New leadership
In January, Michael Giudici became the Director of the centre. John Bamberg has agreed to be the new Deputy Director. Everyone wishes to express their thanks to Gordon for his years of service!
News
Dan Hawtin's thesis "Algebraic symmetry of codes in Hamming graphs" supervised by Neil Gillespie, Michael Giudici and Cheryl Praeger was passed in October. Congratulations to Dan! He is now doing a postdoc with Robert Bailey at Grenfell Campus, Memorial University of Newfoundland.
Alexander Bors arrived in October for a two year visiting research position as a Schrödinger Fellow funded by the Austrian Science Foundation.
Cheryl Praeger was the Australian delegate at the 32nd General Assembly of the International Council for Science (ICSU), which was hosted by the Academy of Sciences located in Taipei (23-24 October), and also at the joint meeting of the general assemblies of ICSU and the International Social Science Council (25-26 October). The latter joint general assembly approved a merger between the two organisations - the new International Science Council (ISC) will have its inaugural meeting in Paris in July 2018.
Alexander Chua (supervised by Michael Giudici and Luke Morgan) and Timothy Harris (supervised by John Bamberg) both received first class honours degrees. Congratulations to Alexander and Tim! They are both now entering the Medicine programme at UWA.
Michael Giudici and Cheryl Praeger were presented with the 2012 Hall Medal and the 2011 Euler Medal (respectively). These medals of the Institute of Combinatorics and its Applications were awarded at the conference dinner of the 5ICC in Melbourne.
Cheryl Praeger was awarded an Honorary Doctor of Mathematics by the University of Queensland. It was conferred during a UQ graduation ceremony on December 9 at which she gave the Graduation Speech.
In January Kyle Rosa (supervised by Luke Morgan and Cheryl Praeger) submitted his MPhil thesis entitled "Structure, Covers, and bounds of semiprimitive groups".
Wei Jin (Jiangxi University of Finance and Economics) arrived in February to begin a one year visiting research position, funded by the China Scholarship Council.
In February, Michael Giudici was promoted to Professor! Congratulations to Michael!
Cheryl Praeger attended meetings of the Inter-Academy Partnership-Research Executive Board at the Royal Society of London, February 8.
Cheryl Praeger will give a colloquium lecture at Primorska University, Slovenia, March 16.
Cheryl Praeger will be awarded an honorary doctorate from Primorska University, Slovenia, March 15, on the occasion of the 15th anniversary of the establishment of the university.
Emilio Pierro has been appointed to a postdoctoral position in CMSC, working with Stephen Glasby and Cheryl Praeger. We expect him to arrive in mid-April for a year.
Michael Giudici is now an editor of the Journal of Group Theory.
Jon Xu (University of Melbourne), supervised by John Bamberg and Arun Ram, has recently submitted his PhD thesis "Chevalley groups and finite geometry".
Dave Roberson (Technical University of Denmark) will be the 2018 Cheryl E. Praeger Visiting Research Fellow.
John Bamberg was awarded the 2017 Hall Medal of the ICA. Congratulations to John!
Annual research retreat
The annual CMSC research retreat was held over the week of 12-16 February this year. We were hosted in the lovely Avon Valley at Moondyne Country Convention.
We are very grateful to our hosts Christine and Peter for taking such excellent care of us. We welcomed two international visitors this year, Tim Boykett of Time's Up and Dillon Mayhew (University of Wellington). We were also pleased to welcome back Cai Heng Li, now at Southern University of Science and Technology China.
We had no less than twelve research problems posed this year, and the seventeen participants divided into teams to tackle these. Swift progress was made on some problems, and on others we certainly learnt something.
Saul Freedman gave two excellent lectures based on what he had absorbed at the 2017 Summer School in Venice. In the social time, some members bravely hiked in 35 degree heat to a nearby dam, whilst others lounged in the pool. We look forward to sharing the output of the retreat in publications.
Visitors
Faezeh Alizadeh, a PhD student from Shahid Rajaee Teacher Training University, Tehran, Iran is visiting Cheryl Praeger and Stephen Glasby for one year.
Dillon Mayhew (Victoria University of Wellington) visited Gordon Royle in February.
Scott Harper (PhD student at University of Bristol) visited in February for several weeks, funded by the Cecil King Travel Scholarship from the London Mathematical Society.
Alejandra Ramos Rivera (PhD student at University of Primorska) will visit for 3 months from March, funded by the Erasmus program.
Colva Roney-Dougal (University of St Andrews) will visit from 26 March to 20 April.
Cheryl E. Praeger Visiting Fellow: Dave Roberson (Technical University of Denmark) will visit in late March.
John Sheekey (UCD Dublin) will visit in July/August to work with John Bamberg.
Groups and Combinatorics Seminars
Stephen Glasby has created a website with historical and current abstracts for our seminar series:
SymOmega
SymOmega is a mathematical blog run by CMSC members John Bamberg, Michael Giudici and Gordon Royle.
Conferences
The Tutte Centenary Retreat, Matrix Mathematical Research Institute, Melbourne, 26 November-2 December 2017. Michael Giudici, Luke Morgan, Cheryl Praeger and Gordon Royle attended.
