The Eurocomb'25 conference will be held between August 25 and 29 at the headquarters of the Hungarian Academy of Sciences by the Rényi Mathematical Research Institute. The most prestigious award in this field of mathematics, the European Prize in Combinatorics, will also be presented here. With the advent of computers and algorithms, the importance of combinatorics has increased significantly in recent decades, and it also has an impact on artificial intelligence research. Over the five days of Eurocomb25 in Budapest, around 300 researchers will participate and follow the lectures closely, including Abel Prize-winning mathematician László Lovász. We ask Ervin Győri and Balázs Patkós, research professors at the Rényi Institute, and Balázs Keszegh, senior scientific fellow at Rényi, about the organizers of this year's conference.
The European Conference on Combinatorics, Graph Theory and Applications is being held in Budapest for the second time. Participants from nearly 30 countries around the world are coming to this year’s Eurocomb. Just like in 2011, there was a record number of applicants this year – says Ervin Győri – who believes that this is not surprising at all, since Hungary and the Rényi Institute are one of the strongholds of combinatorics. This year, about 300 researchers are coming, and more than 150 presentations will be given during the five days of the conference, ten in plenary sessions, and the rest in four parallel sessions.
Traditionally, the European Prize in Combinatorics is awarded at the Eurocomb conferences, which have been held every two years since 2001. It is open to mathematicians no older than 35 years old, and the prize is worth 2,500 euros. Among the awardees so far, we find three Hungarian researchers: Balázs Szegedy received this award in 2009, Péter Pál Pach and István Tomon in 2021.
According to Balázs Patkós, it is very important and a great pride that there will be two Hungarian plenary lectures in the program. Abel Prize winner László Lovász and Péter Frankl. László Lovász, research professor at the Rényi Institute, will give a public lecture for the first time since the news of the awarding of the Erasmus medal. This has enormous prestige value for the mathematicians participating in the conference, as it is a guideline to know what new topics one of the greatest figures in combinatorics, László Lovász, is interested in. Regarding the speakers, Balázs Keszegh says that young talents such as Wojciech Samotij and Matija Bucic are also very strong names within combinatorics, and every prestigious conference is happy to invite them. The well-known and recognized female speakers on the topic - such as Vida Dujmovic, Julia Wolf, Marthe Bonamy - show that combinatorics, like any branch of mathematics, is independent of gender - despite the traditions of the past that may be to the contrary.
The conference topics include algebraic combinatorics, combinatorial geometry, combinatorial number theory, combinatorial optimization, plans and configurations, enumerative combinatorics, extremal combinatorics, graph theory, ordered sets, random methods and topological combinatorics. Eurocomb'25 provides researchers with the opportunity to present their research topics and results to interested parties not only in live lectures, but also in a so-called poster section. Balázs Keszegh considers it particularly important that Eurocomb gives all participants the opportunity to meet and talk with practitioners of their own narrower topics, and the plenary lectures also introduce researchers to the latest main trends in combinatorics. Considering how many PhD students and other young mathematicians come to these conferences, this allows the schools organized around certain topics to continue to live organically. I also recommend to my students, says Balázs Keszegh, that they look for interesting questions, listen to as many lectures as possible, so that they can see many new proof methods, this information can be decisive for them later.
Since the spread of the internet, that is, almost 30 years ago, scientific results can be learned from afar, it is possible to stay in touch from afar, and even conduct research together from thousands of kilometers away - adds Balázs Patkós - yet such large-attended conferences covering a single branch of mathematics are crucial for several reasons. On the one hand, at such times, people listen to a large number of lectures that are not related to their immediate research field, but are nevertheless close to their circle of interest. On the other hand, it is much easier to make personal contact. It is much easier to go to a famous professor after a lecture than to write an introductory email asking about a poorly explained step on page 13 of an article. But these meetings are not only irreplaceable for more experienced and novice researchers. Students can meet their peers from other countries at such times, and co-authors of manuscripts that have been 95 percent complete for months can get a push to finish the last 5 percent, decide on the next problem to tackle, and take the first steps towards proof.
Regarding the significance of combinatorics in the 21st century, Balázs Patkós states: Combinatorics has always been in focus, even if its perception was not always good, but over time this has changed in a positive direction. The basic concepts and most of the questions of combinatorics can be easily understood, often without any scientific background (proofs and proof methods are less so), so many students have turned and continue to turn in this direction. Moreover, graphs, hypergraphs, and set systems often prove to be important tools in combinatorics, but even in research outside of mathematics. Combinatorics basically became truly significant with the spread of computers.
It was important before, but there was also a mathematician - with some malice - who called it a "colored pencil game" - notes Ervin Győri - but as soon as computers and algorithms appeared, more and more areas of combinatorics were involved, and this increased the value of the discipline. In addition to the rapid development of algorithms, it is of great importance that probability calculation methods and random methods can be used more and more among algorithms, and statistics has also entered combinatorics, and is increasingly indispensable in artificial intelligence research. Balázs Keszegh considers another aspect to be important: In recent decades, the close relationship of combinatorics with many other branches of mathematics has also come to light, partly through mathematicians exploring the connections between different fields, and thanks to them, this topic is more lively than ever. Hungarian combinatorics is traditionally strong, and the role of the Rényi Institute is also outstanding in this. It is no coincidence that this is the second time we have held this conference, and that there are many Hungarian speakers at every Eurocomb.