Upcoming Events — Lent 2018
Unless otherwise stated, the talks are held at 7pm in MR2 at the Centre for Mathematical Sciences (the CMS), Wilberforce Road.
21st January 2018 — Pizza and Board Games Night
This event will be held at 6:30pm at Pavilion D, CMS.
26th January 2018 — Prof. Sarah Whitehouse (Sheffield)
Associativity in topology
Familiar operations in arithmetic, such as addition and multiplication of numbers, are associative. This means that the answers we obtain don't depend on the order in which we carry out the operations. For example, (2+3)+4 = 2+(3+4), and so we do not normally bother writing the brackets.
My work involves the interaction of algebraic conditions like associativity with topology, the study of shapes up to continuous deformations. In topological settings, it turns out that a weaker version of associativity is more natural. This leads to very rich and interesting structures which have become important in many different areas of mathematics, including algebra, geometry and mathematical physics. Similar topological games can be played with other familiar algebraic conditions.
Along the way, I'll talk about a famous sequence of numbers known as the Catalan numbers. They play a key role, because the Catalan numbers count how many different bracketings there are.