Mathematician Zdeněk Dvořák: Inspired by the real world ****************************************************************************************** * Theoretical mathematics inspired by the real world ****************************************************************************************** “Most of my work still takes place on paper,” says theoretical mathematician Zdeněk Dvořák Computer Science Institute of Charles University. He focuses on combinatorics, graph theor theoretical informatics, and he received the ERC CZ Consolidator Grant for his research. “Being awarded the grant will allow me to focus on research and fund a postdoc and other d who will work on the project with me. Most importantly, it will allow me to continue in in cooperation,” the mathematician says. “We cooperate especially with McGill University in M and the National Institute of Informatics in Tokyo. I was supposed to be leaving for Japan the coronavirus this had to be postponed,” he adds. Dvořák obtained more than CZK 7 million for solving a project named Algorithms and complex and beyond bounded expansion. “It is a graph-theory project, which may be misleading for n A non-mathematician usually imagines a graph as a line, perhaps the exponential. Mathemati a graph as something which may be called a network. A computer network, a Facebook relatio road network, for example: some points interconnected by relations. What we are interested problems occurring in these networks. To show it in an example – on social networks, we ma patterns of relationships appearing there, and deduce certain qualities based on that, suc community appeared spontaneously, or was it purposely created by somebody? Studies of real problems which we then want to solve also in abstract networks. And we can see that numero cannot be solved effectively in an entirely abstract network,” the mathematician explains. This is why mathematicians invented the theory of bounded expansion. It may be explained a complexity of networks. Once again, they find inspiration in the real world: “Roads, for e intersect arbitrarily – there are rules and limitations in their use. At the same time, th imperfections and exceptions: bridges are a good example.” Zdeněk Dvořák’s research is pur “The goal of the project is to find the hierarchy of qualitative network limitations – whe for example, a certain geometrical structure that might be described.” The entire approach is entirely new and unknown: “We do not know whether there actually is geometrical structure. If we succeed in finding it, it will give us new tools for solving well as inspiration for further research.” The question about examples’ possible practical these algorithms is one he finds slightly annoying. The reason? “Science should be done ou and curiosity. Practical use is, of course, important, but it shouldn’t be the pri-mary mo algorithms might help improve the efficiency of navigation – they might help in finding th quicker.” Cooperation is motivating As a general rule, research teams in mathematics tend to be small, and many mathematicians individually; Zdeněk Dvořák, however, prefers working with colleagues: “I am glad when a f visits us, or when I am visiting somebody for a few weeks. It is great motivation – both i different approaches and thus more ideas, and of performance. I would feel stupid in front if I didn’t get any idea after several hour’s work,” he laughs. The work of theoretical mathematicians takes place in discussing ideas and solutions to pr trying to apply the concepts and verifying whether their ideas are valid in the remaining computers, sometimes. “Ninety per cent of my work takes place on paper. Sometimes, we also – ideas written there may be easily erased, and blackboards are great when you are working but a pencil and paper are winners for me.” Dvořák tries applying various principles that proved effective in other areas on solving p time to time I get an entirely unique idea. This happens, when I have been working for abo problem, and then this new idea comes suddenly, when I am taking a walk, perhaps,” he says Greater interaction is needed The mathematician focuses on teaching and popularization, among other things: “We organize oriented version of Mathematical Olympiad for high school students and also corre-spondenc informatics,” he points out. He got inspiration also during his postdoc stays in the USA and Canada: “The science itsel similar there. In our field we need no special equipment – a pencil and paper is used abro in the Czech Republic. What is interesting, is the way of teaching – university education in the United States. Students may combine mathematics with such subjects as literature or found that interesting.” After returning home, the thing he misses most is more intera-cti with teachers: “What I liked in the US was that the students were more active in their int communication with tutors – they would have consultations. I tried introdu-cing it here in Republic, however, with less success,” he states. Dvořák has been recognised on multiple occasions for his work and received the Neuron Priz scientists in 2011. However, the one he values the most is the European Prize in Combinato is awarded to young promising scientists in the field of discrete mathematics, com-binator theory. I feel honoured that they saw me as promising at that time,” he admits. In his leisure time, he enjoys reading sci-fi literature and doing the Japanese martial ar Jodo. “Jodo has several levels for me; it is, of course, a physical activity – I spend mos work sitting, which means that exercise is a welcome change. But there is also a spiritual relaxation. I also like the fact that although I have been doing it for 15 years, there is learn or improve.” Japanese culture has been his interest for a long time: “I would say it is one of the few countries which is not a western-style one. The Japanese culture and mentality is complete I enjoy discovering more about it and I love the Japanese landscape. Within two hours, you metropolis like Tokyo into the heart of intact nature. I love the contrast,” he says. ░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░ Zdeněk░Dvořák,░Ph.D.,░works░at░the░Computer░Science░Institute░of░Charles░University░focusi Technology░in░Atlanta,░USA░and░Simon░Fraser░University░in░Vancouver,░Canada.░This░year,░he ░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░ ░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░ ERC Grant Information ERC grants are awarded by the European Research Council and funded from the EU budget. The prestigious grants aimed at supporting excellence in science in all fields. A great em-pha entirely new revolutionary ideas with the potential of influencing the given field sig-nif extending its boundaries, or even opening new perspectives of research. Presently, it is possible to apply for 5 types of ERC grants: Starting (early-career resea Con-solidator (young researchers with their own teams or projects), Advanced (excellent se searchers), Synergy (groups of 2 to 4 researchers), and Proof-of-Concept (support in the e commercialization of research outputs). ERC CZ grants are awarded by the Ministry of Education to researchers who have achieved gr the ERC competitions, but received no EU funding due to funding limits.