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Dror Bar-Natan:
Talks:
# Talks in Sydney, August 2017

## Nobody Solves the Quintic

### Undergraduate Talk, August 17, 2017

**Abstract.** Everybody knows that nobody can solve the quintic.
Indeed this insolubility is a well known hard theorem, the high point of a full-semester
course on Galois theory, often taken in one's 3rd or 4th year of
university mathematics. I'm not sure why so few know that the same
theorem can be proven in about 15 minutes using *very* basic and easily
understandable topology, accessible to practically anyone.

**Prerequisites.**

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

**Handout:**
Quintic-Handout.pdf.
**Slides:**
Quintic-Slides.nb.
**Talk video:** .

## The Dogma is Wrong

**Abstract.** It has long been known that there are knot invariants associated to semi-simple Lie
algebras, and there has long been a dogma as for how to extract them: "quantize and use representation
theory". We present an alternative and better procedure: "centrally extend, approximate by solvable, and
learn how to re-order exponentials in a universal enveloping algebra". While equivalent to the old
invariants via a complicated process, our invariants are in practice stronger, faster to compute (poly-time
vs. exp-time), and clearly carry topological information.

This is joint work with Roland van der Veen and continues work by Rozansky and Overbay.

**Handout:**
Dogma.html,
Dogma.pdf,
Dogma.png.

**Talk Video** (in Toulouse).

## The Dogma is Wrong - Extra Details

### Sydney, August 21, 2017

**Handout:** pre-talk (pdf,
nb), post-talk (pdf,
nb).