From November 1 to 5, 2021, the Fifth online workshop on Algebraic Graph Theory and its Applications was held. The workshop was organized by Elena Konstantinova and Grigory Ryabov, the researchers of the MCA research project "Applied Abstract Algebra" headed by A. V. Vasiliev.
The event was attended by scientists from Great Britain, Germany, Slovenia, Slovakia, Israel, India, Croatia, China, the Netherlands, Belgium, Hungary, Malta, as well as researchers from leading mathematical centers in Russia (Moscow, St. Petersburg, Novosibirsk, Nizhny Novgorod, Ekaterinburg). A total of 29 lectures were given. The organizers note that this series of workshops (the first workshop took place in November 2019) has formed its own audience specializing in such areas as the theory of highly regular graphs, the theory of association schemes and coherent configurations, the complexity theory and algorithms, algebraic methods in graph theory, and theoretical and applied aspects of group theory.
Two days of the workshop were devoted to discussing new results on strongly regular graphs, Neumaier graphs, Deza graphs, as well as their application in constructing codes and designs. In particular, in a talk by Rhys Evans, a postdoc at the MCA, a new generalized construction of Neumaier graphs was discussed. The construction is based on perfect codes in graphs associated with Platonic solids, as well as in a graph of a triangular lattice in a Euclidean plane. This fundamentally new approach, undoubtedly, can be applied in the theory of error-correcting codes and in crystallography.
Another approach to constructing Neumaier graphs was presented in a talk by Maarten de Boeck from the Technical University of Eindhoven, The Netherlands. New constructions of Deza graphs, as well as their particular cases, were discussed in talks by Natalia Maslova and Vladislav Kabanov, Krasovskii Institute of Mathematics and Mechanics UB RAS. Audience greatly appreciated a talk given by Oleg Verbitsky from Humboldt University of Berlin, Germany, which was devoted to the problem of the separability of coherent configurations.
For the first time in the history of the workshop series, a thematic day of talks devoted to algebraic and group-theoretical methods in geometry and topology was organized. Talks were given by Gareth Jones from University of Southampton, UK, Josef Lauri from University of Malta, Alexander Mednykh from Sobolev Institute of Mathematics SB RAS, as well as HSE PhD students Polina Filippova and Nadezhda Kodaneva. Their scientific advisor Sergei Lando took part in the discussion of the results. The final day of the workshop was devoted to problems at the intersection of group theory and combinatorics. The remarkable talks were given by Mikhail Muzychuk (Ben-Gurion University, Israel) on the well-known problem of determining CI-groups, proposed by L. Babai in 1978, and by Qing Xiang (Southern University of Science and Technology, China) on the classes Cameron-Liebler.
Detailed information about the workshop can be found at http://mca.nsu.ru/atg5_2021/. The Sixth workshop on algebraic graph theory will be held in March 2022.
