Lectorium on Algebraic

Graph Theory

Graph Theory

Mathematical Center in Akademgorodok,

Novosibirsk, Russia

Novosibirsk, Russia

Lectorium on Algebraic Graph Theory is an International Educational Program of the Mathematical Center in Akademgorodok. The main goal of the program is to educate students and young researchers in the main aspects, directions and problems of algebraic graph theory. In the frame of the program famous young researchers and professors over the world give lectures on a wide range of topics in algebraic graph theory and its application.

Current events

Minicourse: A not so short introduction into Algebraic Graph Theory

by Štefan Gyürki

by Štefan Gyürki

Štefan Gyürki received his PhD from Comenius University (Bratislava, Slovakia) in 2009. He spent a year as a postdoc student at Ben-Gurion University of the Negev (Beer-Sheva, Israel) under the guidance of Prof. Mikhail Klin. He is a (co)author of 10 research publications. He currently works at the Slovak University of Technology as a researcher.

Description of the course

This minicourse provides a gentle introduction into the theory of coherent configurations and association schemes. We start the considerations with the theory of permutation groups and their actions. After that we introduce the terms of a coherent configuration and association scheme. A significant family of coherent configurations and associations schemes arose with the aid of permutation groups, these are called Schurian. We spend some time on the investigations of a few objects which are non-Schurian, while at the end of the minicourse we will approach the most symmetric (in the sense of the number of automorphisms) strongly regular graph with parameters (26,10,3,4).

Basic knowledge of algebra is required, but all other concepts will be explained in the course.

Basic knowledge of algebra is required, but all other concepts will be explained in the course.

News

A special session for solving exercises of the minicourse by Stefan Gyurki

will be held on April 13, at 20:30 Nsk time Zone via zoom-link:

https://us02web.zoom.us/j/83776900540?pwd=cm1rNmREWFVoN0ZPYitYWnU5TFAyQT09

Conference ID: 837 7690 0540

Access code: 480255

will be held on April 13, at 20:30 Nsk time Zone via zoom-link:

https://us02web.zoom.us/j/83776900540?pwd=cm1rNmREWFVoN0ZPYitYWnU5TFAyQT09

Conference ID: 837 7690 0540

Access code: 480255

March 23, 2021

Permutation groups (basics)

Video

Slides

Assignment

Video

Slides

Assignment

April 6, 2021

Invariant relations of permutation groups

Video

Slides

Assignment

Video

Slides

Assignment

April 20, 2021

Coherent configurations and association schemes

May 4, 2021

Coherent closure

May 18, 2021

Some small non-Schurian association schemes and coherent configurations

June 1, 2021

The Paulus-Rozenfeld-Thompson graph of order 26

- M. Klin, Š. Gyürki: Selected Topics
*from Algebraic Graph Theory*(Belianum, Vydavatelstvo Univerzity Mateja Bela, Banská Bystrica, xi+209 pp. (2015) - Š. Gyürki, M. Klin, M. Ziv-Av:
*The Paulus–Rozenfeld–Thompson Graph on 26 Vertices Revisited and Related Combinatorial Structures*. In: Jones G., Ponomarenko I., Širáň J. (eds) Isomorphisms, Symmetry and Computations in Algebraic Graph Theory. WAGT 2016. Springer Proceedings in Mathematics & Statistics, vol 305. Springer, Cham. (2020) - J.D. Dixon, B. Mortimer:
*Permutation groups.*Graduate Texts in Mathematics, 163. Springer-Verlag, New York, 1996. xii+346 pp. - C.D. Godsil, G. Royle:
*Algebraic Graph Theory*. Springer Verlag New York, 2001. - M. Klin, C. Rücker, G. Rücker, G. Tinhofer: Algebraic combinatorics in mathematical chemistry. Methods and algorithms. I. Permutation groups and coherent (cellular) algebras, MATCH 40 (1999), 7-138.

