Groups and Graphs, Algebras and Applications (G2A2-2025)
International Conference and PhD-Master Summer School,
August 3-17, 2025, Novosibirsk, Russia
Main
«Groups and Graphs, Algebras and Applications», G2A2-2025, belongs to the G2-series (G2-series pdf or https://ekonsta.github.io/Slides/G2-series.pdf) including international conferences and summer schools. Since 2014, the G2-events were held in Russia and China, and in Slovenia as satellite events of the 8th European Congress of Mathematics. For more details, visit Links.
G2A2-2025 aims to bring together experts, young researchers and students from different fields of mathematics and their applications mainly based on algebra and group theory, geometry and algebraic graph theory, topology and algebraic combinatorics, coding theory and theory of computational complexity, especially those involving group actions on combinatorial objects.
The official language of the event is English.
Venue
All scientific activities take place at Novosibirsk State University, August 3-17, 2025 (August 3 is the day to arrive and August 17 is the day to leave, that is, there is no activities on these days).
Program
The program of the G2A2-2025 consists of 50-minute invited talks and 25-minute contributed talks in the frame of the International Conference and 4 minicourses in the frame of the PhD-Master Summer School.
A tentative timetable is reached here (Timetable-G2A2-general)
G2A2-PhD-Master Summer School
The scientific program of the G2A2-Summer School is presented by 4 courses each of which consists of 8 lectures.
Minicourse 1: Axial Algebras
Lecturer: Sergey Shpectorov, (https://www.birmingham.ac.uk/staff/profiles/maths/shpectorov-sergey) University of Birmingham, UK
Description: Axial algebras are a recently developed class of non-associative algebras, which are inherently related to groups. The motivating examples include the Jordan algebras, related to classical and some exceptional algebraic groups, Matsuo algebras, related to 3-transposition groups, and the Griess algebra, which was used to realise the Monster sporadic simple groups. This minicourse focusses on the general theory of axial algebras, as well as on examples and classification of the two most interesting classes: algebras of Jordan and Monster type.
Outline of the course:
Lecture 1. Introduction into axial algebras
Lecture 2. Structure theory (radical, sum decompositions)
Lecture 3. Algebras of Jordan type, Matsuo algebras
Lecture 4. Classification for eta not equal to 1/2
Lecture 5. The case of eta=1/2
Lecture 6. Algebras of Monster type, initial examples
Lecture 7. Double axes, the flip construction
Lecture 8. Classification of the 2-generated case
Bibliography
J.I. Hall, F. Rehren, and S. Shpectorov, Primitive axial algebras of Jordan type, J. Algebra, 437 (2015) 79-115.
S. Khasraw, J. McInroy and S. Shpectorov, On the structure of axial algebras, Trans. Amer. Math. Soc., 373 (2020) 2135-2156.
A. Galt, V. Joshi, A. Mamontov, S. Shpectorov and A. Staroletov, Double axes and subalgebras of Monster type in Matsuo algebras, Comm. Algebra 49 (2021) 4208-4248.
J. McInroy, S. Shpectorov, Split spin factor algebras, J. Algebra, 595 (2022) 380-397.
C. Franchi, M. Mainardis and S. Shpectorov, An infinite-dimensional 2-generated primitive axial algebra of Monster type, Annali di Matematica, (2021), https://doi.org/10.1007/s10231-021-01157-8.
Minicourse 2: Closures of finite permutation groups
Lecturers: Ilia Ponomarenko, (http://www.pdmi.ras.ru/~inp/), St. Petersburg Department Steklov Mathematical Institute, St. Petersburg, Russia & Andrey Vasil’ev, Sobolev Institute of Mathematics, Novosibirsk, Russia (http://old.math.nsc.ru/~vasand/)
Description: We start with a discussion on the connection between the graph isomorphism problem and theory of permutation groups. Then we present the basics of Wielandt's classical theory connecting permutation groups and invariant relations. Within the framework of this theory, we introduce and study m-equivalent groups (i.e., groups with the same set of invariant relations of arity m). The largest group in the class of m-equivalent groups is defined as the m-closure of any of them. In the second part of the mini-course, we will derive formulas for the m-closure of products of permutation groups, and discuss the known algorithms for computing the m-closure. In the last lecture, we will make a short overview of the modern theory of closures of permutation groups and present open problems.
Outline of the course:
Lecture 1. Permutation groups and graph isomorphism problem
Lecture 2. Wielandt’s method of invariant relations: the basics
Lecture 3. Products of permutation and matrix groups
Lecture 4. Closures of products of groups
Lecture 5. Classes of groups, invariant with respect to closures I
Lecture 6. Classes of groups, invariant with respect to closures II
Lecture 7. On computing the closures of permutation groups
Lecture 8. New perspectives and open problems
Bibliography
H. Wielandt, Permutation groups through invariant relations and invariant functions, The Ohio State University, 1969.
I. Ponomarenko and A. Vasil'ev, Two-closure of supersolvable permutation group in polynomial time, Comp. Complexity, 2020 Vol. 29, 5 (33 pages).
