March 2012

Wednesday 07 
11:00  SEMINAR  Groups and Combinatorics Seminar: Coprime subdegrees for primitive permutation groups and completely reducible linear groups

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Groups and Combinatorics Seminar
Cheryl Praeger(UWA)
will speak on
Coprime subdegrees for primitive permutation groups and completely reducible linear groups
at 11am on Wednesday 7th of March in MLR2
Abstract. This work was inspired by a question of Gabriel Navarro
about orbit lengths of groups acting on finite vector spaces, and
is joint work with Pablo Spiga, Silvio Dolfi and Bob Guralnick.
If a finite group H acts irreducibly on a finite vector space V, then we proved that
for every pair of nonzero vectors, their orbit lengths a, b have a nontrivial common factor.
This could be interpreted in the context of permutation groups. The group VH
is an affine primitive group on V and a, b are orbit lengths of the point stabiliser H,
that is, a and b are subdegrees of VH. This raises a question about subdegrees for
more general primitive permutation groups. Coprime subdegrees can arise,
but (we show) only for three of the eight types of primitive groups.
Moreover it is never possible to have as many as three pairwise
coprime subdegrees. All proofs depend on the finite simple group classification.

Wednesday 14 
11:00  SEMINAR  Groups and Combinatorics Seminar:Pentagonal geometries

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Groups and Combinatorics Seminar
John Bamberg (UWA)
will speak on
Pentagonal geometries
at 11am on Wednesday 14th of March in MLR2
Abstract: Jacques Tits introduced generalised polygons in order to geometrically describe groups of Lie type, and as their name suggests, they are generalisations of ordinary regular polygons. In this talk, we look at the concept of a "pentagonal geometry" as a generalisation of the pentagon and the Desargues configuration, in the same vein that the generalised polygons share the fundamental properties of ordinary polygons. (This is joint work with Simeon Ball, Alice Devillers and Klara Stokes).

Wednesday 21 
11:00  SEMINAR  Groups and Combinatorics Seminar:Minorclosed classes of graphs and matroids

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Groups and Combinatorics Seminar
Gordon Royle (UWA)
will speak on
Minorclosed classes of graphs and matroids
at 11am in MLR2 on Wed 21st of March
Abstract: This talk will give a general survey of results and problems relating to characterising classes of graphs and matroids that are closed under taking minors.
All welcome

Wednesday 28 
11:00  SEMINAR  Groups and Combinatorics Seminar: The subspace lattice

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Groups and Combinatorics Seminar
Phill Schultz (UWA)
will speak on
The subspace lattice
at 11am on Wed 28th of March in MLR2
Abstract: I describe algebraically, combinatorially and anatomically the lattice of subspaces of a finite dimensional vector space V. The description allows you to calculate, from given subspaces U and W of V, bases for U + W and UW and for all subspaces and complements of U. Also, you can describe the Hasse Diagram of the lattice of subspaces of V.


April 2012

Wednesday 04 
11:00  SEMINAR  Groups and Combinatorics Seminar: sgeodesic transitive graphs

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Groups and Combinatorics Seminar
Wei Jin (UWA)
will speak on
sgeodesic transitive graphs
at 11am on Wednesday 4th of April in MLR2.
Abstract: In a finite graph Gamma, a geodesic from a vertex u to a vertex v is one of the shortest paths
from u to v, and this geodesic is called an igeodesic if the distance between u and v is i. The graph
Gamma is said to be sgeodesic transitive if the graph automorphism group is transitive on the set of sgeodesics. In this talk, I will compare the sgeodesic transitivity with other two wellknown transitive properties, namely sarc transitivity and sdistance transitivity, and determine the local structure of
2geodesic transitive graphs, and also give some results about the family of locally disconnected
2geodesic transitive but not 2arc transitive graphs.
All welcome

Wednesday 11 
10:30  SEMINAR  Groups and Combinatorics Seminar: Polyhedral complexes, locally compact groups and lattices

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Groups and Combinatorics Seminar
Anne Thomas (Sydney)
will speak on
Polyhedral complexes, locally compact groups and lattices
at 10:30am on Wednesday 11th of April in MLR2
***Note earlier time than usual*******
Abstract: This will be an introduction to the part of geometric group theory which is concerned with polyhedral complexes, their automorphism groups and lattices in their automorphism groups. We will show via key examples how finite geometries and groups are used to construct and understand infinite polyhedral complexes and groups which act on them.
All welcome

Wednesday 18 
11:00  SEMINAR  Groups and Combinatorics Seminar: A class of abundant psingular elements in finite classical groups

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Groups and Combinatorics Seminar
Tomasz Popiel (UWA)
will speak on
A class of abundant psingular elements in finite classical groups
at 11am on Wednesday 18th of April in MLR2
Abstract: Elements with order divisible by certain primes have underpinned many algorithms for computing in finite classical groups G. For a prime p dividing the order of G and not dividing q, where G is defined over a field with q elements, we introduce a subfamily of the psingular elements of G (elements with order divisible by p) comprising elements that leave invariant certain "large" subspaces of the natural Gmodule. We determine the exact asymptotic value of the proportion of these elements in G, which turns out to be a constant multiple of the best known lower bound for the proportion of all psingular elements, the latter having been obtained in a 1995 paper of Issacs, Kantor and Spaltenstein. We also present an efficient algorithm for testing whether a given element of G belongs to our new subfamily of psingular elements. This talk represents joint work with Alice Niemeyer and Cheryl Praeger.
All welcome


