General Report by Konstantin Rybnikov
During the summer of 2001 undergraduate students Michael Greene (Harvard), Jody Radowicz (North Central), Sarah Crown (Bryn Mawr) and Kirsten Wikelgren (Harvard) studied geometry of homogeneous and inhomogeneous quadratic forms over integers. I was helped in this project by Cornell Ph.D. students Todd Kemp and Franco Saliola. Students worked in the following directions: geometry and combinatorics of perfect Delaunay polytopes, connections between extreme L-types and perfect forms, and the symmetries of the Voronoi polyhedron (Voronoi polyhedron is the convex hall of all integer points in the cone of positive semidefinitet real matrices).
Keywords: point lattice, quadratic forms over integers,
Delaunay polytope, Delaunay tiling, cone of positive definite matrices,
L-type, Voronoi reduction of the 2nd type, inhomogeneous quadratic form,
extreme hypermetric, diophantian inequality, perfect quadratic form, Voronoi
Last Update: September 16, 2001