DATE: | Thursday, October 31, 2002 |
TIME: | 4:30-5:30 PM |
PLACE: | LN 2205 |
SPEAKER: | Stephen Yau (University of Illinois at Chicago) |
TITLE: | Counting the number of integral points in an n-dimensional tetrahedron, and its applications |
Counting the number of integral points in a tetrahedron is an interesting problem which has attracted many famous mathematicians including Hardy, Littlewood, Mordell, Spencer, etc. Recently there has been significant progress due to the works of Beck, Brion-Vergne, Cappell-Shaneson, Danilov, Diaz-Robin, Ehrhart, Kantor-Khovanskii, Pommersheim, etc. In this talk we shall discuss the applications of this problem in number theory and algebraic geometry. We shall report recent progress on the GLY conjecture on a sharp estimate of the number of integral points in an n-dimensional tetrahedron with real vertices.