Constructions of Expanders and Extremal Graphs

Slovakia-Austria Bilateral Collaboration

SK-AT-23-0019

2024 - 2026


Aim of the Project
The project brings together researchers from Bratislava and Vienna interested in various combinatorial and geometric aspects and applications of algebraic techniques in constructions of expander graphs and extremal graphs of given degree, diameter or girth.

First Meeting, July 15, 2024

Our first meeting was conducted over the internet and it included the main proponents of the proposal, prof. Arzhantseva, prof. Jajcay and prof. Jajcayova. The discussion covered some of the proposed research topics, and the details of the first `in person' meeeting in August in Bratislava.

First Workshop, August 27 - 28, 2024

The first joint workshop of the project takes place in Bratislava, at the Faculty of Mathematics, Physics and Computer Science of the Comenius University, August 27-28, in Mlynska dolina. All lectures take place in the lecture room M-III.


Abstracts (in pdf)

Tuesday, August 27, 2024
14:00 - 14:10
Official opening of the Workshop
M-III
14:10 - 15:10
Markus Steenbock (University of Vienna): Rips-Segev torsion-free groups without the unique product property
 M-III
15:10 - 15:30
Discussion
 M-III
15:30 - 16:30
Robert Jajcay (Comenius University): Extremal Graphs with Expander Properties
M-III
16:30 - 17:00
Shasha Zheng (Comenius University): Cubic graphical regular representations of finite non-abelian simple groups
M-III
19:00 -
Dinner
TBA


Wednesday, August 28, 2024
10:00 - 11:00
Merlin Medici (University of Vienna): Automorphisms of self-similar trees and searching for expanders
M-III
11:00 - 11:20
Discussion
 M-III
11:30 - 12:00
Pavol Kollar (Comenius University): Regular Families of Permutations - Properties, Counting, and More
M-III
12:00 - 14:00
Lunch
TBA
14:00 - 15:00
Tatiana Jajcayova (Comenius University): On the use of partial automorphisms in graph problems
M-III
15:00 - 15:30
Jan Pastorek (Comenius University): Search for correspondences between operations on partial automorphisms and k-dimensional Weisfeiler-Leman algorithm
M-III
15:30 - 16:00
Stefania Glevitzka (Comenius University): Vertex-transitive closures of graphs
M-III
16:00 -
Closing Remarks
M-III


Abstracts (in pdf)


Workshop Location

All talks take place in the Lecture Hall M-III

Faculty of Mathematics, Physics and Computer Science is located in Mlynska dolina and can be accessed via trams 4 and 9 (stop `Botanicka zahrada'), by buses 31 or 39 (from the city, stop `ZOO'), or from the train station bus 32 (stop `ZOO').
All access via public transportation requires about 5 minutes of walk by the end.

Registration

Attending the workshop is free of charge. Everyone interested in the material covered in the lectures is welcome to attend.


Second Workshop, October 9 - 11, 2024

The second meeting took place at the University in Vienna, and included a presentation by Robert Jajcay on October 10, 2024:

14:00 - 15:00
Universal construction of cyclic complementary extensions of finite groups inspired by the structure of automorphism groups of regular Cayley maps
Seminar Room 4

Abstract: The concept of a Cayley map is one of the central concepts of the part of Topological Graph Theory focused on highly symmetric maps. A Cayley map is a 2-cell embedding of a Cayley graph into an orientable surface which admits all the left multiplications by the elements of the group as automorphisms of the map. A Cayley map is regular if its automorphism group acts transitively on its set of darts. The automorphism group of a Cayley map is a cyclic complementary extension of its underlying group, where the cyclic part is generated by a special group mapping called skew-morphism. All cyclic complementary extensions are known to give rise to skew-morphisms, and all skew-morphisms give rise to specific cyclic complementary extensions called skew-products. However, not all cyclic complementary extensions are skew-products; leaving a gap in our understanding of cyclic complementary extensions of finite groups. Recently, together with Kan Hu, we have been able to fill this gap by introducing a generalization of the power function of a skew-morphism we call extended power function, and by finding a universal construction of cyclic complementary extensions of groups by skew-morphisms and their extended power functions. We have shown that all cyclic complementary extensions are constructed in this way. 

Further discussions lead by Goulnara Arzhantseva covered various topics that included Lubotzky's conjecture and its connection to wall structures.


Third Workshop, November 12 - 13, 2024

The third workshop took place at the University of Vienna.


Abstracts (in pdf)

Tuesday, November 12, 2024
15:00 - 16:45
Tatiana Jajcayova (Comenius University): Combinatorial Methods in Inverse Semigroups
SR-08


Wednesday, November 13, 2024
9:15 - 10:00
Christopher Cashen (University of Vienna): Biggs Colored Tree Groups Containing the Alternating Groups
SR-06
10:15 - 11:00
Dominika Zavacka (Comenius University): Algorithmic Approach to Obtaining Values of (k,g)-Spectra
SR-06
12:00 - 14:00
Lunch
TBA
14:00 - 14:45
Goulnara Arzhantseva (University of Vienna): Large Girth Graphs with Bounded Diameter-by-Girth Ratio
 BZ-09
15:00 - 18:00
Discussion
BZ-09


Abstracts (in pdf)



For further information contact: Robert Jajcay or Goulnara Arzhantseva





Last modified 11/19/2024 14:46:30