# Past Events — Easter 2016

*Unless otherwise stated, the talks are held at 7pm on Zoom. For every talk, a sign-up form will be circulated via the mailing list and posted on the Facebook page.*

### 29th April 2016 — Dr. Oscar Randall-Williams

#### Solving equations with topology

Topology is often useful in showing that equations have solutions without necessarily finding out what the solutions are. The first example of this is the intermediate value theorem: a continuous function *f*: **R** → **R** which takes both positive and negative values must take the value 0; the topological input is that **R** is connected. The second of these is the fundamental theorem of algebra: a polynomial function *p*: **C** → **C** of positive degree must take the value 0; the topological input is the calculation of the fundamental group of the circle.

I will explain these as well as the less-well known example of solving equations in groups: given a "polynomial" such as *w(x)=g _{1} x^{2} g_{2} x^{-4} g_{3} x^{3}* with

*g*in a group

_{1}, g_{2}, g_{3}*G*and

*x*a formal symbol, is there a bigger group

*H ≥ G*and a

*h ϵ H*such that

*w(h)=e ϵ H*?

### 1st May 2016 — Pavillion D Common Room

#### Pizza and Board Games Night

*This event was held at 6:30pm.*

### 16th May 2016 — Professor Michael Atiyah

#### Projective Planes and the Magic Square

Few things are more important and more fun than complex numbers and their generalizations: quaternions and octonians. There is a magic about them that has fascinated mathematicians over the centuries. I will tell this story from its origins in the 18th and 19th centuries and bring it right up to to the present time, on the front line of current research.