HUN-REN Alfréd Rényi Institute of Mathematics, Yale University (USA), and the Max Planck Institute for Mathematics in the Sciences (Germany) are establishing a joint Max Planck Center.
Max Planck Center for the Study of Discrete and Continuous Structures in Mathematics and Data Science (DisCoS) is the name of the research unit jointly established by Yale University (USA), the Max Planck Institute for Mathematics in the Sciences (Germany), and the HUN-REN Alfréd Rényi Institute of Mathematics. The Center will operate from sites in Leipzig, New Haven, and Budapest, and is planned to commence its activities on 1 January 2027.
This extensive and complex mathematical collaboration is being established under the auspices of the Max Planck Society, the German research network that enjoys great prestige within the scientific community. It is initially established for a period of five years and, depending on its achievements, may be extended for a further five years. In addition to the Max Planck Society, HUN-REN and Yale University also contribute to its funding. Max Planck Centers bring together researchers from the participating institutions around a common scientific programme.
"The establishment of this prestigious Max Planck Center (MPC) with the participation of Rényi Institute is another positive recognition of Hungarian mathematics and, at the same time, an outstanding opportunity to strengthen our international integration and further enhance our reputation, while paving the way for new scientific discoveries. The most significant component of the collaboration is for young researchers, providing broad research opportunities for PhD students and postdoctoral researchers in Budapest, Germany, and the United States. An MPC such as this – of which only 23 exist worldwide, and which is the first in Hungary – can effectively support the career development of young mathematicians while helping to retain them for Hungarian science,” emphasizes András Stipsicz, Member of the Hungarian Academy of Sciences, Director General of the HUN-REN Alfréd Rényi Institute of Mathematics, and Hungarian Co-Director of the new MPC.
The three centres forming the MPC – the Max Planck Institute for Mathematics in the Sciences in Leipzig, Rényi Institute, and Yale University – each have distinct strengths in different areas of mathematics. Hungary has an outstanding school in discrete mathematics, largely thanks to the work of László Lovász and Endre Szemerédi. Elsewhere, data science has developed more rapidly and has already reached the stage of practical applications. "Both Leipzig and Yale have strong traditions in partial differential equations, a field that, for historical reasons, is scarcely represented in Hungary. By contrast, probability theory is a major strength in Hungary. It provides a particularly suitable language for building bridges between the discrete and continuous worlds and is also one of the fundamental languages of data science. In addition, Rényi Institute is the world's leading centre for the theory of graph limits, which seeks to understand the fundamental objects of discrete mathematics – sequences of large graphs – through continuous limit objects that may be analytic, probabilistic, or geometric in nature. These schools have much to gain by combining their strengths and learning from one another,” adds Gábor Pete, Deputy Co-Director of the MPC on the Hungarian side, Head of the Probability and Statistics Department at Rényi Institute, and recipient of an ERC Consolidator Grant. “To continue the previous thought, at Rényi Institute we have developed techniques for thinking about large graphs through various limit objects, and these techniques can subsequently be applied to structures other than graphs. When another school raises different types of problems that are nevertheless analogous, it may be worthwhile to apply solutions that are natural to us but unfamiliar to them, or to combine them with their own techniques. This, too, is part of the project. The mathematical understanding of turbulence is another possible way in which the MPC may enrich Hungarian mathematics with new motivations and new ideas.”
| Travellers often hear the word turbulence during flights. Engineers are very familiar with the phenomenon and understand it sufficiently from a practical point of view to ensure that aircraft can fly safely. Physicists and mathematicians, however, have still not been able to describe it rigorously, which indicates that it is not yet truly understood. The flow of liquids and gases is an extremely difficult process to calculate and involves many chaotic phenomena. One of Clay Mathematics Institute’s Millennium Prize Problems is the Navier–Stokes Existence and Smoothness problem, which concerns the existence and smoothness of solutions to the Navier–Stokes differential equations describing the motion of fluids and gases. Solving the problem carries a prize of one million US dollars and is closely related to understanding turbulence. From the perspective of discrete mathematics, mathematicians (physicists as well) working in probability theory start from the assumption that everything is made up of particles, and that if these particles can be understood, then the macroscopic world can also be described. However, there are still no truly satisfactory random discrete models capable of describing turbulence and explaining what gives rise to it. |
The Chair of Yale’s Department of Mathematics, Professor Wilhelm Schlag, is a world-renowned researcher in partial differential equations. He was invited by Professor László Székelyhidi, Director of the Max Planck Institute for Mathematics in the Sciences in Leipzig – who is himself of Hungarian origin and whose research also focuses on partial differential equations, particularly turbulence – to bring Yale into the MPC as its third partner.
