Topology Seminar

Poincare invented algebraic topology in an effort to understand how the roots of a polynomial depend on the coefficients. In his study of the cohomology of the braid group, Arnold attempted to develop topological invariants capable of obstructing solutions of a polynomial in one variable. In this talk, I'll recall algebraic functions and their topology, and review some examples of topological obstructions to their solutions (including Arnold's topological proof of Abel's theorem, McMullen's obstruction to iterative algorithms, and Burda's work on the Kronecker-Klein resolvent problem). Time permitting, I'll describe work in progress with Benson Farb and Mark Kisin on the algebraic function (for a given g and n) which assigns to a g-dimensional abelian variety an n-torsion point. Speaker(s): Jesse Wolfson (UC-Irvine)