On Hilbert's 13th Problem

The formulation of the 13th Problem in Hilbert's address of 1900 to the International Congress of Mathematicians in Paris allows many different interpretations. The most general one was solved by Kolmogorov in 1957. However, the more natural ``algebraic" form of the problem is still completely open.

We first describe Hilbert's 13th Problem in its original form and then give an algebraic formulation of it. We explain some very classical results which go back to Bring, Jerrard, Hamilton, Sylvester and Klein. From a modern point of view they can be understood as rationality questions in algebraic geometry. If time allows we will also comment on a recent result by Abhyankar related to a very restrictive form of the 13th Problem.

Refreshments will be served at 2:45 p.m. (Lounge, MATX 1115).