I. Ponomarenko and A. Vasil'ev, The closures of wreath products in product action, Algebra and Logic, 2021 Vol. 60, No. 3, 188-195.
E.A. O'Brien, I. Ponomarenko, A.V. Vasil'ev, and E. Vdovin, The 3-closure of a solvable permutation group is solvable , J. Algebra, 2022, Vol. 607, 618-637.
I. Ponomarenko and A. Vasil'ev, On computing the closures of solvable permutation groups, Internat. J. Algebra Comput., 2024 Vol. 34, no. 1, 137-145.
Minicourse 3: Low dimensional classical groups and their geometries
Lecturer: Tao Feng, (https://person.zju.edu.cn/en/tfeng), Zhejiang University, China
Description: The finite simple classical groups form a major part of finite simple groups, and their geometries play a crucial role in understanding their maximal subgroup structures. They play an important role in the applications of O’Nan-Scott Theorem and the classification of finite simple groups to various group theoretical problems and combinatorial problems. There are also important substructures in their associated polar spaces that have close connections to other branches of mathematics. This introductory minicourse focuses on the low dimensional classical groups and their geometries. We shall define those classical groups, examine their subgroup structures and study important substructures of finite classical polar spaces.
Outline of the course:
Lecture 1. Projective lines and conics
Lecture 2. Klein correspondence and Plucker coordinates
Lecture 3. Polarities and classical polar spaces
Lecture 4. Rank 2 polar spaces and generalized quadrangles
Lecture 5. Intriguing sets, ovoids and spreads
Lecture 6. Tensor algebras and related modules
Lecture 7. Clifford algebras and spin modules
Lecture 8. The maximal subgroups of classical groups
Bibliography
D. E. Taylor, The geometry of the classcal groups. Berlin, Heldermann, 1992.
L. C. Grove, Classical groups and geometric algebra, 2002.
Minicourse 4: Combinatorial search with lies, error-correcting codes, and other applications of finite fields
Lecturer: Grigory Kabatyansky, (https://www.skoltech.ru/en/team/grigory-kabatyansky/), Skolkovo Institute of Science and Technology, Russia
Description: We start from the following famous variation of Twenty Questions Problem when one needs to find one of 10^6 objects by asking an oracle the minimal possible number of questions of the following type “if the given object belongs to some subset”, but the oracle may sometimes lie, see [1,2]. And what if not one, but many elements should be “guessed”? A question-answer model is important here and there are many of them. These discrete problems turned out to be very close to the following continuous problem, known as compressed sensing [3,4], namely, to find an unknown sparse vector in n-dimensional Euclidean space by the minimal number of linear measurements which aren't exact. In these lectures, we show how finite fields, via error-correcting codes, help solve these and many other problems that arise in practice.
Outline of the course:
Lecture 1. The Renyi-Ulam game or how to find an object among a million in just 25 questions, if one answer can be wrong
Lecture 2. On various modifications of the Renyi-Ulam game
Lecture 3. Finding counterfeit coins on accurate scales with a harmful oracle
Lecture 4. Time for finite fields and error correcting codes –simplex and Hamming codes
Lecture 5. Polynomials over finite fields and Reed-Muller and BCH codes
Lecture 6. Non-overlapping convex polytopes with Boolean cube vertices and multimedia digital fingerprinting
Lecture 7. Non-overlapping convex polytopes with Boolean cube vertices and multimedia digital fingerprinting
Lecture 8 How to find sparse vector support using imprecise linear measurements
Bibliography
Реньи А. Трилогия о математике. - М.: Мир, 1980. («Дневник. Записки студента по теории информации»)
Ulam S.M. Adventures of a Mathematician. New York: Scribner, 1976.
Donoho D.L. Compressed Sensing, IEEE Trans. Inform. Theory, 2006, V. 52, No. 4, P. 1289–1306.
Candes E.J., Tao T. Near-Optimal Signal Recovery From Random Projections: Universal Encoding Strategies?, IEEE Trans. Inform. Theory. 2006. V. 52. № 12. P. 5406–5425.
