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Intermediate dimensions, capacities and projections
Multi angle
Authors : Falconer, Kenneth (Author of the conference)
CIRM (Publisher )
28A75 - Length, area, volume, other geometric measure theory
28A78 - Hausdorff and packing measures
28A80 - Fractals
Additional resources :
https://www.cirm-math.fr/RepOrga/2109/Slides/Falconer.pdf
CIRM (Publisher )
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Abstract :
The talk will review recent work on intermediate dimensions which interpolate between Hausdorff and box dimensions. We relate these dimensions to capacities which leading to ‘Marstrand-type' theorems on the intermediate dimensions of projections of a set in $\mathbb{R}^{n}$ onto almost all m-dimensional subspaces. This is collaborative work with various combinations of Stuart Burrell, Jonathan Fraser, Tom Kempton and Pablo Shmerkin.
Keywords : dimensions; fractals; projections
MSC Codes : Keywords : dimensions; fractals; projections
28A75 - Length, area, volume, other geometric measure theory
28A78 - Hausdorff and packing measures
28A80 - Fractals
Additional resources :
https://www.cirm-math.fr/RepOrga/2109/Slides/Falconer.pdf
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 23/01/2020 Conference Date : 12/12/2019 Subseries : Research talks arXiv category : Metric Geometry ; Classical Analysis and ODEs Mathematical Area(s) : Analysis and its Applications Format : MP4 (.mp4) - HD Video Time : 00:39:05 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2019-12-12_Falconer.mp4 
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Information on the Event
Event Title : Jean-Morlet Chair 2019 - Conference - Thermodynamic Formalism: Dynamical Systems, Statistical Properties and their Applications / Chaire Jean-Morlet 2019 - Conférence - Formalisme thermodynamique : systèmes dynamiques, propriétés statistiques et leurs applicationsEvent Organizers : Nicol, Matthew ; Pollicott, Mark ; Troubetzkoy, Serge ; Vaienti, Sandro Dates : 09/12/2019 - 13/12/2019 Event Year : 2019 Event URL : https://www.chairejeanmorlet.com/2109.html
Citation Data
DOI : 10.24350/CIRM.V.19586703Cite this video as: Falconer, Kenneth (2019). Intermediate dimensions, capacities and projections. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19586703 URI : http://dx.doi.org/10.24350/CIRM.V.19586703 |
See Also
- [Multi angle] Besov spaces in multifractal environment, and the Frisch-Parisi conjecture / Author of the conference Seuret, Stéphane.
- [Multi angle] Marked length spectrum rigidity and the geodesic stretch / Author of the conference Knieper, Gerhard.
- [Multi angle] Closed geodesics and the measure of maximal entropy on surfaces without conjugate points / Author of the conference Climenhaga, Vaughn.
- [Post-edited] Emergence of wandering stable components / Author of the conference Berger, Pierre.
Bibliography
- BURRELL, Stuart A., FALCONER, Kenneth J., et FRASER, Jonathan M. Projection theorems for intermediate dimensions. arXiv preprint arXiv:1907.07632, 2019. - https://arxiv.org/abs/1907.07632
- BURRELL, Stuart A., FALCONER, Kenneth J., et FRASER, Jonathan M. Projection theorems for intermediate dimensions. arXiv preprint arXiv:1907.07632, 2019. - https://arxiv.org/abs/1811.06493
- FALCONER, Kenneth J., FRASER, Jonathan M., et SHMERKIN, Pablo. Assouad dimension influences the box and packing dimensions of orthogonal projections. arXiv preprint arXiv:1911.04857, 2019. - https://arxiv.org/abs/1911.04857
