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Today's date is Wednesday, October 21, 2020
Centre for the Mathematics of Symmetry and Computation
 March 2012
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.

13:00 - SEMINAR - Groups and Combinatorics Seminar: Spreads of symplectic spaces of small order More Information
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 non-semifield 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 non-trivial stabiliser. I will present my methods and results thus far, focussing on some interesting new examples of non-semifield 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 More Information
Groups and Combinatorics Seminar

Pablo Spiga (University of Milano-Bicocca)

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 k-composition 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 k-compositions satisfying some "coprimeness" condition. As an application we give a Classification-free 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? More Information
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

 October 2012
Tuesday 02
13:00 - SEMINAR - Groups and Combinatorics: Packing Steiner trees More Information
Groups and Combinatorics Seminar

Irene Pivotto (UWA)

will speak on

Packing Steiner trees

at 1pm Tuesday 2nd of October in MLR2

Abstract: A classic theorem of Nash-Wiliams and Tutte gives necessary and sufficient conditions for a graph to have k pairwise edge-disjoint spanning trees. We will discuss the natural generalization of this problem to trees spanning a distinguished set of vertices (which we refer to as Steiner trees). Finding edge-disjoint spanning trees is a considerably easier problem that finding edge-disjoint Steiner trees. This is due to the fact that spanning trees are bases of the natural matroid associated with a graph, while Steiner trees are not bases of any matroid. We will present a result that provides sufficient conditions for the existence of k edge-disjoint Steiner trees, reducing this problem to finding disjoint bases of a particular matroid. No prior knowledge of matroid theory is required to attend the talk.
Monday 08
13:10 - SEMINAR - Groups and Combinatorics Seminar: Commuting graphs of groups More Information
Groups and Combinatorics Seminar

Michael Giudici (UWA)

will speak on

Commuting graphs of groups

at 1pm Tuesday 9th of October in MLR2

Abstract: The commuting graph of a group G is the graph whose vertices are the noncentral elements of G and two vertices are adjacent if and only if they commute. Iranmanesh and Jafarzadeh conjectured that the commuting graph of a finite group is either disconnected or has diameter bounded above by some constant. I will discuss recent joint work with Chris Parker on this conjecture.

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