Real geometry, from algebraic to subanalytic and beyond.
MATH 649K, Spring 2018

We will study real algebraic sets (with emphasis on geometry over algebra), semialgebraic sets (sets
defined by polynomial equalities and inequalities) , and subanalytic sets. We will consider the basic
properties of these sets, study of appropriate classes of functions on them, topology, applications.
We may get into further classes of “tame geometry” such as o-minimal geometries.
There are no particular prerequisites, just a certain level of mathematical maturity; undergraduate
mathematical analysis and topology should be enough.