, Emil Prodan
We consider synthetic materials consisting of self-coupled identical resonators carrying classical internal degrees of freedom. The architecture of such material is specified by th…
The Friedrichs angle and alternating projections in Hilbert -modules
Bram Mesland, Adam Rennie
Let be a -algebra, a Hilbert -module over and a pair of complemented submodules. We prove the -module version of von Neumann's alter…
A groupoid approach to interacting fermions
Bram Mesland, Emil Prodan
We consider the algebra generated by the inner-limit derivations over the algebra of a fermion gas populating an aperiodic Delone set …
Localised module frames and Wannier bases from groupoid Morita equivalences
Chris Bourne, Bram Mesland
Following the operator algebraic approach to Gabor analysis, we construct frames of translates for the Hilbert space localisation of the Morita equivalence bimodule arising from a…
Toeplitz extensions in noncommutative topology and mathematical physics
Francesca Arici, Bram Mesland
We review the theory of Toeplitz extensions and their role in operator K-theory, including Kasparov's bivariant K-theory. We then discuss the recent applications of Toeplitz algebr…
Curvature of differentiable Hilbert modules and Kasparov modules
Bram Mesland, Adam Rennie, Walter D. van Suijlekom
In this paper we introduce the curvature of densely defined universal connections on Hilbert -modules relative to a spectral triple (or unbounded Kasparov module), obtaining…
Index theory and topological phases of aperiodic lattices
Chris Bourne, Bram Mesland
We examine the noncommutative index theory associated to the dynamics of a Delone set and the corresponding transversal groupoid. Our main motivation comes from the application to…
Sums of regular selfadjoint operators in Hilbert-C*-modules
Matthias Lesch, Bram Mesland
We introduce a notion of weak anticommutativity for a pair (S,T) of self-adjoint regular operators in a Hilbert-C*-module E. We prove that the sum of such pairs is self-adjoi…
Operator *-correspondences in analysis and geometry
David Blecher, Jens Kaad, Bram Mesland
An operator *-algebra is a non-selfadjoint operator algebra with completely isometric involution. We show that any operator *-algebra admits a faithful representation on a Hilbert…
Spectral triples on
Magnus Goffeng, Bram Mesland
We give a construction of an odd spectral triple on the Cuntz algebra , whose -homology class generates the odd -homology group . Using a metric measure sp…
Nonunital spectral triples and metric completeness in unbounded KK-theory
Bram Mesland, Adam Rennie
By considering the general properties of approximate units in differentiable algebras, we are able to present a unified approach to characterising completeness of spectral metric s…