The beauty of theory and its application Benedikt Jahnel is the new professor for applied stochastics

Mathematics and music: these are Benedikt Jahnel‘s two great passions. After his habilitation at TU Berlin last year, he will start work as a professor for applied stochastics at Technische Universität Braunschweig in April 2022. His research topics range from statistical physics to decentralised mobile networks of the future and epidemic research. He can thus contribute new ideas to three TU core research areas: “Infections and Therapeutics”, “Future City” and “Mobility”. Jahnel wants to inspire students with the beauty of theory and its applications, as he told Markus Hörster in an interview.

Mr Jahnel, looking at your CV, it immediately catches one’s eye: you are not only a mathematician, but also have degrees in music education. How did this unusual combination come about?

I took advanced mathematics at school. But another passion was and is music, so I initially decided to study music education at the University of the Arts in Berlin. Towards the end of my studies, I had a bit of a life crisis and reoriented myself. Parallel to my music studies, I had started to study mathematics at the TU Berlin, which I really enjoyed. I had always made music and played the piano, but then stopped practising relatively radically.

After my intermediate diploma in music, I put mathematics on hold for the time being because the DAAD (German Academic Exchange Service – Ed.) gave me the opportunity to go to City College in New York for two years as a Master’s student. I didn’t want to miss out on studying music there, in the Mecca of jazz. Afterwards, I picked up my “maths pen” again and did my diploma at the TU Berlin. After that, I did my doctorate at the Ruhr-Universität Bochum and my habilitation at the TU Berlin.

You are a jazz musician and travel internationally as a pianist with your “Benedikt Jahnel Trio” and other formations. Improvisation is an important element in jazz. Is it a good counterbalance for you to mathematics, which has little to do with feelings and emotions?

Yes, for me it is a counterbalance. Of course, there are rules in music too, and in mathematics there are situations in which you are sometimes very excited and full of emotions. But they are very different things. What I like in both disciplines is that music and mathematics are team sports.

To what extent does your musical knowledge in turn help you in mathematics?

Both mathematics and music have something to do with creating a world with rules. In both worlds there is a framework in which you then move intuitively. And both have a lot to do with practice. Diligence is of central importance in both disciplines.

You are now the new Professor of Stochastics at TU Braunschweig. Why did you choose the Carolo-Wilhelmina?

I am an applied mathematician and did my diploma in Berlin at a Technische Universität, as well. For more than six years now, I have been working at a non-university research institute, the Weierstrass Institute for Applied Analysis and Stochastics in Berlin. In the process, I have become more and more convinced that I like the connection between abstract mathematics and its applications.

I live this out in my everyday research by talking to engineers and physicists and translating their statements into mathematical questions. This creates a dialectic between the application and the abstract language of mathematics. My professorship in the field of “Stochastics for Applications” fits in very well with this, as I have been able to gain many years of experience with stochastic methods for applications in physics or in communication systems. I am looking forward to a good cooperation in the research areas “Infections and Therapeutics”, “Future City” as well as “Mobility” at TU Braunschweig.

A highly topical subject you are working on is the spread of epidemics. What is the particularly big challenge here from a mathematical point of view?

The challenge is the complexity of the system. Many classical models, for example, do not consider the spatial distribution of people, who move uncontrolled and randomly. That’s why I’m convinced that the best way to look at it is through the glasses of probability theory. You see random configurations and agents in space that have contacts and can thus transmit a virus. You are dealing with an extremely high degree of complexity.

It is our wish as scientists to be able to make global statements from this complexity: Is the infection dying out? Yes or no? The phase transitions from a local to a global infection are particularly interesting. The first step is to understand how the spread works and the second step is to understand how to combat it effectively.

When looking at it spatially, it becomes clear that there are so-called “superspreaders”. In epidemics, there are large numbers of people who are barely infectious and then there are others who are strong drivers of the infectious event. Being able to identify these “superspreaders” in time would help us a lot in fighting epidemics. I see myself as part of this huge interdisciplinary field of research.

With 5G, a paradigm shift towards decentralised mobile networks is starting. Your research also focuses on stochastic geometry for telecommunications systems. What does this mean?

A classic field of application is Car-2-Car communication. If you think about self-driving cars of the future, they must be able to communicate with each other very quickly and robustly in order to avoid dangerous situations. The current cellular networks in which cars communicate with a base station are not equipped well enough for this. It would be much better if the cars could communicate directly with each other.

This idea of peer-2-peer communication can be found in many areas of communication. An interesting example is the app “FireChat”, which played an important role in the protests in Hong Kong. After the government switched off the base station, the demonstrators were able to continue communicating via this app using Bluetooth technology. Here, too, the uncontrollable spatial configuration of the network participants plays a central role. Therefore, this can also be looked at very well with probability theory.

Small start-ups could build their own networks with such decentralised mobile technology. This is a development that the established large communications companies, with their infrastructure worth billions, regard with concern. On the other hand, it is an opportunity for regions that are poorly connected to the internet – such as remote islands – to equip themselves with a communication network at low cost.

Your third major research area is statistical physics, in which you also completed your doctorate. What do you deal with in it?

When we look at a material or a liquid, like water in a glass, physics has very good models, depending on how closely you look at the material under the microscope. There is the superfine quantum theoretical level, the molecular level as well as the thermodynamic level, which looks at the state of aggregation. These different levels of description must be transferable into each other.

I start at the interface between the microscopic molecular level and the macroscopic thermodynamic level. When I heat the water in the glass, a phase transition takes place. The water evaporates. The fact that the water abruptly changes its aggregate state must result from the interaction of the molecules. Because the molecules are so complex, these phenomena are also explained with probability theory. For decades, this mathematical modelling has been established for solid structures in which the molecules are in fixed locations. An example of this is the magnetisation of metal. I am a specialist for systems where the locations of the molecules are random, like in liquids.

What role does science communication play in your work?

I have been quite active in recent years with lectures for a non-scientific audience, for example at the “Day of Mathematics” or at the “Night of the Sciences” in Berlin. We mathematicians often have the problem that our research is not so easy to communicate. As an applied mathematician, I am in the situation that in my research I deal with many things that can be described quite well. And since that is very close to my heart, I would like to continue doing that in the future.

What constitutes good teaching for you?

Good teaching has many aspects: I want to engage people and would like to contribute to closing the gender gap, which is a big issue in mathematics. Good teaching creates the bridge to pick up students and inspire them, but also to prepare them for a degree and a professional career. As mathematicians, we have the chance to train a mindset. That you name prerequisites clearly and make the conclusions transparent. Mathematics is also a school of thought. Mathematicians are definitely in demand as graduates because a certain attitude and way of thinking is associated with the subject.

In a few weeks, the lecture period for the 2022 summer semester will begin. What would you like to pass on to the students?

I would like the students not to be deterred by the general conditions in the pandemic, but to keep in mind what they would like to do. That they start the maths lectures with an open mind, that they let themselves be surprised and inspired by the objects I present to them in my lectures. That they are open to the beauty of theory and its application.