May 2012

Wednesday 02 
11:00  SEMINAR  Groups and Combinatorics Seminar: The MerinoWelsh Conjecture

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Groups and Combinatorics Seminar
Steven Noble (Brunel University, UK)
will speak on
The MerinoWelsh Conjecture
at 11am Wednesday 2nd of May in MLR2
Abstract: The MerinoWelsh conjecture states that for any loopless, bridgeless graph G, the maximum of the number of acyclic orientations and the number of totally cyclic orientations of G is at least the number of spanning trees of G.
Each of these invariants is an evaluation of the Tutte polynomial, which is a twovariable graph polynomial with positive coefficients. Computational evidence hints that for bridgeless, loopless graphs, the Tutte polynomial might be convex along the portion of lines x+y = constant lying in the positive quadrant. The conjecture is a first small step towards resolving this question.
We will explain the motivation behind the conjecture and discuss some generalizations, in particular to matroids. We will then show that the most general convexity conjecture holds for a large class of matroids and that something much weaker holds for all loopless, bridgeless matroids. Almost no knowledge of matroids will be assumed!
All welcome

Wednesday 09 
11:00  SEMINAR  Groups and Combinatorics Seminar: Automorphisms and opposition in twin buildings

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Groups and Combinatorics Seminar
Alice Devillers (UWA)
will speak on
Automorphisms and opposition in twin buildings.
at 11am on Wednesday 9th of May in MLR2.
Abstract: Opposition in twin buildings generalises the notion of opposition in spherical buildings. With James Parkison and Hendrik Van Maldeghem, we looked at automorphisms mapping some/all residues to opposite residues.For instance we proved that an automorphism of a thick twin building (swapping the two halves) always maps at least one spherical residue to an opposite. However, if the building is also locally finite and 2spherical, then not every residue of a given type can be mapped to an opposite.

Wednesday 16 
11:00  SEMINAR  Groups and Combinatorics Seminar: Computing with infinite linear groups: results and challenges

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Groups and Combinatorics Seminar
Alla Detinko (NUI, Galway)
will speak on
Computing with infinite linear groups: results and challenges
at 11am in Maths Lecture Room 2 on Wednesday 16th of May
Abstract: In the talk we will discuss methods for computing with infinite linear groups. We also survey recently obtained results for computing with finitely generated linear groups. The main focus will be on the theoretical background of computing in this class of groups.

Wednesday 23 
11:00  SEMINAR  Groups and Combinatorics Seminar:Algebraic Design Theory

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Groups and Combinatorics Seminar
Dane Flannery (NUI, Galway)
will speak on
Algebraic Design Theory
at 11am on Wednesday 23rd of May in MLR2
Abstract: This talk will survey results and open problems in the theory of pairwise combinatorial designs, drawing on a recently published book by the speaker and Warwick de Launey.
All welcome


June 2012

Wednesday 06 
11:00  SEMINAR  Groups and Combinatorics Seminar: SCVTGraphs

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Groups and Combinatorics Seminar
Guang Rao (UWA)
will speak on
SCVTGraphs
at 11am on Wednesday 6th of June in MLR2.
Abstract: A graph is called selfcomplementary if its complement is isomorphic to itself. SCVTgraphs are the graphs that are both selfcomplementary and vertextransitive. My research focuses on undirected SCVTgraphs. In this talk, I will give a brief historical retrospect, present some new results, and outline my future study plan.
All welcome.

Saturday 16 
11:00  SEMINAR  Groups and Combinatorics Seminar:Symmetric graphs of diameter two

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Groups and Combinatorics Seminar
Carmen Amarra (UWA)
will speak on
Symmetric graphs of diameter two
at 11am on Thursday 14th of June in Maths Lecture Room 2
**Note the change of day***
Abstract: Let G be a group. A graph Gamma is Gsymmetric if it
admits G as an arctransitive group of automorphisms, and it has diameter two
if it is not a complete graph and if any two
nonadjacent vertices have a common neighbour. Using normal quotient
analysis, we can reduce the study of symmetric diameter two graphs to
the following cases: (1) all nontrivial, connected Gnormal
quotients of Gamma are complete graphs, or (2) G acts
quasiprimitively on the vertex set of Gamma. Our broad aim is to
classify the symmetric diameter two graphs that satisfy (1) or (2). We
are not able to achieve this for all such graphs; in this talk we
describe our results for some subcases. In particular we focus on the
subcase of (1) where Gamma has at least 3 nontrivial complete
Gnormal quotients, and the subcase of (2) where G is affine. Our
analysis uses the classification of transitive linear groups, and
Aschbacher's classification of subgroups of the general linear group.


