Zobrazeno 1 - 10
of 343
pro vyhledávání: '"Latrémolière A"'
Autor:
Farsi, Carla, Latremoliere, Frederic
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, if two manifolds are close in the Gromov-Hausdorff distance, and belon
Externí odkaz:
http://arxiv.org/abs/2404.00240
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 on noncommutative solenoid for the spectral propinquity? We answer th
Externí odkaz:
http://arxiv.org/abs/2403.16323
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 quantum metrics with distinct domains on infinite-dimensional AF algebr
Externí odkaz:
http://arxiv.org/abs/2402.05520
Publikováno v:
J. Lond. Math. Soc. (2) 108 (2023), no. 4, 1488--1530
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. In particular we prove that these groups and sets are compact in the
Externí odkaz:
http://arxiv.org/abs/2302.09117
Publikováno v:
J. Math. Anal. Appl. 529 (2024), no. 1, Paper No. 127572, 22 pp
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 of strongly Leibniz quantum compact metric spaces. Then, given an induc
Externí odkaz:
http://arxiv.org/abs/2301.05692
Publikováno v:
Adv. Math. 437 (2024), Paper No. 109442, 59 pp
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 Gromov-Hausdorff propinquity, which is a noncommutative analogue of the Gro
Externí odkaz:
http://arxiv.org/abs/2301.00274
We describe, implement and test a novel method for training neural networks to estimate the Jacobian matrix $J$ of an unknown multivariate function $F$. The training set is constructed from finitely many pairs $(x,F(x))$ and it contains no explicit i
Externí odkaz:
http://arxiv.org/abs/2204.00523
Autor:
Liu, Qiang, Xiong, Jiali, Kim, Dong Won, Lee, Sang Soo, Bell, Benjamin J., Alexandre, Chloe, Blackshaw, Seth, Latremoliere, Alban, Wu, Mark N.
Publikováno v:
In Neuron 20 November 2024 112(22):3750-3767
Autor:
Latremoliere, Frederic
Publikováno v:
Math. Ann. 389 (2024), no. 1, 765--817
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 converges for the propinquity, then the spectra of the Dirac operators fo
Externí odkaz:
http://arxiv.org/abs/2112.11000
Autor:
Hamilton, Katrina R., McGill, Lakeya S., Campbell, Claudia M., Lanzkron, Sophie M., Carroll, C. Patrick, Latremoliere, Alban, Haythornthwaite, Jennifer A., Korczeniewska, Olga A.
Publikováno v:
In Gene Reports September 2024 36