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Today's date is Friday, March 29, 2024
Centre for the Mathematics of Symmetry and Computation
 January 2012
Wednesday 25
15:00 - SEMINAR - Groups and Combinatorics Seminars More Information
Groups and Combinatorics Seminars

Eric Swartz (Binghamton)

will speak on

Locally 2-arc transitive graphs admitting an almost simple group of Suzuki type

at 3pm in MLR2

and

Jan Saxl (Cambridge)

will speak on

Conjugation characters of simple groups

at 4pm in MLR2

Abstract 1: A graph Gamma is said to be locally (G,2)-arc transitive for G a subgroup of Aut(Gamma) if Gamma contains a 2-arc, and, for any vertex alpha of Gamma, G is transitive on the 2-arcs of Gamma starting at alpha. In this talk, we will discuss general results involving locally (G,2)-arc transitive graphs and recent progress toward the classification of the locally (G,2)-arc transitive graphs, where G is a subgroup of Aut(Sz(q)) with soc(G) = Sz(q), q = 2^m for some odd natural number m. In particular, we will discuss seven families of vertex-intransitive locally (G,2)-arc transitive graphs. Furthermore, for any graph Gamma in one of these families, the full automorphism group of Gamma is a subgroup of Aut(Sz(q)), and the only locally 2-arc transitive graphs admitting an almost simple group of Suzuki type whose vertices all have valency at least three are (i) graphs in these seven families, (ii) (vertex transitive) 2-arc transitive graphs admitting an almost simple group of Suzuki type, or (iii) double covers of the graphs in (ii). Since the graphs in (ii) have been classified by Fang and Praeger (``Finite two-arc transitive graphs admitting a Suzuki simple group," Comm. Alg., 27(8):3727-3754, 1999), this completes the classification of locally 2-arc transitive graphs admitting a Suzuki simple group.



Abstract 2: In this talk we consider two problems concerning ordinary representations of simple groups: characters of conjugation actions, and squares of irreducible characters. These turn out to be closely related. This is joint work with Heide, A. Zalesskii, and Tiep.

 February 2012
Wednesday 22
11:00 - EVENT - Groups and Combinatorics Seminar: A census of cubic vertex-transitive graphs More Information
Groups and Combinatorics Seminar

Gabriel Verret (University of Primorska, Slovenia)

will speak on

A census of cubic vertex-transitive graphs

at 11am Wednesday 22nd of February in MLR2

Abstract: We explain how some of our recent results have allowed us to compute a census of all cubic vertex-transitive graphs of order at most 1280. We present some data about the census and discuss some interesting related questions. This is joint work with Primoz Potocnik and Pablo Spiga.
Wednesday 29
11:00 - SEMINAR - Groups and Combinatorics Seminar: Neighbour transitive codes and connections with power line communication More Information
Groups and Combinatorics Seminar

Neil Gillespie (UWA)

will speak on

Neighbour transitive codes and connections with power line communication

at 11am in MLR2 on Wednesday 29th of February

Abstract: Power line communication has been proposed as a possible solution to the "last mile" problem in telecommunications i.e. providing economical high speed telecommunications to millions of end users. In addition to the usual background noise, there are two other types of noise that must be considered for any successful implementation of power line communication. In this talk we characterise a family of neighbour transitive codes, and show that such codes have the necessary properties to be useful in power line communication.

 March 2012
Wednesday 07
11:00 - SEMINAR - Groups and Combinatorics Seminar: Coprime subdegrees for primitive permutation groups and completely reducible linear groups More Information
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 non-zero vectors, their orbit lengths a, b have a non-trivial 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 More Information
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:Minor-closed classes of graphs and matroids More Information
Groups and Combinatorics Seminar

Gordon Royle (UWA)

will speak on

Minor-closed 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 More Information
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: s-geodesic transitive graphs More Information
Groups and Combinatorics Seminar

Wei Jin (UWA)

will speak on

s-geodesic 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 i-geodesic if the distance between u and v is i. The graph Gamma is said to be s-geodesic transitive if the graph automorphism group is transitive on the set of s-geodesics. In this talk, I will compare the s-geodesic transitivity with other two well-known transitive properties, namely s-arc transitivity and s-distance transitivity, and determine the local structure of 2-geodesic transitive graphs, and also give some results about the family of locally disconnected 2-geodesic transitive but not 2-arc transitive graphs.

All welcome

Wednesday 11
10:30 - SEMINAR - Groups and Combinatorics Seminar: Polyhedral complexes, locally compact groups and lattices More Information
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 p-singular elements in finite classical groups More Information
Groups and Combinatorics Seminar

Tomasz Popiel (UWA)

will speak on

A class of abundant p-singular 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 p-singular elements of G (elements with order divisible by p) comprising elements that leave invariant certain "large" subspaces of the natural G-module. 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 p-singular 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 p-singular 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 Merino-Welsh Conjecture More Information
Groups and Combinatorics Seminar

Steven Noble (Brunel University, UK)

will speak on

The Merino-Welsh Conjecture

at 11am Wednesday 2nd of May in MLR2

Abstract: The Merino-Welsh 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 two-variable 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 More Information
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 2-spherical, 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 More Information
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 More Information
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: SCVT-Graphs More Information
Groups and Combinatorics Seminar

Guang Rao (UWA)

will speak on

SCVT-Graphs

at 11am on Wednesday 6th of June in MLR2.

Abstract: A graph is called self-complementary if its complement is isomorphic to itself. SCVT-graphs are the graphs that are both self-complementary and vertex-transitive. My research focuses on undirected SCVT-graphs. 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 More Information
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 G-symmetric if it admits G as an arc-transitive 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 G-normal 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 G-normal 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 Website | More Information
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 More Information
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
10:00 - EVENT - 2012 Open Day : Experience what's on offer at UWA Website | More Information
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, hands-on 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 More Information
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.

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