Charles R. dePrima Memorial Lecture in Mathematics

It might be surprising to hear that there are still open problems in Euclidean geometry.  The problems that I'll talk about come from combinatorial geometry.  We consider all the configurations of n points in the plane, and we try to maximize some feature of the configuration.  For many problems, we don't know the exact maximum, and we don't even know the right order of magnitude.  I'll talk about what makes these problems hard, and why I think it would be significant to find out the answers.

There has been significant progress in this area over the last decade.  The progress comes from introducing ideas from other fields - in particular ideas about polynomials that come from the theory of error-correcting codes.  In the second half of the talk, I'll sketch how ideas from error correcting codes can help to understand these types of geometry problems.