July 2012

Wednesday 25 
18:15  EVENT  UWA Historical Society Annual Lecture 2012 : Mathematics and Women  36 years at The University of Western Australia

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The Annual Lecture is the highlight of the year for the UWA Historical Society and Convocation and we are delighted to welcome Winthrop Professor Cheryl Praeger to the podium to reflect upon her years on Campus and subsequent experiences
and achievements.
Mathematician Cheryl Praeger has served the University of Western Australia as Lecturer, Senior Lecturer, and Professor since 1976. She leads a flourishing research group in pure mathematics and is in the top one per cent of highly cited mathematicians in the world.
Attendance is free.


August 2012

Tuesday 07 
13:00  SEMINAR  Groups and Combinatorics Seminar: Algebraic properties of chromatic polynomials

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Groups and Combinatorics Seminar
Graham Farr (Monash)
will speak on
Algebraic properties of chromatic polynomials
at 1pm on Tuesday 7th of August in Maths Lecture Room 2
**Note this is the new regular seminar time for this semester**
Abstract: We give a survey of some recent work on algebraic properties
of chromatic polynomials, including their roots (as algebraic
numbers), factors and Galois groups. Collaborators:
Adam Bohn (Queen Mary), Peter Cameron (Queen Mary),
Daniel Delbourgo (Monash), Bill Jackson (Queen Mary),
Kerri Morgan (Monash).

Sunday 12 
UWA opens up the whole campus to the public.
Come and find out about the courses on offer, career options, scholarship opportunities, our valuable research, community programs and facilities.
There's also residential college tours, handson activities, live music and entertainment, and plenty of fun activities for the whole family.

Tuesday 14 
12:00  EVENT  "What Matters to me and why" : Conversations with UWA Academics about what really matters

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Lunch time talk: What Matters to Winthrop Professor Cheryl Praeger AM FAA
When: Tuesday 14th August 2012, 12pm to 1.30pm
Where: Science Library – 3rd Floor Seminar Room
'What Matters to me and why' is a series of lunch time talks and conversations with UWA Academics. The talks explore personal stories of family, place, formative influences and how these things continue to shape people's lives and academic work.
The next conversation is with Cheryl Praeger, who is the Director of the Centre for the Mathematics of Symmetry and Computation at UWA.
Cheryl will share some of her story and then there will be the opportunity for questions/conversation. BYO lunch. Tea/Coffee is available in the meeting room (at the request of the Science Library, please do not carry coffee through the library).
The Science Library is towards the southern end of the campus just past the Chemistry and Psychology buildings.
13:00  SEMINAR  Groups and Combinatorics Seminar: Spreads of symplectic spaces of small order

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Groups and Combinatorics Seminar
Sylvia Morris (UWA)
will speak on
Spreads of symplectic spaces of small order
at 1pm on Tuesday 14th of August in MLR2
Abstract: Spreads of symplectic spaces are used to construct translation planes, Kerdock codes and mutually unbiased bases. Several families of infinite symplectic spreads are known but these are far from covering all symplectic spreads. In particular, there is little known about symplectic spreads which create a nonsemifield translation plane. For q=2 there is a unique spread of W(5,q) and for q=3 the symplectic spreads have been classified by Dempwolff. For q=4 there is a connection between symplectic spreads and the unique ovoid of Q^+(7,4). I have been using linear programming methods to find spreads in W(5,4) and W(5,5) which have nontrivial stabiliser. I will present my methods and results thus far, focussing on some interesting new examples of nonsemifield symplectic spreads and their stabilisers.

Tuesday 21 
13:00  SEMINAR  Groups and Combinatorics Seminar: Compositions of n and an application to the covering number of the symmetric groups

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Groups and Combinatorics Seminar
Pablo Spiga (University of MilanoBicocca)
will speak on
Compositions of n and an application to the covering number of the symmetric groups
at 1pm in MLR2 on Tuesday 21st of August
Abstract: Given a positive integer n, a kcomposition of n is an ordered sequence of k positive integers summing up to n. In this short talk, we are interested on the number of kcompositions satisfying some "coprimeness" condition. As an application we give a Classificationfree proof of some results on the covering number of the symmetric group.
All welcome

Tuesday 28 
13:00  SEMINAR  Groups and Combinatorics Seminar: Are Three Squares Impossible?

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Groups and Combinatorics Seminar
BIll Smyth (McMaster University/Kings College London/UWA)
will speak on
Are Three Squares Impossible?
at 1pm Tuesday 28th of August in MLR2.
Abstract: This talk describes work done over the last 30 years or so both to understand and to compute repetitions in strings  especially since 1999. We will discover that, although much has been learned, much combinatorial insight gained, there remains much more that is unknown about the occurrence of repetitions in strings and the restrictions they are subject to. I present combinatorial results discovered only recently, and I suggest that possibly extensions of these results can be used to compute repetitions in an entirely new way. I hope that members of the audience will be motivated to work on some of the many open problems that remain, thus to extend combinatorial knowledge even further.
All welcome


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