Applications of Topology and Geometry – 2020 Online School

The School gathered more than three hundred participants from around the world to discuss the applications of geometrical and topological methods in mathematics and computer science.

School’s main goal was to demonstrate how topology and geometry penetrate everywhere from mathematics to art, multidimensional data analysis, and musical harmony. Among the topics were graphs, integer points in polyhedra, symmetries. More philosophical topics like the beauty of mathematical objects were also discussed. Almost every lecture mentioned simplicial complexes – multidimensional sets of graphs.

The participants came from Ukraine, Great Britain, and Germany as well as from Russia. Among them were university students, researchers, and even three high school students. Lecturers from Russia, Japan, China, Serbia, and Great Britain gave presentations.

Anton Ayzenberg
Head of the School, Head of International Laboratory of Algebraic Topology and Its Applications

Heretofore I only took part in schools as lecturer; this was the first School I organised, online or otherwise. On the one hand, online event is simpler to hold: no need to select participants since there is no limit for places, no need to handle transport, accommodation, visas. On the other hand, it is psychologically more difficult to host suchlike School and to give lectures. We did not demand our participants to turn the cameras on, so we were losing the feeling of being listened to. We tracked the reaction only by the questions after the lecture. Chat discussions are, of course, not equal to coffee brakes; however, I still think we managed to do a fine job. We have listened to a variety of fascinating lectures, learned something new and beautiful – mathematically speaking. I am grateful to all participants who were active in questioning and discussing – this is a truly important aspect of any event but especially the online one.

Grigory Solomadin
Speaker of the School, S.M. Nikol’skii Mathematical Institute, RUDN University

My impressions of the Applications of Topology and Geometry School, where I gave a lecture, are perfectly positive. In my opinion, the organisers have selected topics for lectures extremely well, so that they presented a general picture. The topics were discussed appropriately for interested students to understand. The School touched upon both research and more specific topics. For example, in the Rade Zivaljevi’s lecture, I discovered tonnetz, an object both beautiful (because of its application to the theory of music) and known since the times of Euler. Tonnetz is a way to depict major and minor triads on the surface of a two-dimensional torus. Also, Mikiya Masuda formulated several very interesting combinatorial hypotheses.

Rade Zivaljevi
Speaker of the School, Serbian Academy of Sciences and Arts

This School is truly a mathematical feast. It was equally interesting for students of topology and geometry and for accomplished mathematicians who were able to survey the topics of current importance. I would like to thank Anton Ayzenberg and the whole team of organisers for their enthusiasm in holding this event.

 

Andrey Zabolotsky, participant, Dukhov Automatics Research Institute

The lectures of the School are best described as “quality”. The same objects mentioned time and again built up a complete structure of the field. I thank organisers for this experience.

 

Ivan Tuchkov, participant, Moscow Institute of Physics and Technology

Such an event as this School are splendid. It did not matter to me whether it was online or offline lectures’ content was the king. It was important and useful that I was able to see beautiful and unexpected links somewhere I did not expect to find them – thanks to the knowledge I got in the School.