19 citations · 36 across the 9 of their papers we have counts for
6 papers · 1 filter
Orbital Integrals are Motivic
Thomas C. Hales
This article shows that under general conditions, p-adic orbital integrals of definable functions are represented by virtual Chow motives. This gives an explicit example of the phi…
The Honeycomb Problem on the Sphere
Thomas C. Hales
The honeycomb problem on the sphere asks for the perimeter-minimizing partition of the sphere into N equal areas. This article solves the problem when N=12. The unique minimizer is…
Virtual Transfer Factors
Julia Gordon, Thomas C. Hales
The Langlands-Shelstad transfer factor is a function defined on some reductive groups over a p-adic field. Near the origin of the group, it may be viewed as a function on the Lie a…
Some algorithms arising in the proof of the Kepler conjecture
Thomas C. Hales
By any account, the 1998 proof of the Kepler conjecture is complex. The thesis underlying this article is that the proof is complex because it is highly under-automated. Throughout…
Sphere Packings in 3 Dimensions
Thomas C. Hales
This short note describes the tentative form of a finite-dimensional optimization problem that may be of use in a second-generation proof of the Kepler conjecture. In the original…
Can p-adic integrals be computed?
Thomas C. Hales
This article gives an introduction to arithmetic motivic integration in the context of p-adic integrals that arise in representation theory. A special case of the fundamental lemma…