G2A2-International Conference
The scientific program of the G2A2-Conference is presented by 50-minute invited talks and 25-minute contributed talks. Keynote plenary speakers are:
· Sasmita Barik, Indian Institute of Technology Bhubaneswa, India(https://old.iitbbs.ac.in/profile.php/sasmita/)
· Charles Buehrle, Notre Dame of Maryland University, USA (https://www.ndm.edu/directory/charles-buehrle)
· Huye Chen, Guangxi University, China
(https://www.researchgate.net/profile/Chen-Huye)
· Gang Chen*, Hainan University, China
(https://www.researchgate.net/profile/Gang-Chen-94)
· Shaofei Du*, Capital Normal University, China
(https://www.researchgate.net/profile/Shaofei-Du)
· Tao Feng, Beijing Jiaotong University, China
(https://faculty.bjtu.edu.cn/8202/)
· Clara Franchi*, Università Cattolica del Sacro Cuore, Italy (https://dmf.unicatt.it/~franchi/)
· Alexander Gavrilyuk, University of Memphis, USA (https://www.memphis.edu/msci/people/ )
· Jin Guo*, Hainan University, China
(https://www.researchgate.net/profile/Jin-Guo-29)
· Tatsuro Ito, Anhui University, China & Kanazawa University, Japan (https://biography.omicsonline.org/china/anhui-university/tatsuro-ito-82885)
· Alexander A. Ivanov, Hebei Normal University, China
(https://www.scopus.com/authid/detail.uri?authorId=55221997800)
· Vladislav Kabanov, N.N. Krasovskii Institute of Mathematics and Mechanics, Russia(http://kabanov.imm.uran.ru/ )
· Pavel Kolesnikov, Sobolev Institute of Mathematics, Russia (https://scholar.google.com/citations?user=WEWyqyAAAAAJ&hl=en)
· Jack Koolen University of Science and Technology of China (http://staff.ustc.edu.cn/~koolen/)
· Mario Mainardis*, Università degli Studi di Udine, Italy (https://users.dimi.uniud.it/~mario.mainardis/)
· Georgy Shabat, Russian State University for the Humanities, Russia (https://www.rsuh.ru/en/who-is-who/shabat-georgiy-borisovich/)
· Saveliy Skresanov, Sobolev Institute of Mathematics, Russia (https://www.researchgate.net/scientific-contributions/Saveliy-V-Skresanov-2145652827)
· Alexey Staroletov, Sobolev Institute of Mathematics, Russia (https://scholar.google.com/citations?user=hKAcFC8AAAAJ&hl=en)
· Natallia Tokareva, Sobolev Institute of Mathematics & Novosibirsk State University, Russia (http://old.math.nsc.ru/~tokareva/)
· Vladimir Trofimov, N.N. Krasovskii Institute of Mathematics and Mechanics, Russia
(https://www.mathnet.ru/php/person.phtml?personid=8884&option_lang=eng)
· Mikhail Volkov*, Ural Federal University, Russia
(https://csseminar.kmath.ru/volkov/)
· Yaokun Wu*, Shanghai Jiao Tong University, China (https://en.zhiyuan.sjtu.edu.cn/en/faculty/49/detail)
· Min Yan, Hong Kong University of Science and Technology, China
(https://facultyprofiles.hkust.edu.hk/profiles.php?profile=min-yan-mamyan)
* TBC
Useful Links
The G2-series history:
https://conferences.famnit.upr.si/event/13/page/26-history
https://ekonsta.github.io/Slides/G2-series.pdf
G2R2-2018-Video: https://www.youtube.com/watch?v=vKFhYDz4TCU
G2D2-2019-Book: https://www.cambridge.org/core/books/groups-and-graphs-designs-and-dynamics/7F951F7ED3CBA22D1C2BDDC1E2FD5233
G2C2-2024: http://app.hebtu.edu.cn/2024g2c2/index.html
Organizers
The G2A2-2025 is organized by Mathematical Center in Akademgorodok (https://english.nsu.ru/mca), Novosibirsk State University (https://english.nsu.ru) and Sobolev Institute of Mathematics (http://www.math.nsc.ru/english.html) in cooperation with the Sino-Russian Mathematics Center at Peking University (Beijing), Three Gorges Mathematical Research Center at China Three Gorges University (Yichang) and Hebei International Joint Research Center for Mathematics and Interdisciplinary Science, Hebei Normal University (Shijiazhuang).
Main organizers:
Elena Konstantinova, (https://ekonsta.github.io/) Mathematical Center in Akademgorodok, Sobolev Institute of Mathematics, Novosibirsk State University, Russia & Three Gorges Mathematical Research Center, China Three Gorges University, China
Darya Lytkina, (https://english.nsu.ru/mca/governance/#) Mathematical Center in Akademgorodok, Sobolev Institute of Mathematics, Novosibirsk State University, Russia
Andrey Mamontov, (https://www.mathnet.ru/php/person.phtml?personid=28202&option_lang=eng)
Sobolev Institute of Mathematics, Novosibirsk State University, Novosibirsk, Russia
Yaokun Wu, (https://en.zhiyuan.sjtu.edu.cn/en/faculty/49/detail) Shanghai Jiao Tong University, China
Liping Yuan, (https://sxxy.hebtu.edu.cn/a/2019/05/16/28ED3B7A46F84E1B92827163B0B3CB3A.html)
Hebei Normal University, China
Alexey Zakharov, (https://english.nsu.ru/mca/governance/#) Mathematical Center in Akademgorodok, Sobolev Institute of Mathematics, Novosibirsk State University, Russia
English