Sphere packings and Arithmetic Lattices
Kei Nakamura (Rutgers)
Location: Hill 525
Date & time: Tuesday, 03 April 2018 at 3:30PM - 4:30PM
Abstract: It has been known for sometime that the Apollonian packing, as well as certain other infinite circle/sphere packings, are "integral" packings, i.e. they can be realized so that the bends (the reciprocal of radii) of constituent circles/spheres are integers. Most of the known integral packings exhibit a stronger integral property, and we refer to them as "super-integral" packings. Relating them to the theory of arithmetic reflection lattices, we prove that super-integral packings exists only in finitely many dimensions, and only in finitely many commensurability classes.