Page 337 - 8th European Congress of Mathematics ∙ 20-26 June 2021 ∙ Portorož, Slovenia ∙ Book of Abstracts
P. 337
SYMMETRY OF GRAPHS, MAPS AND POLYTOPES (MS-9)
family of designs. Whether the family is infinite depends on the Bunyakovsky Conjecture about
the prime numbers, and the number of examples in a certain range seems to be related to another
number theoretic conjecture, the Bateman—Horn Conjecture. We are grateful to Sasha Zvonkin
and Gareth Jones for their interest in the number theoretic puzzles our construction spawned:
their computer enumerations related to these conjectures showed that there are 12, 357, 532 de-
signs in the family where the point-partition has classes of prime cardinality less than 108.
Edge-biregular maps
Olivia Reade, olivia.jeans@open.ac.uk
The Open Uniersity, United Kingdom
A regular map is an embedding of a graph on a surface such that the automorphism group acts
regularly, that is semi-regularly and transitively, on the set of flags of the map. A map with an
alternate edge colouring is such that every edge is coloured with one of two colours, and the
edges are arranged so that any pair of edges which are adjacent with respect to the embedding
have one edge of each colour. An edge-biregular map has an assigned alternate edge colouring
and is such that the colour-preserving automorphism group acts regularly on the corners of the
map. This poster presents a classification of these maps for the torus and the Klein bottle as
well as a classification for when the colour-preserving automorphism group is dihedral.
Distinguishing discrete groups by their finite quotients
Alan Reid, alan.reid@rice.edu
Rice University, United States
We will survey work on when certain discrete groups arising from low-dimensional topology
and geometry can be distinguished by the set of their finite quotients, or equivalently, when the
profinite completion of a discrete group determines the group up to isomorphism.
On compact Riemann surfaces and hypermaps of genus p + 1 where p is
prime
Sebastián Reyes-Carocca, sebastian.reyes@ufrontera.cl
Universidad de La Frontera, Chile
Coauthors: Gareth A. Jones, Milagros Izquierdo
In this talk we shall discuss a classification of compact Riemann surfaces of genus g, where
g − 1 is a prime p, which have a group of automorphisms of order ρ(g − 1) for some integer
ρ 1. We also provide isogeny decompositions of their Jacobian varieties. As a consequence,
a classification of orientably regular hypermaps of genus p + 1 with automorphism group of
order divisible by the prime p is obtained.
335
family of designs. Whether the family is infinite depends on the Bunyakovsky Conjecture about
the prime numbers, and the number of examples in a certain range seems to be related to another
number theoretic conjecture, the Bateman—Horn Conjecture. We are grateful to Sasha Zvonkin
and Gareth Jones for their interest in the number theoretic puzzles our construction spawned:
their computer enumerations related to these conjectures showed that there are 12, 357, 532 de-
signs in the family where the point-partition has classes of prime cardinality less than 108.
Edge-biregular maps
Olivia Reade, olivia.jeans@open.ac.uk
The Open Uniersity, United Kingdom
A regular map is an embedding of a graph on a surface such that the automorphism group acts
regularly, that is semi-regularly and transitively, on the set of flags of the map. A map with an
alternate edge colouring is such that every edge is coloured with one of two colours, and the
edges are arranged so that any pair of edges which are adjacent with respect to the embedding
have one edge of each colour. An edge-biregular map has an assigned alternate edge colouring
and is such that the colour-preserving automorphism group acts regularly on the corners of the
map. This poster presents a classification of these maps for the torus and the Klein bottle as
well as a classification for when the colour-preserving automorphism group is dihedral.
Distinguishing discrete groups by their finite quotients
Alan Reid, alan.reid@rice.edu
Rice University, United States
We will survey work on when certain discrete groups arising from low-dimensional topology
and geometry can be distinguished by the set of their finite quotients, or equivalently, when the
profinite completion of a discrete group determines the group up to isomorphism.
On compact Riemann surfaces and hypermaps of genus p + 1 where p is
prime
Sebastián Reyes-Carocca, sebastian.reyes@ufrontera.cl
Universidad de La Frontera, Chile
Coauthors: Gareth A. Jones, Milagros Izquierdo
In this talk we shall discuss a classification of compact Riemann surfaces of genus g, where
g − 1 is a prime p, which have a group of automorphisms of order ρ(g − 1) for some integer
ρ 1. We also provide isogeny decompositions of their Jacobian varieties. As a consequence,
a classification of orientably regular hypermaps of genus p + 1 with automorphism group of
order divisible by the prime p is obtained.
335
