The first worksop of Mathematical center in Akademgorodok has finished

The first workshop of the Mathematical center in Akademgorodok is consists of two weekly intensive weeks, connected via a three-week intermodule. 25 projects, most of which are interdisciplinary; 32 mentors, more than 40 curators and 40 lecturers fr om 34 leading educational and scientific organizations, as well as companies in the real sector of the economy; 243 participants fr om 64 institutions, 149 of which completed the entire program and tried themselves in research problems solving; 142 lectures read; more than 50 short reports and 80 presentations — this is far from what makes you feel the scale of The first workshop.

The epidemiological situation in 2020 left no choice but to hold the workshop online. As a result, this format revealed both disadvantages, e.g. the lack of live communication and inability to write mathematical calculations on a real blackboard, and some undeniable advantages. For example, Bogdan Chuzhinov, a participant of the project #1 "Flat virtual nodes and representation of flat virtual braids," analyzes this situation in the following way:

In my opinion, the online format has more advantages than disadvantages. A lot of team members of our project were not from Novosibirsk, and remote communication was the only way for them to participate. In addition, some of the lectures read during the workshop were from foreign experts. At the beginning of the first module, it was unusual to work with strangers, but as the work went on everyone got used to it. When we just started solving our problem, I assumed that the online format would negatively affect the productivity of our team, but, as it turned out, even if intricacies did arise, they were absolutely insignificant. Most likely, this happened because everyone was engaged in the process, since for the majority of participants it was the first experience of conducting research. The workshop also showed that virtual discussions are possible, because after the interim reports of the teams, it was really easy to ask a question. I hope that the next time the workshop will also be held remotely, but not just because of health risks for the participants.

There were several kinds of activities in the workshop. The first of them were classic lectures. Their distinctive feature was that they were specifically selected for the topics of projects.

During the two weeks of our project we managed to listen to five lectures. These lectures were significantly distinct from those that we are used to listening to in the university — they did not create the feeling that after it you would be trapped by an exam on the given material. This made it interesting and easy to perceive, and the information was assimilated without any problems. In addition, you yourself had chosen the project that had interested you, and, therefore, it always turned out so that you are constantly engaged in the work. The lectures were read for a small audience, so after them it was always possible to calmly discuss the questions with the lecturers. 

— notes the participant of project #1 Valery Yakhin.

The main occupation of the students was teamwork in groups of up to 10 people.

The work in the workshop was productive, because there was a discussion between people from different spheres. Before the workshop we were sitting in some kind of small physical "bubble", trying to approach from different sides, but the guys and our curator from Novosibirsk came to help us and the truth was born in the dispute. New ideas were born, not all of which we managed to implement, but this is a great start anyway. I think that it was achieved mostly due to the high level of the participants. When I formed the team, I tried to conduct an experiment to make the most versatile group: I selected both very “small” and also not very young researchers. This experimental approach was risky. Part of the team left in the process, but those who stayed turned out to have a very high level. In general, I'm used to working with teams scattered around the world. Basically, I used worked with people from Irkutsk and Moscow, and Novosibirsk, by the way, came as a pleasant surprise for me. I would love to collaborate with my team members in further work. I think it is worth discussing this separately. To sum up, my expectations from the workshop were met. The only setback is the difficulty of working in the summer.

— comments the head of the project #17 "Neural networks-autoencoders for processing signals from antenna arrays" Dmitry Kostyunin.

Some of the workshop projects can be called more educational-like. According to the curator of the project #26 "Mathematical support of linguistic expertise" Dmitry Morozov, the main trait of the workshop tasks is that they are tasks of the full cycle and the research is actually carried out by students:

Yes, of course, we are still getting a more educational project: the guys are learning to set tasks, program, somehow work in a team, so we didn’t have such a direct wow-result, but they are the ones who do the research, including setting up the initial experiment, collecting data, etc. In my opinion, this is more useful, because the immersion in the interdisciplinarity of research is much stronger, and they understand what exactly is the phenomenon they are studying, and not just some model they are setting on a marked dataset.

Many of the topics presented in the workshop are essentially open problems that scientists around the world cannot solve. Such an intensive course is, first of all, an excellent practice for students. In particular, the practice of working in a situation wh ere no one will give an answer — because no one in the world has it yet. This differs significantly from ordinary educational programs, when the teacher knows everything in advance.

