For more information about this meeting, contact Svetlana Katok, Becky Halpenny, Flossie Dunlop.
| Title: | Geometry and arithmetic of Apollonian gasket |
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| Seminar: | PMASS Colloquium |
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| Speaker: | Alexandre Kirillov, University of Pennsylvania |
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| Abstract Link: | http://www.math.psu.edu/katok_s/Gasket.pdf |
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| Abstract: |
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| One of oldest and beautiful examples of a fractal set is the Apollonian gasket, arising as a maximal tiling of 2-dimensional sphere by non-intersecting discs. There are (at least) two remarkable facts:
1. The Descartes theorem, which gives the algebraic relation between the curvatures of four pair-wise tangent circles on the plane. I shall give the proof based on the geometry of Minkowski space.
2. The existence of integral realisations of the Apollonian gasket, where all curvatures are integers. I show some arithmetic properties of these curvatures and formulate several open questions.
I attached a picture of one integral realisation. |
Room Reservation Information
| Room Number: | MB113 |
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| Date: | 02 / 28 / 2013 |
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| Time: | 02:30pm - 03:20pm |
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