# Complexity in fields of generalized power series

## Julia Knight (University of Notre Dame)

### Thursday, October 19, 2017 4:00 pmMONT 214

Newton (in 1676) and Puiseux (in 1850) showed that if $K$ is real closed, or algebraically closed of characteristic $0$, then the field of Puiseux series with coefficients in $K$ is also real closed, or algebraically closed. Mac Lane extended the Newton-Puiseux Theorem to Hahn fields'' We are interested in measuring complexity of the root-taking process. We want to know whether it is effective? If not, we want to say how far it is from being effective.