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The not-so-local-global conjecture

Algebraic Geometry

Speaker: James Rickards, University of Colorado
Location: 2112 MSB
Start time: Wed, May 15 2024, 3:10PM

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.