Recent news and events

Marston D.E. Conder

Short description of activities

  • Project on GI-graphs. Marston Conder, Tomaž Pisanski and Arjana Žitnik investigated a new class of graphs with interesting geometric properties, determined their symmetries, and classified those which are edge-transtive or vertex-transtive and those which are Cayley graphs. This is written up in a paper that is about to be submitted:
  • Project on regular and chiral polytopes. Marston Conder used computational methods to determine all abstract regular polytopes having up to 2000 flags. The complete list is available online, in two forms: one ordered by number of flags (for each rank), and the other ordered by the Coxeter/Schlaefli type. See http://www.math.auckland.ac.nz/~conder/, under "Lists of regular maps, hypermaps and polytopes, trivalent symmetric graphs, and surface actions". A similar project is underway with Dimitri Leemans to find all chiral polytopes (with maximal symmetry by rotation) having up to 100 flags.
  • Project on regular covers of arc-transitive graphs. Marston Conder and his student Jicheng Ma (University of Auckland) developed a new method for determining all symmetric regular covers of symmetric cubic graphs, with abelian covering group, and applied this to find all such covers of $K_4$, $K_{3,3}$, $Q_3$, the Petersen graph and the Heawood graph. This work is written up in two papers, as follows:
  • Project on regular maps with simple underlying graphs. Marston Conder and his student Jicheng Ma (University of Auckland) constructed families of regular maps on orientable surfaces with simple underlying graph, to show that these occur on orientable surface of over 83\% of all possible genera.

Awards and special achievements

  • Marston Conder was appointed to a Distinguished Professorship at the University of Auckland (one of 18 across all subject areas)
  • Marston Conder was selected by the American and New Zealand Mathematical Societies as the first "Maclaurin Lecturer", to make a tour of universities in the USA in the first half of 2013
  • Marston Conder was awarded a two-year James Cook Fellowship by the Royal Society of New Zealand, for full-time research from March 2012 to February 2014

Conferences

  • Marston Conder, "Regular maps admitting all Wilson operators", Invited lecture at minisymposium on Group Actions, 7th Slovenian International Conference on Graph Theory, Bled, Slovenia, June 2011
  • Marston Conder, "The smallest regular polytopes of each rank", Invited lecture at minisymposium on Polytopes and Incidence Geometries, 7th Slovenian International Conference on Graph Theory, Bled, Slovenia, June 2011
  • Marston Conder, "Computational methods in Algebraic Graph Theory" Invited mini-series of lectures at Summer School on Algebraic Graph Theory, Rogla, Slovenia, June 2011
  • Marston Conder, "Regular Maps and Polytopes", Invited series of six lectures at Fields Institute, Toronto, Canada, October 2011
  • Marston Conder, "Large groups acting on surfaces of given genus, and the symmetric genus of a given group",  Invited lecture at Workshop on Symmetry and Rigidity, Fields Institute, Toronto, Canada, October 2011
  • Marston Conder, "The smallest regular polytopes of each rank", 35th Australasian Conference on Combinatorial Mathematics & Combinatorial Computing, Melbourne, Australia, December 2011
  • Marston Conder, "A new approach to finding covers of arc-transitive graphs", Invited lecture at Workshop on Algebraic, Topological and Complexity Aspects of Graph Coverings, Eugene, Oregon, January 2012
  • Marston Conder, "Finitely-presented groups in MAGMA", Mini-course at Conference on Symmetries of Discrete Objects, Queenstown, New Zealand, February 2012
  • Marston Conder, "The orders of symmetric graphs", Invited lecture at minisymposium on Graphs and Groups,    SIAM Discrete Mathematics Conference, Halifax, Canada, June 2012