Understanding the growth of Laplace eigenfunctions (part 1 of 2) | Vidéo | Carmin.tv

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Understanding the growth of Laplace eigenfunctions (part 1 of 2)

By Yaiza Canzani

Appears in collection : Méthodes microlocales en analyse et géométrie / Microlocal Methods in Analysis and Geometry

In this talk we will discuss a new geodesic beam approach to understanding eigenfunction concentration. We characterize the features that cause an eigenfunction to saturate the standard supremum bounds in terms of the distribution of $L^{2}$ mass along geodesic tubes emanating from a point. We also show that the phenomena behind extreme supremum norm growth is identical to that underlying extreme growth of eigenfunctions when averaged along submanifolds. Using the description of concentration, we obtain quantitative improvements on the known bounds in a wide variety of settings.

Information about the video

Date of recording 08/05/2019
Date of publication 03/06/2019
Institution CIRM
Licence CC BY NC ND
Language English
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.19521503
Cite this video Canzani, Yaiza (08/05/2019). Understanding the growth of Laplace eigenfunctions (part 1 of 2). CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19521503
URL https://dx.doi.org/10.24350/CIRM.V.19521503

Domain(s)

Bibliography

Canzani, Y., & Galkowski, J. (2019). Eigenfunction concentration via geodesic beams. arXiv preprint arXiv:1903.08461. - https://arxiv.org/abs/1903.08461
Canzani, Y., & Galkowski, J. (2018). A Novel Approach to Quantitative Improvements for Eigenfunction Averages. arXiv preprint arXiv:1809.06296. - https://arxiv.org/abs/1809.06296
Canzani, Y., & Galkowski, J. (2017). On the growth of eigenfunction averages: microlocalization and geometry. arXiv preprint arXiv:1710.07972. - https://arxiv.org/abs/1710.07972
Canzani, Y., Galkowski, J., & Toth, J. A. (2018). Averages of eigenfunctions over hypersurfaces. Communications in Mathematical Physics, 360(2), 619-637. - https://arxiv.org/abs/1705.09595

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