This research is concerned with the algebraic K-groups of infinite fields. The principal investigator is studying aspects of the geometric significance of some filtration quotients of these K-groups. These quotients bring together various fields of mathematical research including the homology of the general linear group, the higher Chow groups of Bloch and certain scissors congruence groups of polytopes. Algebraic geometry is the study of the geometric objects arising from the sets of zeros of systems of polynomial equations. This is one of the oldest and currently one of the most active branches of mathematics. There are widespread applications of algebraic geometry in mathematics, physics and computer science.