5th International Combinatorics Conference (5ICC), Monash University, Australia, 4-9 December 2017. Michael Giudici, Stephen Glasby, Dan Hawtin, Mark Ioppolo, Luke Morgan, Cheryl Praeger and Gordon Royle attended and gave talks.
2018 NZMRI Summer Workshop on Algebra and Representation Theory, Nelson, New Zealand, 7-13 January 2018. Saul Freedman attended.
International Workshop on Symmetries of Graph and Networks at TSIMF, Sanya, Hainan, China. 29 January-2 February 2018. Cheryl Praeger and Luke Morgan attended.
Ischia Group Theory 2018, Ischia (Naples, Italy), 19-23 March 2018. Cheryl Praeger will be a main speaker.
John Bamberg is an invited speaker for Combinatorics 2018 , Arco di Trento, 3-9 June 2018.
Papers
Published papers
Adel Alahmadi, Stephen P. Glasby, Cheryl E. Praeger, Patrick Sole and Bahattin Yildiz. Twisted centralizer codes. Linear Algebra and its Applications 524 (2017), 235-249. arxiv.
Adel Alahmadi, Stephen P. Glasby and Cheryl E. Praeger. On the dimension of twisted centralizer codes. Finite Fields Appl. 48 (2017), 43--59. arxiv.
M. Aljohani, John Bamberg and P. J. Cameron. Synchronization and separation in the Johnson schemes. Portugaliae Mathematica 74 (2018), no. 3, pp. 213-232.
John Bamberg, Anurag Bishnoi and Gordon F. Royle, On regular induced subgraphs of generalized polygons. Journal of Combinatorial Theory Series A 158 (2018), pp. 254-275.
John Bamberg, Joanna B. Fawcett and Jesse Lansdown. Bruck nets and partial Sherk planes. Journal of the Australian Mathematical Society 104 (2018), no. 1, 1-12.
John Bamberg, Tomasz Popiel and Cheryl E. Praeger. Point primitive, line-transitive generalised quadrangles of holomorph type. J. Group Theory 20 (2017), 269-287. arxiv.
John Bamberg, Cai Heng Li and Eric A. Swartz. A classification of finite antiflag-transitive generalized quadrangles. Transactions of the American Mathematical Society 370 (2018), 3, 1551-1601.
John D. Dixon, Cheryl E. Praeger and Ákos Seress. Strong involutions in finite special linear groups of odd characteristic. Journal of Algebra. 498, (2018), 413-447.
Joanna B. Fawcett, Michael Giudici, Cai Heng Li, Cheryl E. Praeger, Gordon Royle and Gabriel Verret. Primitive permutation groups with a suborbit of length 5 and vertex-primitive graphs of valency 5. Journal of Combinatorial Theory, Series A, 157, (2018), 247-266. arxiv
Michael Giudici and Luke Morgan. A theory of semiprimitive groups. Journal of Algebra, 503, (2018), 146-185.
Yian Xu. On constructing normal and non-normal Cayley graphs. Discrete Mathematics, Volume 340, (2017), 2972-2977.
Accepted papers
John Bamberg, Stephen P. Glasby, Luke Morgan and Alice C. Niemeyer. Maximal linear groups induced on the Frattini quotient of a p-group. Accepted in Journal of Pure and Applied Algebra. arxiv
David Pearce and Gordon Royle. Chapter on "Computational Resources", in the Handbook of the Tutte Polynomial (to be published 2018).
Cheryl E. Praeger and Csaba Schneider. Group factorisations, uniform automorphisms and permutation groups of simple diagonal type. Accepted in Israel J. Math. arxiv.
Submitted papers
John Bamberg, T. Harris, T. Penttila. On abstract ovals with Pascalian secant lines.
John Bamberg, Cheryl E. Praeger and Binzhou Xia. The covering radii of the 2-transitive unitary, Suzuki, and Ree groups.
Alexander Bors. Computation of orders and cycle lengths of automorphisms of finite solvable groups.
Alexander Bors. Worst-case approximability of functions on finite groups by endomorphisms and affine maps.
Alexander Bors. Finite groups with a large automorphism orbit.
Timothy C. Burness and Michael Giudici. On the Saxl graph of a permutation group.
Alexander Y. Chua, Michael Giudici and Luke Morgan. Coprime Subdegrees of Twisted Wreath Permutation Groups.
Stephen P. Glasby and Cheryl E. Praeger. On the minimum distance of intertwining codes.
Stephen P. Glasby, Cheryl E. Praeger, Kyle Rosa and Gabriel Verret. Bounding the composition length of primitive permutation groups and completely reducible linear groups.
Stephen P. Glasby, Cheryl E. Praeger and Binzhou Xia. Norman involutions and tensor products of unipotent Jordan blocks.
Stephen P. Glasby, Alice Niemeyer and Tomasz Popiel. On the second-largest Sylow subgroup of a finite simple group of Lie type.
Luke Morgan, Primož Potočnik and Gabriel Verret. Arc-transitive digraphs of given out-valency and with blocks of given size.
Cheryl E. Praeger, Jacqui Ramagge and George Willis. A graph-theoretic description of scale-multiplicative semigroups of automorphisms.