Diophantine analysis in thin orbits

Special Seminar
Topic:Diophantine analysis in thin orbits
Speaker:Alex Kontorovich
Affiliation:Rutgers University; von Neumann Fellow, School of Mathematics
Date:Friday, December 8
Time/Room:1:15pm - 2:00pm/S-101
Video Link:https://video.ias.edu/special/2017/1208-AlexKontorovich

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.