“Yale’s participation enriches the collaboration,” explains Gábor Pete. “Yale has researchers who approach probability theory from the perspective of partial differential equations, and their field – or school of thought – connects naturally with the Leipzig school of partial differential equations and the Hungarian school of probabilistic discrete mathematics. This creates an excellent synergy and, at the same time, an opportunity that should be fully exploited among the three centres – not only professionally, in terms of their respective schools of thought, but also on a personal level. Another major strength of Yale is the school founded by the Fields Medal-winning Russian-born American mathematician Gregory Margulis, which studies the symmetries of dynamical systems and geometries and their group-theoretic aspects. This area connects, in different ways, with the research interests of Miklós Abért, Balázs Szegedy, András Stipsicz, and Gábor Pete at Rényi Institute.”
| A Max Planck Center (MPC) is an institutionalised, long-term research collaboration between the German Max Planck Society and a leading international partner institution. It is essentially a “virtual center of excellence” in which researchers from the participating institutions pursue joint scientific research programmes. The purpose of the Max Planck Society’s Max Planck Centers is to establish long-term collaborations between world-leading research groups; combine the partners’ complementary methods and expertise; promote the exchange of researchers and doctoral students; organise joint workshops, summer schools, and training programmes; share research infrastructure; and jointly apply for international research funding. The Max Planck Center programme was launched in the early 2010s as part of the Max Planck Society’s internationalisation strategy. The 23 Max Planck Centers currently operating in 14 countries include among their partners many of the world’s leading research universities and research institutes, such as Princeton University, the University of Tokyo, University College London, the Chinese Academy of Sciences, and Nanyang Technological University. Their research fields range from particle physics through artificial intelligence, climate research, and biochemistry to the social sciences. In 2026, two new Centers were established in China, while the first two collaborations with Singapore were also launched. The Rényi–MPI–Yale Max Planck Center is the first Max Planck Center dedicated to mathematics. |
The Budapest–Leipzig–New Haven Max Planck Center is an internationally unique organisation that will conduct innovative mathematical research, bringing together researchers from fields that have traditionally been separate. It will include scientists working in geometry, group theory, graph theory, probability theory, partial differential equations, data science, and mathematical physics. As a result, the boundaries between these disciplines will become increasingly blurred, just as geographical boundaries will, since the participants from the three institutions are planning numerous joint research activities. According to the successful proposal, all participants are committed to stepping outside their comfort zones, developing new ideas, and acquiring new techniques through the collaboration.
“The project aims to develop and implement a comprehensive programme of activities. This includes a summer school, conferences, and workshops. In response to renyi.hu’s question about what day-to-day work within the MPC will look like from January onwards, Gábor Pete highlights the role of the joint postdoctoral researchers and PhD students. ‘Young researchers are the ones from whom we can most expect not only to understand the work of a scientific school flourishing at another MPC partner institution, but also to begin conducting research within it. For example, I can assign a research topic to a young Hungarian researcher that requires learning something specific from colleagues working at Yale. He/she will spend two years here and two years there, acquiring the methods of both schools. This is why the project places such strong emphasis on talent development and on training the next generation of researchers. The largest share of the funding is allocated to the activities of jointly appointed postdoctoral researchers. For our German partner, it may also be particularly attractive to spark the interest of young Eastern European researchers in German mathematics, as they would otherwise tend to look towards the English-speaking world when considering research opportunities abroad.’”
It is a fact that, in mathematics as well, people learn from one another through maintaining professional connections. As a Deputy Co-Director, Gábor Pete also believes that the collaboration enabled by the MPC represents a significant commitment to the mathematical community. Coordination will be one of his key responsibilities, as seven researchers with strong scientific backgrounds from Rényi Institute will participate in the MPC. However, the significance of the MPC, which will begin operating in January, extends beyond its participants and their students. One of its objectives is to find ways for Hungarian mathematics as a whole to benefit from access to the expertise available in Leipzig and at Yale.
