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Random algebraic geometry - lecture 4
Multi angle
Authors : Lerario, Antonio (Author of the conference)
CIRM (Publisher )
14P05 - Real algebraic sets, See also {12Dxx}
14P25 - Topology of real algebraic varieties
52A22 - Random convex sets and integral geometry
14N15 - Classical problems, Schubert calculus
CIRM (Publisher )
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Abstract :
4. The zonoid ring and the nonarchimedean world. In the last lecture I will explain a ring-theoretical interpretation of the computations in random algebraic geometry, using a recently discovered ring structure on special convex bodies. This leads to the construction of a probabilistic version of Schubert calculus. In the final part of the lecture I will export some of the ideas from the previous lectures to the case $\mathbb{K}=\mathbb{Q}_{p}$, leaving with some open questions.
Keywords : real algebraic geometry; Schubert calculus
MSC Codes : Keywords : real algebraic geometry; Schubert calculus
14P05 - Real algebraic sets, See also {12Dxx}
14P25 - Topology of real algebraic varieties
52A22 - Random convex sets and integral geometry
14N15 - Classical problems, Schubert calculus
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 18/11/2022 Conference Date : 26/10/2022 Subseries : Research School arXiv category : Algebraic Geometry Mathematical Area(s) : Geometry ; Algebraic & Complex Geometry Format : MP4 (.mp4) - HD Video Time : 00:57:17 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2022-10-27_Lerario_Part4.mp4 
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Information on the Event
Event Title : Real Algebraic Geometry / Géometrie algébrique réelleEvent Organizers : Bihan, Frédéric ; Brugallé, Erwan ; Dickenstein, Alicia ; Dutertre, Nicolas Dates : 26/10/2022 - 30/10/2022 Event Year : 2022 Event URL : https://conferences.cirm-math.fr/2626.html
Citation Data
DOI : 10.24350/CIRM.V.19980203Cite this video as: Lerario, Antonio (2022). Random algebraic geometry - lecture 4. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19980203 URI : http://dx.doi.org/10.24350/CIRM.V.19980203 |
See Also
- [Multi angle] Random algebraic geometry - lecture 3 / Author of the conference Lerario, Antonio.
- [Multi angle] Random algebraic geometry - lecture 2 / Author of the conference Lerario, Antonio.
- [Multi angle] Random algebraic geometry - lecture 1 / Author of the conference Lerario, Antonio.
- [Multi angle] Poincaré-Reeb graphs of real algebraic domains / Author of the conference Sorea, Miruna-Stefana.
Bibliography
- BREIDING, Paul, BÜRGISSER, Peter, LERARIO, Antonio, et al. The zonoid algebra, generalized mixed volumes, and random determinants. Advances in Mathematics, 2022, vol. 402, p. 108361. - https://doi.org/10.1016/j.aim.2022.108361
- BÜRGISSER, Peter et LERARIO, Antonio. Probabilistic schubert calculus. Journal für die reine und angewandte Mathematik (Crelles Journal), 2020, vol. 2020, no 760, p. 1-58. - https://doi.org/10.1515/crelle-2018-0009
- DIATTA, Daouda Niang et LERARIO, Antonio. Low-degree approximation of random polynomials. Foundations of Computational Mathematics, 2022, vol. 22, no 1, p. 77-97. - http://dx.doi.org/10.1007/s10208-021-09506-y
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- GAYET, Damien et WELSCHINGER, Jean-Yves. What is the total Betti number of a random real hypersurface?. Journal für die reine und angewandte Mathematik (Crelles Journal), 2014, vol. 2014, no 689, p. 137-168. - https://doi.org/10.1515/crelle-2012-0062
- GAYET, Damien et WELSCHINGER, Jean-Yves. Betti numbers of random real hypersurfaces and determinants of random symmetric matrices. Journal of the European Mathematical Society, 2016, vol. 18, no 4, p. 733-772. - https://doi.org/10.4171/jems/601
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- KOSTLAN, Eric. On the distribution of roots of random polynomials. In : From Topology to Computation: Proceedings of the Smalefest. Springer, New York, NY, 1993. p. 419-431. - http://dx.doi.org/10.1007/978-1-4612-2740-3_38
- LERARIO, Antonio. Lecture notes on metric algebraic geometry, 2022. - https://www.mn.uio.no/math/english/research/groups/algebra/events/conferences/nordfjordeid2022/metrics.html
- LERARIO, Antonio et LUNDBERG, Erik. Statistics on Hilbert's 16th problem. International Mathematics Research Notices, 2015, vol. 2015, no 12, p. 4293-4321. - https://doi.org/10.1093/imrn/rnu069
- SARNAK, Peter. Letter to B. Gross and J. Harris on ovals of random plane curves, 2011, p. 1-14. - https://publications.ias.edu/node/510
- SHUB, Michael et SMALE, Steve. Complexity of Bezout's theorem II Volumes and probabilities. In : Computational algebraic geometry. Birkhäuser, Boston, MA, 1993. p. 267-285. - http://dx.doi.org/10.1007/978-1-4612-2752-6_19
- LERARIO, Antonio. What is... random algebraic geometry ? - https://drive.google.com/file/d/1qZ2ebeV4gv7TTEyFRdebGhWZpEp8XY5V/view
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