19 citations · 36 across the 9 of their papers we have counts for
18 papers
A Statement of the Fundamental Lemma
Thomas C. Hales
These notes give a statement of the "fundamental lemma," which is a conjectural identity between p-adic integrals that arises as part of the Langlands program.
What is Motivic Measure?
Thomas C. Hales
These notes give an exposition of the theory of arithmetic motivic integration, as developed by J. Denef and F. Loeser. An appendix by M. Fried gives some historical comments on Ga…
Good orbital integrals
Clifton Cunningham, Thomas C. Hales
This paper concerns a class of orbital integrals in Lie algebras over p-adic fields. The values of these orbital integrals at the unit element in the Hecke algebra count points on…
A computer verification of the Kepler conjecture
Thomas C. Hales
The Kepler conjecture asserts that the density of a packing of congruent balls in three dimensions is never greater than . A computer assisted verification confirmed t…
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…