I have to say that when I proposed such a research problem for a workshop, I took some risk. Although the problem is formulated in elementary terms, it is a real problem, needs not just an answer, but also a method that is guaranteed to lead to it. Moreover, it is not known whether this answer can be found using elementary mathematics or whether more advanced sections of it will need to be connected. Nevertheless, I tried to formulate the problem in the form of a sequence of steps, starting with the most elementary examples. For the first few cases, the answer was well known. I tried to motivate the participants in the workshop so that, armed with new methods after these examples, they went for the free flight and began to generate ideas and move on their own. The end goal proved to be difficult, and, despite the efforts of the group, it still remains unresolved. However, on the way to it, those cases were reproduced for which the answer was known before. These answers were received, among other things, by new methods, which in itself is already a positive result. Some of the ideas actually came from the students’ brainstorming sessions. Therefore, there are benefits of working on this project, even for myself. I am very grateful to the students and curators for being not afraid to take on real research work and, overcoming obstacles, moving forward.

— thinks the mentor of the project #2 "The problem of the existence of a vacuum" Igor Ivanov.

At the same time, Yuri Efremenko, a participant of project #2, comments on the impressions of the workshop as follows:

As soon as I found out that the workshop would be held, I immediately decided to participate in it, as it is a great opportunity to apply the knowledge gained during the course of my studying. To be honest, at first I was a little upset by the remote format, which deprives the participants of live communication and the opportunity to write with chalk on the blackboard... But when I saw the announced projects and the geography of the workshop, my opinion changed a lot, and I became a participant in a project that came to us from Portugal. This problem combined an understandable and simple mathematical formulation and its application in elementary particle physics. But, despite the simplicity of the formulation, it turned out to be a very difficult task to crack it... There were many ideas for the solution: algebraic, geometric, analytical and even using computer tools. I really liked the fact that most of the methods were available to non-specialists in the field of algebra, geometry or physics, so everyone could offer their ideas and start working on them. Although in the end we were unable to obtain any absolutely new results, the developed methods allowed us to rediscover the already known results much more beautifully. We also hope that all of them will be useful in the further development of this task. We will continue to work on this task further and hope that at some point it will succumb to our pressure. Maybe we will accidentally discover new physics...

Most of the lecturers, curators and mentors note the high level of motivation and knowledge of the participants. So, the mentor of project #22 "Averaging of a thermoelastic composite by the method of two-scale convergence" Sergey Golushko notes:

To participate in the project, a team of young researchers was formed, representing various universities in Russia and France, which worked under the guidance of three doctors of physical and mathematical sciences — specialists from fields of mathematics and mechanics. The positive aspects of the project team's work include its qualitative composition, which ensured the multidisciplinarity of the research, as well as its quantitative composition, which made it possible to parallelize individual stages of work. There were no negative aspects in the work. The young participants of the project who reached the finish of the second intensive week showed a high level of mathematical training, high efficiency and great interest in the success of the project.

Of course, the workshop participants achieved significant results thanks to the professionalism of mentors who directly verified hypotheses, reasoning and evidence, as well as the comprehensive help and support of the curators. For the duration of the workshop, the curators became relatives for the participants: they really were 24/7 in touch and helped with their advice. The curator of the project #21 "How to develop Open Source Intelligence framework from Scratch" Anthony Nikolaev tells about how it was:

For me, it was an interesting and fresh experience, when the curating really took place 24/7 in messengers, in code review on Github, in meetings in Zoom and so on in real time, almost on all platforms. In general, I can say that this is a great experience, because from answering various questions, especially those that are not obvious, and understanding something, everybody (both students and teachers) get a little benefit.

The curator of the project #18 “Digital Urbanism: Geodata Analysis, Modeling of Urban Processes and Machine Learning” Anna Avdyushina notes:

We, as curators, really liked the format of the workshop. It helps to structure our knowledge, carry out the most intensive work in a short time, as well as share our knowledge and find people interested in it. Since in our work it is necessary to deal with software tools for a long time, our communication with students was reduced to constant debugging of code and more time was taken to control the work. The last week mostly passed non-stop. Long calculations, limited free time and inconsistencies in time zones required us to push it to the lim it. And the most important thing is the presence of strong involvement of students and their desire to work with us further.

