Harnack's Theorem via Bredon Cohomology

Harnack’s Curve Theorem is a classical result in plane curve geometry concerning the maximum number of connected components of a real algebraic curve. In this talk, we translate this classical problem into topology and present a proof using Smith theory and equivariant Bredon cohomology. If time permits, we will also discuss the theme of understanding the homotopy type of real/complex points of algebraic varieties.