##### SymOmega

SymOmega is a mathematical blog run by three CMSC Mathematicians, Michael Giudici, John Bamberg and Gordon Royle, including a recent newsflash on Sudoku!

##### Arxiv

Find in one click all the publications of our members that are deposited on the Arxiv.

##### Conferences

### International Workshop on Hadamard Matrices and their Applications at RMIT, November 28 ñ 30 2011

In honour of Kathy Horadam, author of Hadamard Matrices and their Applications, an international workshop was held in Royal Melbourne Institute of Technology (RMIT University) in Melbourne. Cheryl Praeger opened the conference. *Website*.

### Victorian Algebra Conference, December 01-02 2011

Michael Giudici and John Bamberg attended the annual Victorian Algebra Conference, held this time at La Trobe University. John Bamberg gave the opening plenary "Algebraic combinatorics applied to finite geometry". Michael Giudici gave a talk entitled "Rank 3 permutation groups" *Website**.*

### 35 ACCMCC Monash, December 5-9 2011

Cheryl Praeger was an invited speaker at Monash University. She gave a talk on Symmetry of codes in graphs. John gave a talk entitled "Low dimensional models of the split Cayley hexagon", Michael Giudici spoke about "Generalised quadrangles with a group acting primitively on points and lines" and Gordon Royle spoke on "Minimum degree, graph minors and binary matroids". *Website*.

### AMSI workshop, February 01-03 2012

John Bamberg, Alice Devillers, Michael Giudici, Cai-heng Li, Cheryl Praeger and Akos Seress will attend AMSI workshop on 'Connecting finite and infinite mathematics through symmetry' February 1-3 *Website*.

### Symmetries of Discrete Objects, February 2012

Michael Giudici and Akos Seress will attend Symmetries of Discrete Objects in Queenstown, New Zealand. *Website*

##### Recent and upcoming visitors

Jan Saxl, University of Cambridge, 26 December 2011- 31 January 2012

Eric Swartz, University of Binghamton, 4 January - 27 January 2012

Martin Liebeck, Imperial College 06 January -31 January 2012

Gabriel Verret, University of Ljubljana, 01 February - 01 March 2012

Harald Helfgott, ENS, Paris, March 2012

##### News

Cheryl Praeger was a member of the Review Panel for the Research Council of Norway, reviewing research in the Mathematical Sciences (October 9-15 2011).

Congratulations to Neil Gillespie whose PhD thesis "Neighbour transitivity on codes in Hamming Graphs" has been classified as pass.

ARC Grant success: several CMSC members were obtained ARC Discovery Project grants in the last round: John Bamberg and Cai-Heng Li, "Cayley graphs and their associated geometric and combinatorial objects"; andMichael Giudici, "Harnessing symmetry to advance the study of graphs'.See

*this link*for research grants received by our research group.On 7 November 2011, the School held its second Showcase of Modern Mathematics which was attended by many Year 9 and 10 students. John, Michael and Alice were involved in organising the event. Gordon entertained the students by giving a talk on Sudoku.

John Bamberg and Sylvia Morris held NYSF 13th and 19th January 2012. They gave a presentation entitled "Maths: not what you think it is".

##### Papers

### Published papers

N. Ankaralioglu, A. Seress: Computing tensor decompositions of finite matrix groups, Discrete Mathematics and Theoretical Computer Science 13 (2011), issue 4, 5-14.

Ashraf Daneshkhah, Alice Devillers and Cheryl E. Praeger, Symmetry properties of subdivision graphs, Discrete Mathematics, 312 , pp. 86-93 (2012).

Alice Devillers, Michael Giudici, Cai Heng Li and Cheryl E. Praeger, An infinite family of biquasiprimitive 2-arc transitive cubic graphs, Journal of Algebraic Combinatorics: Volume 35, Issue 2 (2012), Page 173-192.

Alice Devillers, Michael Giudici, Cai Heng Li and Cheryl E. Praeger, Locally s-distance transitive graphs, Journal of Graph Theory, 69(2), pp. 176-197 (2012).

Alice Devillers, Michael Giudici, Cai Heng Li, Geoffrey Pearce and Cheryl E. Praeger, On imprimitive rank 3 permutation groups, J. London Math. Soc., 84, pp. 649-669 (2011) .

Michael Giudici, C.H. Li, C. E. Praeger and J. Xu,, Invariant relations and Aschbacher classes of finite linear groups, Electron. J. Combin. 18 (1) (2011), Research Paper 225, 33pp.

A. Seress, T.-L. Wong, X. Zhu: Distinguishing labelling of the actions of almost simple groups, Combinatorica 31 (2011), 489-506.

### Accepted papers

John Bamberg, Alice Devillers, and Jeroen Schillewaert, Weighted intriguing sets of finite generalised quadrangles. Accepted in Journal of Algebraic Combinatorics.

John Bamberg, Nicola Durante, Low dimensional models of the finite split Cayley hexagon, Accepted in Contemporary Mathematics.

John Bamberg, Michael Giudici, Martin Liebeck, Cheryl Praeger and Jan Saxl, The classification of almost simple 3?2-transitive groups. to appear in Trans. Amer. Math. Soc.

John Bamberg, Michael Giudici, Joy Morris, Gordon Royle, Pablo Spiga, Generalised quadrangles with a group of automorphisms acting primitively on points and lines, Accepted in JCTA.

John Bamberg, Michael Giudici and Gordon F. Royle, Hemisystems of small flock generalized quadrangles, Accepted in Des. Codes .Cryptogr.

S. Fujita, A. Gyarfas, C. Magnant and A. Seress: Disconnected colors in generalized Gallai colorings, Accepted in J. Graph Theory.

Neil Gillespie and Cheryl Praeger. Neighbour transitivity on codes in Hamming graphs. Accepted in Des. Codes Crypt .

Michael Giudici , Geoffrey Pearce, and Cheryl Praeger. Basic and degenerate pregeometries Accepted in Eur. J. Combin.

Cheryl Praeger, Pablo Spiga and Gabriel Verret. Bounding the size of a vertex-stabiliser in a finite vertex-transitive graph. Accepted in J. Combin. Theory, Series B.

Cheryl Praeger and Akos Seress. Regular semisimple elements and involutions in finite general linear groups of odd characteristic. Accepted in Proc. Amer. Math. Soc .

Cheryl Praeger and Csaba Schneider. Embedding permutation groups into wreath products in product action J. Austral. Math. Soc. Accepted January 16, 2012.

P. Puliyambalath, A. Seress, I. Weisz: All lambda-designs with small lambda are type-1, Accepted in J. Combinatorial Designs.

### Submitted papers

Carmen Amarra, Michael Giudici and Cheryl Praeger, Symmetric diameter two graphs with affine-type vertex-quasiprimitive automorphism group.

Carmen Amarra, Michael Giudici and Cheryl Praeger. Symmetric diameter two graphs with affine-type vertex-quasiprimitive automorphism group.

Timothy Burness, Cheryl Praeger, and Akos Seress. Extremely primitive sporadic and alternating groups.

Alice Devillers, Wei Jin, Cai Heng Li and Cheryl E. Praeger, On s-geodesic transitive graphs.

Alice Devillers, Wei Jin, Cai Heng Li and Cheryl E. Praeger, Line graphs and 2-geodesic transitivity.

Neil Gillespie and Cheryl Praeger. Uniqueness of certain completely regular Hadamard codes.

Alice C. Niemeyer and Cheryl Praeger. Elements in finite classical groups whose powers have large 1-Eigenspaces.

Akos Seress, 2-closed Majorana representations