The development of the participants’ versatility was ensured by making two-minute presentations of the groups, as well as participation in the final plenary sessions. It should be noted that within the framework of the second module, all the reports were made by the participants, not the curators.

I think that the two-minute presentation was a success for me: in general, I told what we had done, and did not make any fatal mistakes. The people apparently liked the way I spoke, they praised me. It was not particularly difficult to prepare, because there were various engineering seminars at the SSC NSU, at which this was also actively practiced. However, to be honest, we were given a little bit more than 2 minutes — more like 3–5.

— Ravil Bildanov, the youngest participant of the workshop, a graduate of SSC 2020, assesses his performance. It should be noted that Ravil also became the only participant in the workshop who was able to work in parallel in two research projects:

It so happened that the projects were complimentary. Sergey Vladimirovich Avgustinovich began work on his project a little earlier than the official start of the workshop — at the very beginning of July. Then I somehow managed to glorify and combine projects #13 and #9, which I chose according to the requirements. Project #9, according to the requirements, was quite liberal: you only need to know the course of secondary school, and project 1#3 was advised to me by my supervisor Andrey Viktorovich Vasiliev. As part of Project #13, Viktor Panshin and Grigory Konstantinovich Ryabov and I classified certain graphs and proved that the isomorphism can be checked by the Weisfeiler-Lehmann algorithm. So it is more of a concealment than a discovery. A few more open questions remain, but a definite point has already been set. In general, the workshop was useful, effective and generally good for me, and the second article pleases me.

Ravil became interested in mathematics for a long time: from the second semester of the 9th grade, he began his research activities under the leadership of Andrei Viktorovich Vasiliev. But in the 9th grade, he did not yet know that he was going to study mathematics and precisely at NSU.

By the 11th grade, I realized that I wanted to do fundamental mathematics, and by the time the first article was published [May 2020,] I realized by 85-90% that I am staying in Novosibirsk and entering the Research Group.

— he comments.

The final presentations of the projects that took place on August 14 and 15, unlike the first modules, were not parallel, which made it possible to listen to all of them. The time schedule shifted the focus from the reports to the discussions, which were very lively. Many groups noted that they plan to continue working on the tasks of the workshop, both in order to formalize the result in the form of a complete article, and in order to solve new research problems.

On the whole, our expectations almost completely coincided with the results. There were both obvious difficulties and expected positive results. We understand what can be changed in the future and how we can participate in similar events together with the Mathematical center. We, of course, plan to continue collaboration with students in the framework of joint work with laboratories of universities and research institutes. This workshop for us, among other things, is precisely the development of united approaches to cooperation, the search and support of student groups.

— notes the mentor of the project #5 "BigData - open source project Apache Flink" Igor Solodov.

My expectation was, above all, to see the students' keen interest in the difficult problems of modern fundamental mathematics. This expectation was fully justified. In addition to NSU students, our team included students and postgraduates from St. Petersburg and young scientists from Tomsk. Teamwork allowed each participant to show their strengths. The workshop allowed me to see new candidates and test them in their work. I can say with great confidence that they will be attracted to new grants close to the theme of the workshop. The undoubted advantage of teamwork was also the fact that “horizontal” scientific ties were formed at the level of students from different universities. I am sure that in a couple of years, our team members will meet with each other at scientific conferences. 

— evaluation of the workshop’s efficiency by the mentor of project #1, director of the Regional mathematics center of TSU Andrey Vesnin.

Based on the results of the workshop, 18 out of 25 teams set themselves the ambitious task of preparing an article for publication in a peer-reviewed journal. These tasks seem to be feasible, in particular for the reason that many have already begun to formulate the results obtained.

In the near future, everyone will be able to get acquainted with short reports of the groups, as well as full-fledged presentations on the Department of Mathematics and Mechanics of NSU channel on YouTube, as well as on the Instagram of the Mathematical center. Based on the results of the work, each project team will also prepare a popular-science article. According to the organizers and participants, this way everyone can find out about the results in an accessible format.