Whether it is about finding the optimum solution for resource allocation, medical simulations or training neural networks, digital applications are necessitating increasingly complex calculation methods based on mathematical principles. And it is these kinds of optimization problem that Professor László Végh will be studying at the newly established Hertz Chair for Mathematics, Modelling and Simulation of Complex Systems. “The University of Bonn enjoys an exceptional reputation in mathematics,” says Professor Végh, who is looking forward to his new responsibilities. “But there are also some outstanding groups here working in related fields, such as mathematical economics.”

The Hertz Chair comes under the Transdisciplinary Research Area (TRA) “Modelling”. “The TRA Modelling has members from many different departments and teams. My main aim is to bridge the gap between mathematics, computer science and economics—focusing specifically on algorithms and optimization—and to foster collaboration between the various groups.”

Discrete optimization problems are about finding the best option from among a finite but very large number of possibilities. “Although you can’t hope to find an optimum solution to your problem, you can identify a solution that’s guaranteed not to be far off that optimal state,” Végh explains. One of the best-known optimization problems is the traveling salesperson problem, which involves finding the shortest possible route for a traveler to visit multiple cities one after the other without passing the same one twice. “As well as routing problems for vehicles, this particular problem is also relevant to areas that seem unconnected to it, such as chip design,” László Végh says. “And the Research Institute of Discrete Mathematics at the University of Bonn has some major longstanding industry partnerships in place in this field.”

At the University, he is currently focusing on coming up with new approaches to general mathematical optimization models such as network flows, convex programs and linear complementarity problems. The latter is a general model that also encompasses questions of calculating equilibrium in games and markets. “I’ve also been looking at questions of optimization posed by problems of fair distribution and the allocation of resources as well as at how machine-learning methods can be applied to the design of mechanisms.”

### Profile of the new Hertz Professor

László Végh studied mathematics at Eötvös Loránd University in Budapest, where he also completed his doctorate on connectivity augmentation algorithms in 2010. He went on to work as a research fellow at his alma mater and the Hungarian Academy of Sciences and as a postdoc at Georgia Institute of Technology in the US. He has been a faculty member at the London School of Economics and Political Science since 2012 and was appointed a full professor in its Department of Mathematics in 2020. László Végh has held the Hertz Chair for Mathematics, Modelling and Simulation of Complex Systems at the University of Bonn since August 2024.

Hungarian-born Professor László Végh has been teaching and researching at the Hertz Chair for Mathematics, Modelling and Simulation of Complex Systems since early August. He will be studying optimization problems as part of the Modelling Transdisciplinary Research Area and is particularly looking forward to teaching and exchanging ideas with his students. He spoke to Katrin Piecha.

**Let's start at the beginning. What made you want to be a mathematician?**

Both my parents were physicists, so I grew up in an academic family. My father would throw mathematical problems at me from an early age. My secondary school was also a big influence on me. In Debrecen, the city in Hungary where I grew up, I was in a special class for math. I had excellent teachers that made the subject fascinating through how they taught it. Solving problems and puzzles was great fun.

**You’re particularly interested in algorithms and optimizations. What exactly are you working on?**

Optimization is about finding the best solution from a large number of possibilities. Think about the allocation of resources, where you have various limiting factors such as raw materials, labor and time. Now you want to identify the best production schedule. However, you could also be looking to find the best possible train timetable, or at least one that’s good enough. Training neural networks is also a large scale optimization problem where you need to find the parameters that’ll deliver the best—or at least very good—results. You get optimization problems a lot in the economy too, such as in online markets, where it’s a question of developing search engines that’ll find the best hits, for example.

What I’m looking at is the abstract, mathematical version in each case. Rather than working directly with applications, therefore, I’m studying the core of a mathematical abstraction.

**What persuaded you to come to the University of Bonn?**

The University enjoys an exceptional reputation in mathematics and has some of the best students in Europe learning here. In particular, the Research Institute of Discrete Mathematics—my core field of expertise—has a long history of excellence. But there are also some outstanding groups here working in related fields, such as mathematical economics. My Hertz Chair brings these groups together in the Modelling Transdisciplinary Research Area. Developing and expanding these partnerships between the various departments strikes me as a very exciting challenge.

**When you collaborate with researchers from different fields, do you ever fancy changing places with them for a day?**

What’s great about science is that you can learn new things and shift your interests around a bit. Naturally, there are many areas of economics that I haven’t a clue about. But, when I tackle specific problems, I learn a bit about the theories they’re based on. Although I can’t transform myself completely, I can “put on a different hat” and think differently. After all, it stands to reason that economists and mathematicians will come at the same problem from completely different angles, and it can be very interesting to talk to them and understand how differently we look at things and to learn from that.

**Is there a specific optimization problem you’re working on?**

With discrete optimization problems, we have a finite set of possibilities, from which we want to find the best one. There’s an astronomically high number of these possibilities. One branch of mathematics—complexity theory—says you can’t really hope to find an optimum solution to your problem. But you can hope to identify a solution that’s guaranteed not to be far off that optimal state.

One of the problems like this that I’ve worked on in the past is the traveling salesperson problem. It involves a traveling salesperson who’s supposed to visit a series of cities in such a way that they never pass through anywhere apart from their starting point more than once, they keep their route as short as possible and they end up back where they began. This problem crops up a lot in chip design, for instance, which is why the Research Institute of Discrete Mathematics maintains numerous industry partnerships in this area.

There’s a variant of the traveling salesperson problem called the “asymmetric traveling salesperson,” where the distance or travel time from one city to another can be different in the two directions. For example, one city could be at the foot of a hill and the other at the top, or there might be a lot of one-way streets. For this variant, there’s long been the challenge of devising algorithms that guarantee a solution that comes close enough to the best one possible. I created an initial algorithm of this kind together with some colleagues that’s been developed further by colleagues here in Bonn.

**What does your normal working day look like?**

My favorite thing to do is to find a whiteboard, a blackboard or simply a sheet of paper and tackle some mathematical problems with students or colleagues. From my experience, the best results can come out of discussions like these.

**Are you looking forward to teaching at the University of Bonn?**

Yes, very much so. Teaching is one of the things that motivates me most. Mathematics students in Bonn have an outstanding reputation. Whereas I mainly taught introductory courses in London, here in Bonn I can teach ones that are more closely related to my research and my interests. I'm looking forward to getting students excited about research and interacting with them.

**What would you say to students who are afraid of mathematics?**

Many students enjoy solving puzzles and brainteasers, and this is one approach you can use to give schoolchildren an understanding of mathematics: it can be a very rewarding experience when they’re challenged to solve riddles and made to come up with their own ideas. But this kind of “teaching by discovering” is also a big challenge for teachers.

**How has it been for you and your family to swap England for Germany?**

My wife and I have moved to Bonn with our three children, who are eleven, nine and six. The children weren’t keen on the idea of moving. They’ve had to leave their friends behind and start school in a new language. But Bonn felt like home right from week one. Although we had reservations about leaving such a vibrant place, we’re enjoying the more peaceful life in a beautiful city, living near work and school and being able to cycle everywhere. One of our favorite places is the Botanic Garden. We’re loving going for long walks on the Venusberg and in the Siebengebirge mountains on the sunny fall weekends.