# 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

### Location

Simonyi 101 and Remote Access### Speakers

James Rickards, University of Colorado Boulder

## Event Series

## Categories

## Notes

**Meeting ID: 920 2195 5230**

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

Video link: https://www.ias.edu/video/not-so-local-global-conjecture