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Geometric and Harmonic Analysis with Interdisciplinary Applications

Deliverables

learning geometrical invariances and applications

two preprints will be prepared one on learning invariances UAMJHUMAR one on geometrical cortical organization CNRSUNIBOYALE

minimal surfaces and geometric PDE

Two preprints will be obtained: one on geometric PDE (UNIBO-PU), one on minimal surfaces (UGR-PITTS).

Infinite dimensional representation

A preprint will be prepared (UNIBO - UC).

Conformally covariant operators and k forms

Two preprints willl be obtained one on conformally covariant operators UAMPU one on kforms UNIBOPU

degenerate PDE

A preprint will be obtained on the regularity of solutions (UNIBO - MIT)

minimal surfaces and isoperimetric inequality

Two preprints willl be obtained one on minimal surfaces PSUDMIT one on isoperimetric inequality UGRPU

image analysis and vision

Three preprints will be prepared: one on geometrical cortical organization (CNRS-YALE), one on image analysis (UNIBO-UC-GMV,) one on stochastic propagation (CNRS-UNIBO-MIT).

Extensions of Peter-Weyl theorem

A preprint will be prepared UNIBO UC

reproducing kernel spaces and Fourier analysis

Two preprints will be obtained: one on on reproducing kernel Hilbert spaces (UNIBO - WU), one on restriction of the Fourier transform (UAM - UC).

sampling in group invariant spaces

A preprint will be obtained (UAM -UBA).

nonlocal and non linear PDE

Two preprints will be delivered: one on nonlocal diffusion (UAM-UT). One on p-Laplacian in Euclidean spaces (UAM-UBA).

Outreach presentations

Organization of outreach events, press releases, communication actions and web site, and development of a Communication Plan.

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Publications

Conformality and Q-harmonicity in Sub-Riemannian manifolds

Author(s): L. Capogna, G. Citti, E. Le Donne, A. Ottazzi,
Published in: cvgmt.sns.it, 2018
Publisher: CVGMT

Sharp Extinction Rates for Fast Diffusion Equations on Generic Bounded Domains

Author(s): Matteo Bonforte, Alessio Figalli
Published in: arxiv.org, 2019
Publisher: Cornell University

From receptive profiles to a metric model of V1

Author(s): Noemi Montobbio, Giovanna Citti, Alessandro Sarti
Published in: arxiv.org, 2019
Publisher: Cornell University press

Lagrangian study of the final warming in the southern stratosphere during 2002: Part I. The Vortex Splitting at Upper Levels

Author(s): Jezabel Curbelo, Carlos R. Mechoso, Ana M. Mancho, Stephen Wiggins
Published in: arxiv.org, 2019
Publisher: Cornell University Press

Neurogeometry of perception: isotropic and anisotropic aspects

Author(s): Giovanna Citti, Alessandro Sarti
Published in: arxiv.org, 2018
Publisher: Cornell University press

Conformality and Q -harmonicity in sub-Riemannian manifolds

Author(s): Luca Capogna, Giovanna Citti, Enrico Le Donne, Alessandro Ottazzi
Published in: Journal de Mathématiques Pures et Appliquées, 2017, ISSN 0021-7824
Publisher: Elsevier BV
DOI: 10.1016/j.matpur.2017.12.006

Extending an Example by Colding and Minicozzi

Author(s): Lorenzo Ruffoni, Francesca Tripaldi
Published in: The Journal of Geometric Analysis, 30/1, 2020, Page(s) 1028-1041, ISSN 1050-6926
Publisher: American Mathematical Society
DOI: 10.1007/s12220-019-00177-4

Nonlocal diffusion equations with dynamical boundary conditions

Author(s): Pablo M. Berná, Julio D. Rossi
Published in: Nonlinear Analysis, 195, 2020, Page(s) 111751, ISSN 0362-546X
Publisher: Pergamon Press Ltd.
DOI: 10.1016/j.na.2020.111751

Lebesgue inequalities for Chebyshev thresholding greedy algorithms

Author(s): P. M. Berná, Ó. Blasco, G. Garrigós, E. Hernández, T. Oikhberg
Published in: Revista Matemática Complutense, 2019, ISSN 1139-1138
Publisher: Universidad Complutense de Madrid
DOI: 10.1007/s13163-019-00328-9

Quantitative a priori estimates for fast diffusion equations with Caffarelli–Kohn–Nirenberg weights. Harnack inequalities and Hölder continuity

Author(s): Matteo Bonforte, Nikita Simonov
Published in: Advances in Mathematics, 345, 2019, Page(s) 1075-1161, ISSN 0001-8708
Publisher: Academic Press
DOI: 10.1016/j.aim.2019.01.018

Calderón-type inequalities for affine frames

Author(s): Davide Barbieri, Eugenio Hernández, Azita Mayeli
Published in: Applied and Computational Harmonic Analysis, 2019, ISSN 1063-5203
Publisher: Academic Press
DOI: 10.1016/j.acha.2019.07.004

Asymptotic mapping class group of closed surfaces punctured along Cantor sets

Author(s): J. Aramayona, L. Funar
Published in: Moscow Mathematical Journal, 2017, ISSN 1609-3321
Publisher: Independent University of Moscow

A Geometric Interpretation of Stochastic Gradient Descent Using Diffusion Metrics

Author(s): Rita Fioresi, Pratik Chaudhari, Stefano Soatto
Published in: Entropy, 22/1, 2020, Page(s) 101, ISSN 1099-4300
Publisher: Multidisciplinary Digital Publishing Institute (MDPI)
DOI: 10.3390/e22010101

Correction to: From receptive profiles to a metric model of V1

Author(s): Noemi Montobbio, Giovanna Citti, Alessandro Sarti
Published in: Journal of Computational Neuroscience, 47/2-3, 2019, Page(s) 231-231, ISSN 0929-5313
Publisher: Kluwer Academic Publishers
DOI: 10.1007/s10827-019-00728-2

Nonlocal diffusion equations with dynamical boundary conditions

Author(s): P.M. Berna, J. D. Rossi
Published in: Nonlinear Analysis, Theory, Methods and Applications, 2019, ISSN 0362-546X
Publisher: Pergamon Press Ltd.

Optimal translational-rotational invariant dictionaries for images

Author(s): Davide Barbieri, Carlos Cabrelli, Eugenio Hernández, Ursula Molter
Published in: Wavelets and Sparsity XVIII, 2019, Page(s) 3, ISBN 9781-510629707
Publisher: SPIE
DOI: 10.1117/12.2528890