BPML: Irrationality in Algebraic Geometry - Dr Michel van Garrel

We are all used to working with shapes given by algebraic equations. In dimension 1, these could range from circles to hyperbolas, as well as more complicated ones involving higher degree equations. A fundamental question asks when we should consider two shapes to actually be the same. For example, a circle can be related to a hyperbola in a geometric way suggesting that they are fundamentally the same.

In higher dimensions, we can ask which equations give shapes that look like the coordinate axes with their independent dimensions. Determining these rational shapes is a surprisingly tricky question and trying to answer it has been a potent driving force for over 150 years in the field of algebraic geometry, the study of shapes given by algebraic equations. In the foreseeable future, an application of this apparently theoretical problem might even find its way into your mobile phone. In this talk I will show you how simply trying to understand the geometry of algebraic equations leads to a fascinating mathematical journey that has only just started.

The Birmingham Popular Maths Lecture series runs in the Watson Building (School of Mathematics) on the last Wednesday of each month, arriving from 18:30 onwards for a 19:00 start. We will also be showing the lecture live on Zoom for those that are unable to attend the lecture. 

To watch the lecture on Zoom you will need to register using the link above. If you plan on attending the lecture in person there is no need to register. Please note that attendees in the lecture theatre will be given priority for the Q&A, but some questions will be taken from Zoom.

The Birmingham Popular Mathematics Lectures are open to all members of the public and the University who are interested in the study of Mathematics. They are particularly suitable for those studying Mathematics at A Level and we also welcome advanced GCSE students. Young people are welcome on their own, with parents or with a school group.