Prime components in Apollonian circle packings

Speaker:

Damaris Schindler

Affiliation:

University of Göttingen

Date:

Tue, 06/05/2025 - 14:30 - 14:55

Location:

MPIM Lecture Hall [2]

Parent event:

Conference on "Asymptotic Counting and L-Functions" [3]

In this talk we discuss prime components and thickened prime components in Apollonian circle packings. In particular, we are interested in the set of curvatures that appear in these subsets of Apollonian circle packings and we prove first lower bounds on the number of curvatures of bounded height that appear in a thickened prime component. This is joint work with Elena Fuchs, Holley Friedlander, Piper Harris, Catherine Hsu, James Rickards, Katherine Sanden and Katherine Stange.