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Dror Bar-Natan:
Talks:
# Commutators

## Math Union Guest Speaker

### 4PM Friday January 16 2015, Bahen B024

**Abstract.** The commutator of two elements $x$ and $y$ in a
group $G$ is $xyx^{-1}y^{-1}$. That is, $x$ followed by $y$ followed
by the inverse of $x$ followed by the inverse of $y$. In my talk I will
tell you how commutators are related to the following four riddles:

- Can you send a secure message to a person you have never communicated
with before (neither privately nor publicly), using a messenger you
do not trust?
- Can you hang a picture on a string on the wall using $n$ nails,
so that if you remove any one of them, the picture will fall?
- Can you draw an $n$-component link (a knot made of $n$
non-intersecting circles) so that if you remove any one of those $n$
components, the remaining $n-1$ will fall apart?
- Can you solve the quintic in radicals? Is there a formula for the
zeros of a degree $5$ polynomial in terms of its coefficients, using
only the operations on a scientific calculator?

**Prerequisites.**

- The first week of any class on group theory.
- Knowing that every complex number other than to $0$ has exactly $n$ roots
of order $n$, and how to compute them.