Professor Jan Schumann, Vice President for Research at the University of Passau, welcomes guests to Lecture Theatre 9 (Audimax Building) at the start of the new lecture series.
When mathematics manages to fascinate through clarity and depth, it is often thanks to individuals who have an unusual perspective on complex problems. The Czech mathematician Svatopluk Poljak was one such individual.
One area of research that he significantly influenced is the so-called Max Cut problem. This involves dividing a graph – i.e. a set of nodes and connecting lines – into two groups in such a way that as many of the edges as possible run between the groups. This seemingly simple problem is actually quite tricky: it is a classic example of a so-called NP-complete problem, for which no efficient algorithms are known to provide an exact solution. It is likely that no such algorithms exist; this is one of the greatest unsolved problems in mathematics and computer science. However, the significance of the max cut problem goes beyond pure theory: it plays a central role in network engineering, statistics, artificial intelligence and the physical modelling of complex systems. This makes it all the more important to develop efficient approximation methods.
Building bridges between disciplines
Initiator of the new lecture series: Professor Stefan Glock.
Poljak chose a new approach to the problem: he combined discrete structures with methods of continuous optimisation. With this interdisciplinary approach, he succeeded in developing new bounds and approximation methods for max cut problems. His work bridged the gap between combinatorial mathematics and convex optimisation – a path that seems obvious today, but was visionary at the time.
It was this pioneering spirit that inspired Professor Stefan Glock, assistant professor (Juniorprofessor) of Discrete Mathematics at the University of Passau, to name a new lecture series after Poljak – the “Poljak lecture”. Its motto is “illustrare – promovere – inspirare”. The envisioned purpose of the lectures is to illustrate the beauty of mathematical research and its significance to our society, to promote interdisciplinary collaboration and to inspire the next generation of researchers. Glock came across Poljak's work while conducting research in his field. During his short time as a professor of mathematics at the University of Passau, Poljak initiated important publications, some of which were only published after his death. Poljak died in a tragic car accident in 1995 at the age of only 43.
Widow and companions remember Poljak
On the occasion of the 30th anniversary of his death, Professor Glock launched the first edition of the Poljak Lecture at the University of Passau. Following welcome addresses from Professor Jan Schumann, Vice-President for Research at the University of Passau, and Professor Fabian Wirth, Vice-Dean of the Faculty of Computer Science and Mathematics, Jana Poljaková set an emotional tone. The mathematician's widow showed pictures from the researcher's life and talked about his childhood and how his parents – who had no mathematical education themselves – marvelled at their son's talent.
In her presentation, Jana Poljaková made the mathematician tangible as a human being.
She spoke about his optimism after the fall of the Eastern Bloc. He had a head full of plans and invited Prague's intellectual scene to their apartment. But not everyone shared his enthusiasm. So he concentrated on mathematics and took his family on many trips, including to Bonn, where he received a scholarship from the renowned Alexander von Humboldt Foundation. Poljaková quoted her husband as saying, ‘I do mathematics to travel and meet great people.’ In her presentation, the mathematician came across as a real person – full of energy, open-minded and full of ideas.
In 1994, a year before his tragic death in an accident, he accepted a position at the University of Passau – another pioneering achievement given the short time that had passed since the fall of the Iron Curtain. Professor Franz Brandenburg, who was a member of the appointment committee at the time, described how there was considerable political opposition to appointing a civil servant from a former Eastern Bloc country.
Among Poljak's companions who were also guests at the inaugural event in Lecture Theatre 9 in the Audimax Building was mathematician Dr. Daniel Turzík from the University of Chemistry and Technology in Prague. He was not only a colleague in professional terms. He also lost his best friend in the car accident 30 years ago. Another companion was Professor Franz Rendl from Graz. He reported on his first encounters with Poljak during their joint research on the Max Cut problem: He knew little about it. But he remembered how patiently Poljak explained the details of the conjecture to him. His enthusiasm for the topic was contagious. In video messages, leading scientists from the USA, including Professor Michel X. Goemans from the Massachusetts Institute of Technology and Professor Ryan O'Donnell from Carnegie Mellon University, as well as Professor Monique Laurent from the Centrum Wiskunde & Informatica Amsterdam and Tilburg University, paid tribute to Poljak's achievements in the field of research.
Science in the spirit of Poljak
Professor Jaroslav Nešetřil from Charles University in Prague was also a colleague of Svatopluk Poljak.
The scientific highlight of the event was the guest lecture by Professor Jaroslav Nešetřil from Charles University in Prague, who has also co-authored several articles with Poljak and has been one of the world's leading researchers in discrete mathematics for 50 years. In his lecture ‘Subgraphs, orderings and homomorphisms’, he introduced the audience to current issues in structural graph theory and complexity theory. The focus was on the question of how difficult it is, from an algorithmic point of view, to recognise certain substructures in complex networks. This topic tied in directly with Poljak's research interests: the internal order of networks and the possibility of describing them mathematically. Among other things, Nešetřil reported on one of his new results, which solves a problem that had been open for decades, namely that the recognition problem of certain ordered graphs, like the max cut problem, is NP-complete.
The Poljak Lecture contributes to the visibility of the field of discrete mathematics at the Faculty of Computer Science and Mathematics at the University of Passau, which has gained profile with the appointment of Professor Glock to the junior professorship created with funds from the Bavarian High-Tech Agenda. Professor Glock heads an Emmy Noether junior research group on structure and randomness in mathematics. The DFG uses these grants to support outstanding researchers in the early stages of their careers. The Poljak Lecture is to take place annually in future – as a stage for excellent research and as a living memory of a man who shaped mathematics with passion and vision.
This text was machine-translated from German.
DFG Emmy Noether junior research group on the interplay of structure and randomness in mathematics
An Emmy Noether junior research group funded by the German Research Foundation (DFG) and led by mathematician Professor Stefan Glock from the University of Passau investigates the mathematical foundations of the structures that form the basis of the digital world: Network structures that go to infinity.