“We are a small country, and although we are strong in mathematics, we are active in a relatively limited number of fields. This collaboration will broaden the opportunities available to young researchers. At the same time, we also hope that the methods we have developed and the perspective we have established—for example, in the field of graph limits mentioned earlier—will prove useful in other areas as well. This will increase the visibility of Hungarian mathematics.”
Elevating the exchange of knowledge and experience to the level of the Institute as a whole is all the more important because the composition of the Hungarian research team participating in the MPC may change by the end of the initial five-year period. As shown below, the MPC’s research at the three institutions will be organised around eight major thematic areas. On the Hungarian side, there will be seven research area leaders, and each thematic area will have one principal coordinator from each of the three participating institutions.
As his first initiative within the MPC, Gábor Pete plans to organise an MPC summer school at Rényi Institute together with András Gilyén and young colleagues from Yale. Through these collaborations, he hopes to invite speakers who would otherwise be inaccessible or only very difficult to bring to Hungary. The topic of the summer school will be stochastic localization, a relatively recent major development in the theory of Markov chains. It is closely connected not only to Pete’s own favourite research area, noise sensitivity, but also constitutes one of the fundamental techniques underlying diffusion models in generative AI, and is of considerable interest from the perspective of quantum algorithms.
An important element of the MPC’s activities is to bring research results closer to practical applications. In the case of fundamental research, this is particularly challenging, as it is impossible to predict which discoveries will eventually lead to practical applications, or when this might happen. Nevertheless, the Max Planck Institute for Mathematics in the Sciences has considerable experience in identifying promising results with application potential and presenting them to the appropriate applied mathematics communities. For this reason, the MPC programme also includes so-called Translational Workshops. Among the possible application areas, Gábor Pete expects developments related to generative AI to emerge, while noting that, at present, this is still only a reasonable expectation rather than something that can already be observed. According to the plans, specialists interested in potential practical applications will already participate in the first MPC workshop.
“‘We will make a conscious effort,’ he says, ‘to ensure that potential applications reach those who are interested in putting them into practice.’ The MPC will explore which scientific fields could benefit from its results and where researchers may be able to build applications on them, for example, statisticians making use of advances in data science. “I will learn,” he adds, “how to organise workshops of this kind, which help move theoretical knowledge towards practical applications, and how to communicate regularly with applied mathematicians. The Max Planck Society is highly advanced in this respect, and our young colleagues at Yale also have publications with applied relevance. It is worthwhile and possible to learn from them: in the United States, there are departments in computer science whose staff carry out serious theoretical research, and which train researchers who initially work on theoretical problems, but who later become scientists with a deep understanding of applications, either working at major multinational companies or collaborating closely with them.”
Overall, a Max Planck Center represents one of the highest forms of international collaboration within the Max Planck Society’s research network: an institutional partnership established only with outstanding research institutes that have already demonstrated scientific excellence.
At the end of the interview, Gábor Pete also outlines the Rényi Institute’s long-term vision: “As mathematicians, what we enjoy most is doing mathematics itself, and the milestones of our careers are the mathematical results we achieve. Establishing and developing an MPC like this is also a service to the community. Mathematics is an essential part of humanity’s collective intelligence and one of our common public goods. For the intellectual and ethical development of humankind, it is indispensable that we continue to do mathematics, and for that to happen, the discipline itself must continue to evolve. Mathematics makes a fundamental contribution to ensuring that the collective intellect of the human species does not become diminished. This is also why it would be a mistake to outsource everything to AI. To use a football analogy, we will still play football even if we can build robots that play better than we do. We do not play football solely to create ever better games. It is understandable that society primarily pays mathematicians to produce new results that move science forward. But it also supports mathematics so that humanity, as a species, continues to engage with it, even in collaboration with AI – understanding not only the latter's outputs but also how it works. On a personal level, it is important to me that both Hungarian mathematics and mathematics worldwide continue to develop. Building collaborations, supporting talented researchers, and strengthening mathematical communities is a mission while it also holds the promise of outstanding scientific discoveries.”
