Page 275 - 8th European Congress of Mathematics ∙ 20-26 June 2021 ∙ Portorož, Slovenia ∙ Book of Abstracts
P. 275
CONFIGURATIONS (MS-81)
the lines. In a series of papers, Branko Grünbaum showed that geometric (n4) configurations
exist for all n ≥ 24, using a series of geometric constructions later called the “Grünbaum Cal-
culus”. In this talk, we will show that for each k > 4, there exists an integer Nk so that for all
n ≥ Nk, there exists at least one (nk) configuration, by generalizing the Grünbaum Calculus
operations to produce more highly incident configurations. This is joint work with Gábor Gévay
and Tomaž Pisanski.
Transitions between configurations
Gábor Gévay, gevay@math.u-szeged.hu
University of Szeged, Hungary
In this talk we briefly review (without aiming at completeness) various procedures by means
of which new configurations can be obtained from old configurations. Among them, there
are binary operations, like e.g. the Cartesian product and the incidence sum. Several other
operations are collectively called the Grünbaum calculus. The incidence switch operation can
be defined on the level of incidence graphs (also called Levi graphs) of configurations, and in
some cases it is in close connection with realization problems of configurations as well as with
incidence theorems. Considering point-line, point-circle and point-conic configurations, there
are interesting ad hoc constructions by which from a configuration of one of these geometric
types another one can be derived, thus realizing transitions between configurations in a very
general sense. We also present interesting examples and applications. The most recent results
mentioned in this talk are based on joint work with Tomaž Pisanski and Leah Wrenn Berman.
Combinatorial Configurations and Dessins d’Enfants
Milagros Izquierdo, milagros.izquierdo@liu.se
Linköping University, Sweden
In this talk we give an overview, with many examples, of how dessins d’enfants (maps and
hypermaps) on Riemann surfaces produce point-circle realisations on higher genus of combi-
natorial configurations. The symmetry of the hypermap is transfered to the symmetry of the
configuration.
Highly symmetric configurations
Jurij Kovicˇ, jurij.kovic@siol.net
UP FAMNIT, Koper, Slovenia, and IMFM, Ljubljana, Slovenia
Coauthor: Aleksander Simonicˇ
In the talk some general methods and special techniques for the construction of highly symmet-
ric configurations will be presented.
As an application of these theoretical principles, some examples of highly symmetric spatial
geometric configurations of points and lines with the symmetry of Platonic solids will be given.
273
the lines. In a series of papers, Branko Grünbaum showed that geometric (n4) configurations
exist for all n ≥ 24, using a series of geometric constructions later called the “Grünbaum Cal-
culus”. In this talk, we will show that for each k > 4, there exists an integer Nk so that for all
n ≥ Nk, there exists at least one (nk) configuration, by generalizing the Grünbaum Calculus
operations to produce more highly incident configurations. This is joint work with Gábor Gévay
and Tomaž Pisanski.
Transitions between configurations
Gábor Gévay, gevay@math.u-szeged.hu
University of Szeged, Hungary
In this talk we briefly review (without aiming at completeness) various procedures by means
of which new configurations can be obtained from old configurations. Among them, there
are binary operations, like e.g. the Cartesian product and the incidence sum. Several other
operations are collectively called the Grünbaum calculus. The incidence switch operation can
be defined on the level of incidence graphs (also called Levi graphs) of configurations, and in
some cases it is in close connection with realization problems of configurations as well as with
incidence theorems. Considering point-line, point-circle and point-conic configurations, there
are interesting ad hoc constructions by which from a configuration of one of these geometric
types another one can be derived, thus realizing transitions between configurations in a very
general sense. We also present interesting examples and applications. The most recent results
mentioned in this talk are based on joint work with Tomaž Pisanski and Leah Wrenn Berman.
Combinatorial Configurations and Dessins d’Enfants
Milagros Izquierdo, milagros.izquierdo@liu.se
Linköping University, Sweden
In this talk we give an overview, with many examples, of how dessins d’enfants (maps and
hypermaps) on Riemann surfaces produce point-circle realisations on higher genus of combi-
natorial configurations. The symmetry of the hypermap is transfered to the symmetry of the
configuration.
Highly symmetric configurations
Jurij Kovicˇ, jurij.kovic@siol.net
UP FAMNIT, Koper, Slovenia, and IMFM, Ljubljana, Slovenia
Coauthor: Aleksander Simonicˇ
In the talk some general methods and special techniques for the construction of highly symmet-
ric configurations will be presented.
As an application of these theoretical principles, some examples of highly symmetric spatial
geometric configurations of points and lines with the symmetry of Platonic solids will be given.
273
