##### Department of Mathematics,

University of California San Diego

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### Math 295 - Mathematics Colloquium

## Danny Neftin

#### University of Michigan

## Galois groups of rational functions

##### Abstract:

A fundamental invariant associated to every complex rational function f is its monodromy group, that is, the Galois group of the covering $f:P^1->P^1$ on the projective line $P^1$. We shall discuss the accumulating work towards determining the degree n complex rational functions with a specified monodromy group that is not $A_n$ or $S_n$, and its applications to problems in number theory, complex analysis, and complex dynamics. Joint work with Michael Zieve.

Hosts: Adrian Wadsworth and Cristian Popescu

### February 5, 2015

### 3:00 PM

### AP&M 6402

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