Random algebraic geometry - lecture 1 | Vidéo | Carmin.tv

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Random algebraic geometry - lecture 1

De Antonio Lerario

Apparaît dans la collection : Real Algebraic Geometry / Géometrie algébrique réelle

In the last years there has been an increasing interest into the statistical behaviour of algebraic sets over non-algebraically closed fields: when the notion of 'generic' is no longer available, one seeks for a 'random' study of the objects of interest. In this course, divided into four lectures, I will present the major ideas in the subject (lecture notes will be made available):

Generic and random. In the first lecture I will discuss how to switch from the notion of generic, from classical algebraic geometry, to the notion of random. Of course, this depends on the choice of the probability distribution on the 'moduli space' of the objects of interest. I will discuss what are the reasonable choices in the case $\mathbb{K}=\mathbb{C}$ (where still these questions make sense, and 'random' and 'generic' are synonymous) and in the case $\mathbb{K}=\mathbb{R}$ (where spherical harmonics play a crucial role).

Informations sur la vidéo

Date de captation 26/10/2022
Date de publication 18/11/2022
Institut CIRM
Licence CC BY NC ND
Langue Anglais
Audience Chercheurs
Réalisateur(s) Guillaume Hennenfent
Format MP4

Données de citation

DOI 10.24350/CIRM.V.19978403
Citer cette vidéo Lerario Antonio (26/10/2022). Random algebraic geometry - lecture 1. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19978403
URL https://dx.doi.org/10.24350/CIRM.V.19978403

Domaine(s)

Géométrie algébrique

Bibliographie

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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
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LERARIO, Antonio. What is... random algebraic geometry ? - https://drive.google.com/file/d/1qZ2ebeV4gv7TTEyFRdebGhWZpEp8XY5V/view

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