On March 7,
the Fourth Workshop "Algebraic Graph Theory and Its Applications", organized by the staff of the research project "Applied Abstract Algebra: Algebraic Methods in Topology, Combinatorics and Computational Complexity" (headed by
Andrey V. Vasil'ev) of the Mathematical Center in Akademgorodok, was successfully finished. The organizer of this event,
Elena V. Konstantinova, a leading researcher at MCA, says:
The Workshop on algebraic graph theory has become a traditional event for many researchers in this field. Like its predecessor, the workshop was held online. 22 foreign and 9 Russian scientists gave 20 hour-long and 11 half-hour-long talks. Leading scientists from the Netherlands, Japan, Germany, Slovakia, Croatia, China, India, Great Britain, Slovenia, Israel participated as speakers. Graph isomorphism recognition is one of the popular topics of the workshop. Two excellent talks in this direction were made by Oleg Verbitsky from the Humboldt University in Berlin and Pascal Schweitzer from the Technical University of Darmstadt. Among the talks devoted to spectral graph theory, I would like to note a talk by Jack Koolen on new results on improving the Delsarte estimate, as well as a talk by Edwin van Dam, in which new matrix representations for directed graphs are proposed. Great interest was aroused by the talk of Aida Abiad, dedicated to the Neymaer graphs with several eigenvalues. The chromatic properties of strongly regular graphs were considered by Willem Haemers, in whose talk he conjectured that, with the exception of the Petersen graph, strongly regular graphs of even order always have a chromatic index equal to the degree of the graph. New results on Deza graphs were presented in the talks of Dean Crnković, Vladislav Kabanov and Dmitry Panasenko.
Elena Konstantinova also noted that the workshop contributes to the emergence of new projects, uniting participants from different countries and strengthening the possibilities of successful project implementation. After the
3rd workshop, a project on finite group recognition by graphs was organized, in which
Peter J. Cameron, a well-known expert in the field of group theory, combinatorics, and coding theory, plays an important role. Four presentations were made in this direction.
Several talks were given by young members of the MCA research group on applied abstract algebra. In particular,
Dmitry Churikov presented new results obtained jointly with the famous Australian mathematician
Cheryl Praeger, and
Grigory Ryabov spoke about the achievements in the classification of Abelian Schur groups. For the first time,
Yu Jiang, the winner of the MCA postdocs competition, gave a presentation on relationship schemes.
On the last day of the workshop, all participants had the opportunity to make short presentations to present open questions and unsolved problems. In addition to the main speakers, more than 60 listeners took part in the workshop, including researchers from Canada, Belgium, Italy, Hungary, New Zealand, Yekaterinburg and St. Petersburg. At the end of the event, there was a lot of positive feedback, in particular, the young participants noted that "these workshops are very useful". Therefore, it was decided to organize an online lectorium on algebraic graph theory. In the spring semester, two mini-courses will be taught by
Štefan Gyürki from Slovakia and
Andrea Švob from Croatia. The first lecture will take place on
March 23. More information about the content of mini-courses can be found on
the lectorium's website. Detailed information about the workshop itself can be found on
its website, and video recordings of the workshop are available on
the MCA YouTube channel. The fifth workshop on algebraic graph theory will be held in
November 2021.
