5 citations · 8 across the 8 of their papers we have counts for
9 papers
The Geometric Arveson-Douglas Conjecture through Veronese Embeddings
Francesca Arici, Yufan Ge, Dimitris Michail Gerontogiannis
We prove invariance of the geometric Arveson-Douglas conjecture under Veronese embeddings of projective varieties. This provides new examples of singular varieties satisfying the c…
Five shades of KMS: Statistical properties in the spectral geometry of Cuntz--Krieger algebras
Dimitris Michail Gerontogiannis, Magnus Goffeng
We study spectral invariants arising in the noncommutative geometry of topological Markov chains and Cuntz--Krieger algebras. Their noncommutative geometry is described by spectral…
Quantum isometry groups of log-Laplacians on Cuntz--Krieger algebras
Amaury Freslon, Dimitris Michail Gerontogiannis, Adam Skalski
We compute the quantum isometry groups of Cuntz-Krieger algebras endowed with the spectral triples coming from the Ahlfors regular structure of the underlying topological Markov ch…
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…
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…
KK-duality for the Cuntz-Pimsner algebras of Temperley-Lieb subproduct systems
Francesca Arici, Dimitris Michail Gerontogiannis, Sergey Neshveyev
We prove that the Cuntz-Pimsner algebra of every Temperley-Lieb subproduct system is KK-self-dual. We show also that every such Cuntz-Pimsner algebra has a canonical KMS-state, whi…
The logarithmic Dirichlet Laplacian on Ahlfors regular spaces
Dimitris Michail Gerontogiannis, Bram Mesland
We introduce the logarithmic analogue of the Laplace-Beltrami operator on Ahlfors regular metric-measure spaces. This operator is intrinsically defined with spectral properties ana…
On finitely summable Fredholm modules from Smale spaces
D. M. Gerontogiannis
We prove that all K-homology classes of the stable (and unstable) Ruelle algebra of a Smale space have explicit Fredholm module representatives that are finitely summable on the sa…
Ahlfors regularity and fractal dimension of Smale spaces
D. M. Gerontogiannis
We prove that, up to topological conjugacy, every Smale space admits an Ahlfors regular Bowen measure. Bowen's construction of Markov partitions implies that Smale spaces are facto…