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.
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.
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.
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.
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.
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...
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.
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.
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.
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.
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.
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.
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.