Some numbers, such as
can be written as a sum of two cubes. Are there any numbers that can be written like this in two (or more) different ways? This seemingly innocuous question will lead us into a beautiful region where number theory, geometry, algebra, and even a smidgeon of calculus interact in surprising ways.
The talk is a description of an easy combinatorial algorithm called Schensted's algorithm and how it can be used to find nice connections between simple algebraic and combinatorial objects. It does not require much mathematical maturity -- anyone past the calculus sequence should be fine.
Following a cosmic surveyor who tries to measure the distances to cosmic objects, we encounter a fundamental question: what is the geometry of space and time? Attempts to answer this question led to beautiful ideas of General Relativity and recent breakthrough discoveries in cosmology.
This file was last modified on Sunday, 17-Apr-2005 23:25:51 CDT.