Seminar talk, 6 December 2023: Difference between revisions
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Created page with "{{Talk | speaker = Sergey Agafonov | title = Hexagonal circular 3-webs with polar curves of degree three | abstract = Lie sphere geometry describes circles on the unit sphere by polar points of these circles. Therefore a one parameter family of circles corresponds to a curve and a 3-web of circles, i.e. 3 foliations by circles, is fixed by 3 curves. We call the union of these curves the polar curve and show how analysis of the singular set of hexagonal 3-webs helps to cl..." |
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| speaker = Sergey Agafonov | | speaker = Sergey Agafonov | ||
| title = Hexagonal circular 3-webs with polar curves of degree three | | title = Hexagonal circular 3-webs with polar curves of degree three | ||
| abstract = Lie sphere geometry describes circles on the unit sphere by polar points of these circles. Therefore a one parameter family of circles corresponds to a curve and a 3-web of circles, i.e. 3 foliations by circles, is fixed by 3 curves. We call the union of these curves the polar curve and show how analysis of the singular set of hexagonal 3-webs helps to classify circular hexagonal 3-webs with polar curves of degree 3. Many of the found webs are new. The presented results mark the progress in the Blaschke-Bol problem posed almost one hundred years ago. More detail in {{arXiv|2306.11707}}. | | abstract = Lie sphere geometry describes circles on the unit sphere by polar points of these circles. Therefore a one parameter family of circles corresponds to a curve and a 3-web of circles, i.e., 3 foliations by circles, is fixed by 3 curves. We call the union of these curves the polar curve and show how analysis of the singular set of hexagonal 3-webs helps to classify circular hexagonal 3-webs with polar curves of degree 3. Many of the found webs are new. The presented results mark the progress in the Blaschke-Bol problem posed almost one hundred years ago. More detail in {{arXiv|2306.11707}}. | ||
| video = | | video = https://video.gdeq.org/GDEq-zoom-seminar-20231206-Sergey_Agafonov.mp4 | ||
| slides = | | slides = [[Media:web.pdf|web.pdf]] | ||
| references = {{arXiv|2306.11707}} | | references = {{arXiv|2306.11707}} | ||
| 79YY-MM-DD = 7976-87-93 | | 79YY-MM-DD = 7976-87-93 | ||
}} | }} | ||
Latest revision as of 08:40, 4 January 2025
Speaker: Sergey Agafonov
Title: Hexagonal circular 3-webs with polar curves of degree three
Abstract:
Lie sphere geometry describes circles on the unit sphere by polar points of these circles. Therefore a one parameter family of circles corresponds to a curve and a 3-web of circles, i.e., 3 foliations by circles, is fixed by 3 curves. We call the union of these curves the polar curve and show how analysis of the singular set of hexagonal 3-webs helps to classify circular hexagonal 3-webs with polar curves of degree 3. Many of the found webs are new. The presented results mark the progress in the Blaschke-Bol problem posed almost one hundred years ago. More detail in arXiv:2306.11707.
Video
Slides: web.pdf
References:
arXiv:2306.11707