### Mathematics Colloquium

# Russell Lodge

### (Stony Brook University, USA)

## "Classification of Newton's method for polynomials"

** Date: ** |
Mon, November 27, 2017 |

** Time: ** |
17:15 |

** Place: ** |
Lecture Hall, Research I |

**Abstract:** Newton's method is of fundamental importance in root-finding; however, there exist "bad" open sets of starting values for which Newton's method does not converge to a root. Smale proposed a systematic study of the set of polynomials with this property, which I will do by classifying the "bad" sets combinatorially. This result can be extended to give a combinatorial classification of all (postcritically finite) Newton maps for polynomials using Thurston's theorem. I will then highlight aspects of this theory that are crucial in the ongoing project to classify rational maps as dynamical systems. This is joint work with Y. Mikulich and D. Schleicher.

*The colloquium is preceded by tea from 16:45 in the Resnikoff Mathematics Common Room, Research I, 127.*