Joint PU/IAS Number Theory

The Not-So-Local-Global Conjecture

I will introduce Apollonian circle packings, and describe the local-global conjecture, which predicts the set of curvatures of circles occurring in a packing. I will then describe reciprocity obstructions, a phenomenon rooted in reciprocity laws (for instance, quadratic reciprocity), that disproves the conjecture in most cases. I will also describe follow-up work, where we obtain a similar result in a situation related to Zaremba's conjecture on continued fraction expansions, disproving a conjecture of Kontorovich.

Date & Time

April 04, 2024 | 4:30pm – 5:30pm


Simonyi 101 and Remote Access


James Rickards, University of Colorado Boulder

Event Series



Meeting ID:  920 2195 5230

Passcode:    The three-digit integer that is the cube of the sum of its digits.

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