### Graduate Student Seminar, 4:30pm November 11, 2002, Hayes-Healy
231

#### Speaker:

Sindi Sabourin
#### Title:

Hilbert Functions of Points
#### Abstract:

We first define the projective plane as the extension of the affine plane
where we demand that parallel lines meet at infinity. We study finite
sets of points in the projective plane and we introduce the Hilbert
function as an algebraic tool that provides geometric information about
the set of points. The information is encoded as a sequence of dimensions
of certain vector spaces. We show how Hilbert functions can be used to
solve the following classical geometry problem:
Given a hexagon whose vertices lie on a conic, then the three points of
intersection in the projective plane of pairs of lines which extend
opposite sides of the hexagon are collinear.
To volunteer to give a talk, or for any other questions regarding this schedule, contact Wesley Calvert