|Topic:||Diophantine analysis in thin orbits|
|Affiliation:||Rutgers University; von Neumann Fellow, School of Mathematics|
|Date:||Friday, December 8|
|Time/Room:||1:15pm - 2:00pm/S-101|
We will explain how the circle method can be used in the setting of thin orbits, by sketching the proof (joint with Bourgain) of the asymptotic local-global principle for Apollonian circle packings. We will mention extensions of this method due to Zhang and Fuchs-Stange-Zhang to certain crystallographic circle packings, as well as the method's limitations.