Undergraduate Colloquium

Tangents to Four Unit Spheres:
An Introduction to Enumerative Algebraic Geometry
by

David Cox
William J. Walker Professor of Mathematics at Amherst College
Chair of Mathematics
 
sponsored by
Department of Mathematics
University of Kentucky
Lexington
March 5, 2009

In order to enhance the visibility of mathematics among the diverse population of the University of Kentucky students, the 2nd Bluegrass Algebra Conference will be preceded by a lecture aimed at the undergraduate level. The lecture will be delivered by Professor David Cox (Amherst College) and it is scheduled at 4:00 pm on Thursday, March 5, 2009, in room 114 of the Classroom Building (CB114).

Abstract: Given four spheres of radius one in three-dimensional space, how many lines can be simultaneously tangent to all four? The answer is easy to state, but understanding where it comes from requires some interesting mathematics, including Bezout's Theorem and the projective plane. This lecture will explain how these tools apply to the four sphere problem and put this problem into a larger context by introducing other counting problems that arise from algebraic equations (this is "enumerative algebraic geometry"). I will give numerous examples, including some that arise in string theory in mathematical physics.

For most of the lecture, knowledge of first semester calculus will be sufficient. In some places, Professor Cox will use dot product and cross product from third semester calculus.