15:00 - 15:30
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Jan Pastorek (Comenius University): Search for correspondences between operations on partial automorphisms and k-dimensional Weisfeiler-Leman algorithm
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M-III
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15:30 - 16:00
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Stefania Glevitzka (Comenius University): Vertex-transitive closures of graphs
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M-III
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16:00 -
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Closing Remarks
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M-III
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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.
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Registration
Attending the workshop is free of charge. Everyone interested in the material
covered in the lectures is welcome to attend.
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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:
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14:00 - 15:00
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Universal construction of cyclic complementary extensions of finite groups inspired by the structure of automorphism groups of regular Cayley maps
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Seminar Room 4
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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.
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Tuesday, November 12, 2024
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15:00 - 16:45
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Tatiana Jajcayova (Comenius University): Combinatorial Methods in Inverse Semigroups
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SR-08
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Wednesday, November 13, 2024
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9:15 - 10:00
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Christopher Cashen (University of Vienna): Biggs Colored Tree Groups Containing the Alternating Groups
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SR-06
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10:15 - 11:00
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Dominika Zavacka (Comenius University): Algorithmic Approach to Obtaining Values of (k,g)-Spectra
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SR-06
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14:00 - 14:45
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Goulnara Arzhantseva (University of Vienna): Large Girth Graphs with Bounded Diameter-by-Girth Ratio
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BZ-09
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15:00 - 18:00
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Discussion
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BZ-09
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Fourth Workshop, May 15 - 19, 2025
The fourth workshop took place at the Comenius University.
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10:00 - 11:00
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Goulnara Arzhantseva (University of Vienna): Metric Approximations of
Infinite Groups
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C
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13:30 - 14:30
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Christopher Cashen (University of Vienna): Biggs Colored Tree Groups Containing the Alternating Groups Continued
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B
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14:40 - 15:10
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Martin Macaj (Comenius University): r-Regular Families of Permutations
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B
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15:15 - 15:45
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Pavol Kollar (Comenius University): Enumeration of Large Families of
Combinatorial Objects
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B
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10:00 - 12:00
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Merlin Incerti-Medici and Markus Steenbock (University of Vienna): Discussion on
constructing expanders from self-similar actions on trees
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M-XI
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13:15 - 14:15
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Goulnara Arzhantseva (University of Vienna): Origami Expanders
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M-IX
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14:15 - 17:00
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Discussion
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M-IX
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10:00 - 14:00
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Work on Biggs' Tree Groups and Connections to C* Algebras
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M-126
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Fifth Workshop, November 5 - 10, 2025
The fifth workshop took place at the Smolenice Castle in Slovakia and at the Comenius University
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Wednesday, November 5, 2025, Smolenice Castle
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11:00 - 12:00
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Arrival
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Smolenice Castle
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12:00 - 13:00
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Tatiana Jajcayova: Introductory remarks and progress update
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14:30 - 15:30
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Christopher Cashen (TU Vienna): An application of a family of edge-girth-regular graphs to a problem about the coarse geometry of right-angled Coxeter groups
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15:40 - 16:20
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Pavol Kollar (Comenius University): Boundary matrices and their connection
to de Bruijn graphs
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16:30 - 18:00
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Discussion of the progress on permutation groups generated by involutions
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Thursday, November 6, 2025, Smolenice Castle
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10:00 - 12:00
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Markus Steenbock (University of Vienna): Product set growth for groups acting on trees
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14:00 - 15:00
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Goulnara Arzhantseva (University of Vienna): On minor ex/in- cluded Cayley graphs
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15:00 - 17:00
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Discussion and work in groups
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Friday, November 7, 2025, Smolenice Castle
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9:30 - 10:30
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Jan Pastorek (Comenius University): Partial automorphism inverse monoids
and Maximal Asymmetric Depth of graphs
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10:30 - 12:30
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Work on Biggs' Tree Groups and Connections to C* Algebras
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14:00 - 17:00
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Work on Biggs' Tree Groups and Connections to C* Algebras
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Monday, November 10, 2025, Comenius University
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11:30 - 12:10
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Stefania Glevitzka (Comenius University): Combinatorial aspects of the diameter/girth ratio problem
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M-XII
|
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13:30 - 14:20
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Robert Jajcay (Comenius University): On the connections between Biggs groups, maps and polytopes
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M-XII
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14:30 - 15:00
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Workshop Conclusion and Final Remarks
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M-XII
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Research visit of prof. Arzhantseva, Dec. 10 - 15, 2025
The visit took place at the Comenius University, Faculty of Mathematics, Physics and Computer Science, Bratislava, Slovakia
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As the main purpose of the visit was more intense collaboration between the
Slovakian team members and prof. Arzhantseva, the visit had a different format
and consisted of a series of collaboration meetings taking place
throughout the entire visit.
The theme and aim of the visit and the corresponding discussions was:
Graph C*-algebras, wall structures, and partial automorphisms of graphs
During the visit prof. Arzhantseva discussed individually with prof. Jajcayova
her doctoral students Jan Pastorek and Pavol Kollar and prof. Jajcay's doctoral
student Stefania Glevitzka.
On Dec. 11, all the above mentioned participants attended a presentation of Robert Lukotka from the Department of Computer Science of the Faculty of Mathematics, Physics and Computer Science.
The talk took place as a part of the
Bratislava Graph Theory Seminar and was entitled:
Rich nowhere-zero flows in general graphs
On Dec. 12, all the above mentioned participants attended a presentation of a member of the Slovak team Jan Pastorek.
The talk took place as a part of the
Algebraic Graph Theory Seminar and was entitled:
Forth from Extensions of Partial Automorphisms to the
Weisfeiler–Leman Algorithm & Counting Logic & Bijective Pebble Games—and
Back Again
Abstract:
The graph isomorphism (GI) problem sits in an unresolved position between
P and NP-complete and is polynomially equivalent to computing an orbit
partition of a graph’s automorphism group. The Weisfeiler–Leman (WL)
algorithm is a central combinatorial method for isomorphism testing that
iteratively aggregates local neighbourhood information to approximate this
orbit structure. A partial automorphism of a graph is an isomorphism
between induced subgraphs of a graph. The set of all partial automorphisms
under composition and inverses forms a partial automorphism inverse monoid
which encodes complete algebraic information.
In this talk, we discuss how these viewpoints of WL and partial
automorphisms can be related. In particular, we review four different but
equivalent perspectives on WL and show how they interact. After reviewing
the necessary background, we revisit the k-dimensional WL algorithm and
its logical characterization via bijective pebble games. From duplicator
strategies in the bijective k-pebble game played on two copies of the same
graph, one can collect all pebbled positions into a set of partial
automorphisms of rank at most k. Among others, this set inherits
back-and-forth extension properties from the underlying game.
For further information contact:
Robert Jajcay
or
Goulnara Arzhantseva
