## Science Research at UvA-VU: Dynamic Analysis Seminar

Talking about their research is an important activity for mathematicians, but an audience of five colleagues is just too small. And so, every two weeks, UvA researchers and their VU colleagues come together to attend a lecture on dynamic analysis. ‘We often have twenty people in the lecture hall, that's a nice crowd.’

These are the words of researcher Han Peters of the Korteweg-de Vries Institute for Mathematics (KdVI), organiser of the seminar on behalf of the UvA. The venue alternates between De Boelelaan and the Science Park. ‘It's like this,’ says Peters, ‘someone stands at the blackboard for 50 minutes describing their work, often writing up formulas, and now and then they answer questions. Afterwards we all go for a drink.’

Naturally, VU and UvA researchers talk about their own work at the seminar, but mathematicians from other institutes in the Netherlands or neighbouring countries are also invited to speak. The choice of an inclusive name was a deliberate one, explains Peters. ‘It covers a broad range: symplectic geometry, real and complex dynamics, applied dynamics.’

### Great wealth of behaviours

This field of research concerns how things change over time. From the very abstract to the very concrete, says Peters. By way of example, he mentions his own research: polynomial iteration. ‘Let's say I have a function x²+5. I can input a number in this function, calculate the output, then use the output as the input, and so on. That creates an orbit that you could see as, say, a model for the path of a satellite.’ In his actual research, he works with polynomials that depend on several variables. ‘The paths involved in realistic practical models are usually so complex that they can no longer be described with certainty. We look at systems that are so rigid that they can be precisely understood, yet at the same time produce a great wealth of behaviours. This is exactly the place where interesting mathematics can be found.’

### Unexpected questions

Peters came to work at the UvA six years ago with a Marie Curie grant, which he used to invite speakers. Something similar existed at the VU, he explains. ‘I gave two lectures there, and then I was asked to combine the events. Right at the outset that seemed like a great idea.’

Whereas many fields of science involve collaboration, as a rule Peters doesn't work directly with colleagues in Amsterdam. ‘Accordingly, the aim of the seminars is not to publish jointly, although that would be nice,’ he explains. ‘The most important thing is to have a really thorough discussion of your work with other mathematicians.’ And a combined group of VU and UvA researchers includes enough colleagues that you can tackle issues from different perspectives, he continues. ‘Sometimes I am asked questions I'm not expecting; but they can help develop my thinking.’