Next week, Friday@4 will be a North meets South colloquium, featuring talks by our colleagues. These are designed to be accessible to the whole department, and are a great way to find out what others are working on, so please do come along to support our early-career colleagues. After the talks, there will be free pizza in the common room, along with Happy Hour. If you would like free pizza, please sign up online. (The pizza is free, but the organisers need to know how much to order.)
Laura Capuano will talk about Pell equations and continued fractions in number theory:
"The classical Pell equation has an extraordinary long history and it is very useful in many different areas of number theory. For example, they give a way to write a prime congruent to 1 modulo 4 as a sum of two squares, or they can also be used to break RSA encryption when the decryption key is too small. In this talk, I will present some properties of this wonderful equation and its relation with continued fractions. I will also treat the case of Pell equations in other contexts, such as the ring of polynomials, showing the differences with the classical case."
Noemi Picco will talk about Cortical neurogenesis: how humans (and mathematicians) can do more than macaque, with less
The cerebral cortex is perhaps the crowning achievement of evolution and is the region of the brain that distinguishes us from other species. Studying the developmental programmes that generate cortices of different sizes and neuron counts is the key to understanding both brain evolution and disease. I will show what mathematical modeling has to say about cortex evolution, when data resolution is poor. I will then discuss why humans are so special in the way they create their cortex, and how we are just like everybody else in many other aspects of brain development.
