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Today's date is Tuesday, October 20, 2020
Centre for the Mathematics of Symmetry and Computation
 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 Ė 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.
Monday 15
18:00 - PUBLIC LECTURE - The solution of the Poincare conjecture Website | More Information
A Public Lecture by Professor J. Hyam Rubinstein, Department of Mathematics & Statistics, University of Melbourne.

The Poincare conjecture was one of the most celebrated questions in mathematics. It was amongst the seven millennium problems of the Clay Institute, for which a prize of $1million was offered.

The Poincare conjecture asked whether a 3-dimensional space with `no holesí is equivalent to the 3-dimensional sphere.

In 2003 Grigori Perelman posted three papers on the internet ArXiv outlining a marvellous solution to the Poincare conjecture, as part of the completion of Thurstonís geometrisation program for all 3-dimensional spaces. Perelman introduced powerful new techniques into Richard Hamiltonís Ricci flow, which `improvesí the shape of a space. Starting with any shape of a space with no holes, Perelman was able to flow the space until it became round and therefore verified it was a sphere.

A brief history of the Poincare conjecture and Thurstonís revolutionary ideas will be given. Hamiltonís Ricci flow will be illustrated.

Famously, Perelman turned down both the Clay prize and a Fieldís medal for his work.

Cost: Free. RSVP to [email protected]
Tuesday 16
13:00 - SEMINAR - Groups and Combinatorics: Finite meta-primitive permutation groups More Information
Groups and Combinatorics Seminar

Cai Heng Li (UWA)

will speak on

Finite meta-primitive permutation groups

at 1pm Tuesday 16th of October in MLR2

Abstract: A transitive permutation group is called meta-primitive if its any imprimitive quotient action is primitive, namely, each of the block systems is maximal. I will discuss the structural properties of meta-primitive groups.

All welcome.
Tuesday 23
13:00 - SEMINAR - Groups and Combinatorics Seminar: Clifford theory and Hecke algebras More Information
Groups and Combinatorics Seminar

Arun Ram (University of Melbourne)

will speak on

Clifford theory and Hecke algebras

at 1pm on Tuesday the 23rd of October in MLR2

Abstract: The usual Clifford theory describes the irreducible representations of group G in terms of those of a normal subgroup. Generalizing, Clifford theory constructs the irreducible representations of semidirect product rings and invariant rings. In this work with Z. Daugherty we use Clifford theory to index the irreducible representations of two pole Hecke algebras and relate this indexing to a labeling coming from statistical mechanics (following work of de Gier and Nichols) and to a geometric labeling (coming from K-theory of Steinberg varieties following Kazhdan-Lusztig). Despite the maths-physics and geometric motivations for the project, in the talk I shall assume only that the audience is familiar with the notions of groups, rings, and modules.

All welcome

 November 2012
Tuesday 20
13:00 - SEMINAR - Groups and Combinatorics Seminar: Finite s-Geodesic Transitive Graphs More Information
Groups and Combinatorics Seminar

Wei Jin (UWA)

will speak on

Finite s-Geodesic Transitive Graphs

at 1pm on Tuesday 20th of November in Maths Lecture Room 2

Abstract: A geodesic from a vertex u to a vertex v in a graph is one of the shortest paths from u to v, and this geodesic is called an s-geodesic if the distance between u and v is s.

A graph is said to be s-geodesic transitive if, for each i less than or equal to s, all i-geodesics are equivalent under the group of graph automorphisms. In this talk, I will show the relationship of 2-geodesic transitive graphs with a certain family of partial linear spaces. I will also compare s-geodesic transitivity of graphs with two other well-known transitivity properties, namely s-arc transitivity and s-distance transitivity.

This is a joint work with my supervisors.

All welcome
Tuesday 27
13:00 - SEMINAR - Groups and Combinatorics Seminar: Graphs and general preservers of zero products More Information
Groups and Combinatorics Seminar

Bojan Kuzma (University of Primorska, Slovenia)

will speak on

Graphs and general preservers of zero products

at 1pm on Tuesday 27th of November in MLR2

Abstract: We survey some results in preserver problems where graphs were used as the main tool. In particular, the classification of maps which preserve Jordan orthogonality (AB+BA=0) reduces to the fact that a certain graph is a core and has chromatic number 4. We also give a classification of certain matrices (rank-ones, semisimple, non-derogatory) in terms of a commuting graph.

All welcome.

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