Minicourse: Construction of combinatorial structures from finite groups

by Andrea Švob

by Andrea Švob

Andrea Švob obtained her PhD thesis at the University of Zagreb, Croatia, under the supervision of Professor Dean Crnković, in the year 2013. Since November 2007, she had been employed at the Department of Mathematics of the University of Rijeka and currenty works there as an assistant professor. She is a (co)author of 24 research papers.

Description of the course

In this minicourse we will give an introduction to one of the methods for construction of combinatorial structures from finite groups. The focus will be on distance-regular graphs and combinatorial designs. In the first part of the course we will give a construction of transitive combinatorial structures i.e. the structures on which finite groups act transitively. In the second part we will extend and generalize the method to obtain non-transitive structures. The methods will be followed up with various examples. Finally, we will show some of the applications of the constructed structures.

Tuesday, 6 pm

Novosibirsk, Time zone UTC+7

Zoom-Conference https://us02web.zoom.us/j/7612939528

Novosibirsk, Time zone UTC+7

Zoom-Conference https://us02web.zoom.us/j/7612939528

June 15, 2021

Construction of transitive combinatorial structures

June 29, 2021

Construction of non-transitive combinatorial structures

July 13, 2021

Applications

- E. Brouwer, Strongly Regular Graphs, in: C. J. Colbourn, J. H. Dinitz (Eds.), Handbook of Combinatorial Designs, 2nd ed., Chapman Hall/CRC, Boca Raton, 2007, pp. 852 - 868.
- E. Brouwer, A. M. Cohen, A. Neumaier, Distance-Regular Graphs, Springer-Verlag, Berlin, 1989.
- D. Crnković, R. Egan, A. Švob, Self-orthogonal codes from orbit matrices of Seidel and Laplacian matrices of strongly regular graphs, Adv. Math. Commun. 14 (2020), 591-602.
- D. Crnković, A. Švob, V. D. Tonchev, Strongly regular graphs with parameters (81,30,9,12) and a new partial geometry, J. Algebraic Combin. 53 (2021), 253-261.
- D. Crnković, V. Mikulić Crnković, A. Švob, On some transitive combinatorial structures constructed from the unitary group U(3,3), J. Statist. Plann. Inference 144 (2014), 19-40.
- J. D. Dixon, B. Mortimer, Permutation groups, Graduate Texts in Mathematics, 163. Springer-Verlag, New York, 1996.
- D. Godsil, G. Royle, Algebraic Graph Theory, Springer Verlag New York, 2001.

The information about past events will appear hear as soon as the first minicourse will be finished.

Useful links

Workshops, seminars and conferences on algebraic graph theory organized by our team

http://mca.nsu.ru/atg4_2021/

http://mca.nsu.ru/atg3_2020/

http://mca.nsu.ru/atg2020/

http://mca.nsu.ru/atg2019en/

We would be glad to see you as a participant of our future events.

Videos of talks given on workshops, seminars and conferences on algebraic graph theory organized by our team:

https://www.youtube.com/playlist?list=PLaX3n04-uUZr9jVGOCYzPsB9L0Qzo9KeN

Videos of talks which will be given on Lectorium on Algebraic Graph Theory are submitted to the playlist.

http://mca.nsu.ru/atg4_2021/

http://mca.nsu.ru/atg3_2020/

http://mca.nsu.ru/atg2020/

http://mca.nsu.ru/atg2019en/

We would be glad to see you as a participant of our future events.

Videos of talks given on workshops, seminars and conferences on algebraic graph theory organized by our team:

https://www.youtube.com/playlist?list=PLaX3n04-uUZr9jVGOCYzPsB9L0Qzo9KeN

Videos of talks which will be given on Lectorium on Algebraic Graph Theory are submitted to the playlist.

Lectorium is organized by

We adore mail!

Organizer

e_konsta@math.nsc.ru

e_konsta@math.nsc.ru

Organizer

ntr@math.nsc.ru

ntr@math.nsc.ru

Supported by Mathematical Center in Akademgorodok under agreement No. 075-15-2019-1675 with the Ministry of Science and Higher Education of the Russian Federation