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Project on Patterns in Random Tilings

Published Jun 22, 2021

Maurice Duits was awarded a five-year grant for the project Patterns in Random Tilings with a total budget of 10 MSEK. We met Maurice to talk about the project as well as future plans regarding the awarded grant.

Maurice Duits

Tell us a bit about yourself and your educational background, what inspired your interest in mathematics?

My interest in mathematics came relatively late. It was only through my first mathematics courses at university that I realized that I wanted to pursue a career in mathematics. As a teenager I dreamt about a career in music, philosophy or astronomy. I did not pay much attention to gymnasium mathematics. Still, convinced by my father that mathematics is excellent preparation for any further studies, I decided to enroll in the mathematics program at the TU/Eindhoven in the Netherlands for one year. There, for the first, I had to work with proofs and abstraction and I never expected that mathematics could be so beautiful! I remember I worked very hard, but, oh boy, it was so rewarding to explore this fascinating new world! After my master’s degree, I decided to pursue a PhD degree in mathematics at the KULeuven in Belgium. During that time I also spent a very enjoyable 4 months at KTH. I liked the academic atmosphere at the department very much and loved Stockholm. This is also why I gladly returned some years later!

Receiving a new grand must be exciting. How are you planning to utilize the grand?

Yes, it is very exciting. It is also reassuring to know that the community believes in your research ideas. This grant will give me the opportunity to fully focus on my research ideas for the next five years. This is very important, since academic life can be very busy. I also plan to recruit new young members to our research team to invest in the future generation.

What is your research about? Tell us about ‘’Patterns in Random Tilings’’.

My research is centered around the idea that large random systems are not as wild as one would imagine. When the size of these systems grows large, you will often see that patterns emerge and that the limiting fluctuations are described by universal laws (think of the classical example of the Central Limit Theorem from classical probability, making the normal distribution one of the key probability distributions). Finding such laws, studying their properties and establishing their universality are among the key objectives in my research field. One usually starts with a playground that contains a wide variety of interesting behavior, but also sufficiently simple so that there is hope for rigorous analysis. In the project, I chose random tilings for this. Random tilings were originally introduced in statistical physics literature, but there are also many fascinating connections to various branches of mathematics. Their rich mathematical structure can even help understanding their features. The project “Patterns in Random Tilings” is centered around some very recent ideas for analyzing certain classes of random tiling models that are yet poorly understood.

What are the biggest challenges your work/research combats?

The biggest challenge for the project is that there are not many techniques in the literature to fall back on. In fact, the objectives of this project will require the development of new techniques beyond the state-of-the-art. In our research group we have already made some first steps in the last years, and hopefully these ideas can be forged into a more solid approach in tackling the important questions for these models.

Are you planning to develop your research in new directions?

Yes, in fact, most of the objectives in the project have the purpose of opening up new directions. Some find great challenge in solving important longstanding open problems. Personally, I find much more joy in finding new questions and working on problems that are relatively unexplored.

What do you view as your most important research accomplishment?

In my research I try to look for questions that can combine different areas. I am not a person to try to push a well-known difficult technical problem within a certain field to new limits, but prefer to find and exploit new connections between seemingly unrelated areas. The project “Patterns in Random Tilings” is partially based on two particular examples of such in my previous research work and I count those as my most important accomplishments.

What were the effects of the pandemic on your work?

At first, I tried to see the positive effect of the pandemic. Working from home means less distraction. It also opened up all kinds of online research seminars and I started connecting with international collaborators on a more regular basis. But ultimately, I can see that most of us have become very bored with zoom-lectures, zoom-seminars and zoom-meetings. Online interaction has severe limitations and can never fully replace in-person meetings. One comes to realize how much more happens around the in person meeting and how important that is. I do find online tools are very valuable for some specific tasks, but I do not expect that they will become dominant in our daily work. That said, the pandemic may further disturb our lives for some years to come, and such tools are a very important back-up.

What advice would you give to youngsters interested in becoming scientists?

If you feel something is interesting then do not hold back, work hard, be stubborn and feed your curiosity.

How could we attract more young minds into the field of sciences? Are there any actions taken by your work environment about it?

Looking at statistics then it is clear that we miss out on an important target group: women. I believe that prejudices in society are a very important factor in this. In popular media and news there are strong stereotypes of how a mathematician should look like, heavily leaning on the male genius idea. These are just silly stereotypes but can have a powerful influence. I see it as an important duty to present a more truthful picture of what mathematics is about and what it means to be a mathematician. If we manage to convince the media and the general public, then I think many more young women will choose to study mathematics.

Is it important for you to communicate your research to the world? If yes, why and how do you do that?

Yes, I think this is very important. My research field is one that can be used effectively for popularizing mathematics. The types of questions that we ask are often easy to explain, but not so easy to solve. The solutions will be difficult to communicate, but the questions and some interpretation of their answers could inspire non-mathematicians and especially young aspiring scientists. I have not been very active yet in this, but I would be more than happy to contribute now that I am more senior. I think an easy thing that most of us can do, is to present popular research descriptions on personal homepages. I am always happily surprised by the master's students that have visited my homepage, or the one of my research group, and found it inspirational.