There are still completely open fundamental questions about one-variable polynomials. One example is Hilbert’s 13th Problem, which concerns formulas for the roots of a polynomial in terms of its coefficients. Work on this problem really goes back hundreds of years; indeed, it inspired a lot of modern mathematics. In this talk I will explain part of the circle of ideas surrounding this problem. Along the way we will see some beautiful classical objects – the space of monic, degree d square-free polynomials, hyperplane complements, algebraic functions, discriminants, braid groups, Galois groups, and configuration spaces – all intimately related to each other, all with mysteries still to reveal.
Thackeray Hall 704