Mathematician who proved A2 conjecture returns to his roots

Tuomas Hytönen started as professor of mathematics at Aalto University at the turn of the year
Tuomas Hytonen
Tuomas Hytönen. Image: Mikko Raskinen

What are you studying and why?

My field of research is mathematics, more specifically harmonic analysis. One way of describing it is to say that it involves the theoretical foundations of signal processing. The pitfall of this formulation is a possible follow-up question about what 6G networks I am currently working on – the answer is none, I am doing basic research. It can be said that today's signal processing is yesterday's harmonic analysis, while the practical applications for today's research are still unexplored territory. It is therefore a matter of basic curiosity research.

How did you become a researcher?

I have been a researcher for about 20 years. I am an alumnus of Aalto University, or rather its predecessor, the Helsinki University of Technology, where I majored in mathematics. During my undergraduate studies at the latest it became clear to me that a PhD was a natural extension of my studies. I am still on that path.

I have also been abroad, and the first place I went to after leaving Otaniemi was the Delft University of Technology in the Netherlands. I have also spent a year in Turku, and the longest stretch of time in the eastern port city of Helsinki.

What do you consider the highlight of your career so far?

Here I would mention proving the so-called A2 conjecture. It used to be an open question in my field, and in the summer of 2010 I managed to find a solution. Of course, the publication process took time and the results only appeared in a journal in 2012. This was a key moment in my career and has carried on to this very day.

What is the most important characteristic of a researcher?

Perhaps a kind of critical curiosity that does not just accept ready-made answers but asks whether this really is it. Even when it comes to something that is indisputably true, you can still ask whether it is all, whether it could be summarized even more clearly or concisely, or whether what you are dealing with is a set of truths or just manifestations of one topic. As the amount of information around us increases, the ability to summarize becomes more and more important in order to keep information usable.

What do you expect from the future?

I have high hopes of being able to do my own research here to the full. What's more, at Aalto, I'm fascinated by the opportunity to engage in dialogue with more applied disciplines. Basic research also thrives on this kind of interaction in order to find good questions. As such though I don't see myself jumping on the bandwagon of application development, but will continue to stick to basic research.

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