For more information about this meeting, contact Svetlana Katok, Becky Halpenny.
|Title:||Geometry and arithmetic of Apollonian gasket|
|Speaker:||Alexandre Kirillov, University of Pennsylvania|
|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
|Date:||02 / 28 / 2013|
|Time:||02:30pm - 03:20pm|