PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact Svetlana Katok, Becky Halpenny, Flossie Dunlop.

Title:Geometry and arithmetic of Apollonian gasket
Seminar:PMASS Colloquium
Speaker:Alexandre Kirillov, University of Pennsylvania
Abstract Link:
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
Date:02 / 28 / 2013
Time:02:30pm - 03:20pm