Complexity in fields of generalized power series
Julia Knight (University of Notre Dame)
Thursday, October 19, 2017
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.