# Professor Dr. Eugen Hellmann

Eugen Hellmann is a professor of Theoretical Mathematics. He specializes in the field of arithmetic geometry, in particular the Langlands programme. Specifically, he looks at p-adic limits of automorphic forms and Galois representations, as well as at the connection between these geometric objects.

"Mathematics has always fascinated me," says Eugen Hellmann. While still at school in his hometown of Wuppertal, he attended his first maths lectures and these set him on the path, at an early age, for the subject he chose to study. During his time as an undergraduate and as a PhD student at the University of Bonn, he discovered arithmetic geometry for himself – a special area of number theory – which set him on a successful mathematical journey that is still ongoing. After a year as a postdoc in Paris, he returned to Bonn, where he took his habilitation. In 2016 he moved to the University of Münster to take up a position as Professor of Theoretical Mathematics.

And what exactly does Hellmann spend his time working on? This is not so easy to explain, because p-adic Galois representations, the Langlands programme and the Kazhdan-Lusztig theorem are things which even people who paid attention in their Maths lessons at school won’t have heard of. "I carry out pure basic research," Hellmann says, "which in turn can stimulate work in other mathematical directions." Expressed simply, it’s all about solution sets of polynomial equation systems in rational numbers or integers. "The aim isn’t to solve a concrete given equation, but rather to recognize structures and conceptual connections," he explains.

Some of Hellmann’s results have turned out to be groundbreaking for arithmetic geometry and have been published in leading scientific journals, which is why the young researcher is already one of the world’s leading experts in his field. "While Eugen Hellmann was working on his PhD, I could already see quite clearly that he was developing an exceptional talent for mathematics," says Prof. Peter Schneider, a fellow mathematician of many years’ standing. Prof. Christopher Deninger, who is also a professor at the Institute of Mathematics, adds, "His particular strength lies in the fact that he not only knows many different techniques from a variety of mathematical areas, but that he also knows how to use and combine them creatively."

What this ability leads to is that he – "sometimes with youthful abandon", as Hellmann himself says retrospectively – repeatedly identifies and works on new questions relevant to his subject. Incidentally, he often has good ideas for his research work out in the fresh air – for example, in the mountains or while playing tennis. He frequently works with other well-known researchers, for example as of late with his old friend from undergraduate days Peter Scholze, from the University of Bonn, who was awarded the Fields Medal – the "Nobel Prize" for Mathematics – in 2018.

No matter who you talk to – colleagues, PhD students or undergraduates – Hellmann is admired not only for his brilliance in his subject field. With his sunny disposition, his infectious laugh and his enthusiasm for mathematics, they all say, he’s an asset for every meeting of a working group, for every lecture and for every plodding Zoom conference.

*This text was published similarly in the university's newspaper "wissen I leben" [de] 02/03 2021 (p. 3).*