June 2nd (Thursday) 15:00-16:00 / N902

Speaker: Xin Zhang (University of Illinois Urbana-Champaign)

Title: Local-global Phenomenon in Circle Packings

Abstract: A circle packing is an arrangement of circles whose interiors are disjoint. It was discovered recently that many types of circle packings have integer curvatures (the reciprocal of radii). Fixing such a circle packing, we will show that the integers arising as curvatures satisfy a local-global phenomenon. That is, almost every integer lying in some congruence classes is a curvature. This is a joint work with Elena Fuchs and Kate Stange, which extends the work of Bourgain-Kontorovich on the Apollonian case.