# Past Events — Lent 2019

*Unless otherwise stated, the talks are held at 7pm in MR2 at the Centre for Mathematical Sciences (the CMS), Wilberforce Road.*

### 25th January 2019 — Dr Ana Khukhro (University of Cambridge)

#### The geometry of groups

Groups are extremely natural algebraic objects, allowing us to express the notion of symmetry in a mathematical language. While they can be studied in a purely algebraic or combinatorial way, groups truly come alive when imbued with geometry. We will talk about how to construct graphs from groups, the interactions between geometric and algebraic properties of groups, and some surprising applications, including how group theory can help you save money on cables.

### 1st February 2019 — Dr James Newton (King's College London)

#### Dividing squares into triangles

I will talk about Monsky's theorem, which says that a square cannot be divided into an odd number of triangles of equal area. The proof involves a weird (but fun) application of a non-archimedean distance function on the rational numbers; I'll spend some portion of the talk explaining what non-archimedean distance functions are and why they are as important (from some points of view) as the usual notion of distance between two numbers.