Marston Conder
- Distinguished Professor of Mathematics (and former Co-Director of the
New Zealand Institute of Mathematics and its Applications (the
NZIMA))
- Email: m.conder@auckland.ac.nz
- Telephone: +64 9 9238879
- Fax: +64 9 3737457
- Office: Rm 417 SMIS/Physics building
Research interests
My main areas of interest are group theory and graph theory (sections 20 and
05 in Math Reviews). I am especially interested in the methods and applications of combinatorial group theory, including computational techniques for handling finitely-presented groups and their images.
Publications
Click where underlined for a list of my refereed academic
publications
and some
preprints
of recent papers (available as postscript files).
Lists of regular maps, hypermaps and polytopes, trivalent symmetric graphs, and surface actions
Click where underlined to see and download recently-found lists of
Regular/chiral maps and hypermaps
- all
orientable regular maps
on surfaces of genus 2 to 101, up to isomorphism and duality,
with defining relations for their automorphism groups
- all
non-orientable regular maps
on surfaces of genus 2 to 202, up to isomorphism and duality,
with defining relations for their automorphism groups
- all
chiral (irreflexible) orientably-regular maps
on surfaces of genus 2 to 101, up to isomorphism, duality and reflection,
with defining relations for their automorphism groups
- all
proper orientable regular hypermaps
on surfaces of genus 2 to 101, up to isomorphism and triality,
with defining relations for their automorphism groups [WARNING: this is a 4.34MB file!]
- all
proper non-orientable regular hypermaps
on surfaces of genus 2 to 202, up to isomorphism and triality,
with defining relations for their automorphism groups
- all
proper chiral orientably-regular hypermaps
on surfaces of genus 2 to 101, up to isomorphism, triality and reflection,
with defining relations for their automorphism groups
- New!! [August 2012] all
reflexible orientable regular maps on surfaces of genus 2 to 301,
up to isomorphism and duality, with defining relations for their automorphism groups
- New!! [August 2012] all
chiral (irreflexible) orientably-regular maps on surfaces of genus 2 to 301,
up to isomorphism, duality and reflection, with defining relations for their automorphism groups
- New!! [December 2012] all
non-orientable regular maps of genus 2 to 602,
up to isomorphism, duality and reflection, with defining relations for their automorphism groups
- New!! [December 2012] all
rotary maps on closed surfaces with up to 1000 edges, up to isomorphism and duality and other transformations (including Petrie duality and opposite, when the map is fully regular, and missor image when the map is chiral)
- New!! [December 2012] all
fully regular maps on closed surfaces with up to 1000 edges,
up to isomorphism and transformation under the six "Wilson" operators (duality, Petrie duality, opposite, etc.)
- New!! [December 2012] all
chiral rotary maps on orientable surfaces with up to 1000 edges,
up to isomorphism, mirror image and duality
Group actions on surfaces
- all
quotients of triangle groups
that act on compact Riemann surfaces of genus 2 to 101, up to isomorphism, duality/triality and reflection,
with defining relators (normal generators for the kernel) [WARNING: this is a 4.0MB file!]
- all
large groups of automorphisms
of compact Riemann surfaces of genus 2 to 101, up to equivalence of the group action,
listed by the type of Fuchsian group (with triangular or quadrangular signature),
along with defining relators (normal generators for the kernel) [WARNING: this is a 22.8MB file!]
- all
large groups of automorphisms
of compact Riemann surfaces of genus 2 to 101, up to equivalence of the group action,
listed by genus, along with the type of Fuchsian group (with triangular or quadrangular signature),
and group defining relators (normal generators for the kernel) [WARNING: this is a 25.6MB file!]
- New!! [August 2012] a summary of the
maximum orders of group actions on compact Riemann surfaces of genus 2 to 301, with signature types for the actions that have the maximum order
- New!! [August 2012] a summary of the
maximum orders of group actions on compact non-orientable Klein surfaces of genus 3 to 302, with signature types for the actions that have the maximum order
- New!! [June 2013] a summary of the strong symmetric genus of all groups of order 2 to 127, including the signature types for the actions of the group on (orientable) surfaces of the corresponding genus
- New!! [June 2013] a list of all the finite groups with strong symmetric genus 2 to 32, including the signature types for the actions of the group on (orientable) surfaces of the corresponding genus
- New!! [June 2013] a summary of the symmetric genus of all groups of order 2 to 127, including the signature types for the actions of the group on (orientable) surfaces of the corresponding genus
- New!! [June 2013] a list of all the finite groups with symmetric genus 2 to 32, including the signature types for the actions of the group on (orientable) surfaces of the corresponding genus
- New!! [June 2013] a summary of the symmetric cross-cap number of all groups of order 2 to 127, including the signature types for the actions of the group on (non-orientable) surfaces of the corresponding genus
- New!! [June 2013] a list of all the finite groups with symmetric cross-cap number 3 to 65, including the signature types for the actions of the group on (non-orientable) surfaces of the corresponding genus
Symmetric graphs
Regular/chiral polytopes
- New!! [June 2012] all
regular polytopes with up to 2000 flags,
up to isomorphism and duality, ordered by the number of flags under each rank, excluding those of rank 2 (regular polygons) and
the degenerate examples that have a '2' in their Schlaefli symbol
- New!! [June 2012] all
regular polytopes with up to 2000 flags,
up to isomorphism and duality, ordered by their type under each rank, excluding those of rank 2 (regular polygons) and
the degenerate examples that have a '2' in their Schlaefli symbol
- New!! [September 2012] all
chiral polytopes with up to 2000 flags,
up to isomorphism, reflection and duality, ordered by the number of flags under each rank
- New!! [September 2012] all
chiral polytopes with up to 2000 flags,
up to isomorphism, reflection and duality, ordered by their type under each rank
These things were obtained (from August 2006 onwards) with the help of the new "LowIndexNormalSubgroups"
routine in MAGMA.
Other information and useful contacts
- The
New Zealand Mathematical Society
- The
New Zealand Journal of Mathematics
- Our
Centre for Discrete Mathematics and Theoretical Computer Science
- The
Group Pub Forum
- The
World Combinatorics Exchange
- The
- The
- The
- The
Graph Theory White Pages
- Gordon Royle's
Combinatorial catalogues
- The
Mathematics Genealogy Project website.
Photos
Click below for links to some photos from my recent visits to
Address
Prof. M.D.E. Conder
Department of Mathematics
University of Auckland
Private Bag 92019, Auckland
NEW ZEALAND