January 2011

Tuesday 18 
15:00  SEMINAR  Groups and Combinatorics Seminar: Totally Disconnected Groups and Discrete Mathematics

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Groups and Combinatorics Seminar
George Willis (University of Newcastle)
will speak on
Totally Disconnected Groups and Discrete Mathematics
at 3pm on Tuesday 18th of January in MLR2
Abstract:
Totally disconnected, locally compact groups are typically not discrete. The potential for using techniques from discrete mathematics to study totally disconnected groups arises however because these groups may often be represented as automorphism groups of (infinite) discrete structures. Analogy with the study of automorphism groups of finite structures as well as specific results about graphs and permutation groups may have a role to play.
The talk will begin with a survey of totally disconnected groups, including key examples. Particular results and problems which relate to graph theory, finite group theory and permutation groups will then be discussed.
All welcome.

Thursday 27 
11:00  SEMINAR  Groups and Combinatorics Seminar: Positive Techniques in Parameterized Complexity and Limitations

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Groups and Combinatorics Seminar
Rod Downey (Victoria University of Wellington)
will speak on
Positive Techniques in Parameterized Complexity and Limitations
at 11am Thursday 27th of January in MLR2
Abstract: I will give a general introduction to the area, and illustrate several positive techniques, such as kernelization, bounded search trees, colour coding, treewidth, iterative compression, and less practical methods like WQO theory.
All welcome.


February 2011

Tuesday 08 
11:30  SEMINAR  Groups and Combinatorics Seminar: Matroid representation and partial fields

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Groups and Combinatorics Seminar
Dillon Mayhew (Victoria University of Wellington)
will speak on
Matroid representation and partial fields
at 11:30am on Tuesday 8th of February in MLR2
Abstract: Partial fields are algebraic objects that resemble fields, except that they may not be closed under addition. They arise extremely naturally in questions of matroid representation, but are of interest in their own right. This talk will be a survey of their history, and will list some open questions. No knowledge of matroid theory will be assumed.
All welcome.


March 2011

Tuesday 08 
12:00  SEMINAR  Groups and Combinatorics Seminar: The Cayley Isomorphism (CI) problem

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Groups and Combinatorics Seminar
Joy Morris (University of Lethbridge, Canada)
will speak on
The Cayley Isomorphism (CI) problem
at 12 noon in MLR2 on Tuesday 8th of March
Abstract: In a perfect world in which all isomorphisms between graphs must be in
some sense ``natural," it would be possible to attack the problem of
determining whether or not given graphs are isomorphic, simply by
checking a (hopefully small) class of ``natural" isomorphisms. For
Cayley graphs, ``natural" isomorphisms between the graphs Cay(G;S)
and Cay(G;S') on the group G, would consist exclusively of automorphisms of the group G. Alas, our world is not perfect. However, there are some Cayley graphs
X=Cay(G;S) for which the isomorphism problem can be solved in this manner. That is, for such a graph X, the Cayley graph Cay(G;S') is isomorphic to X if and only if there is an automorphism of G that takes S to S' (and hence acts as a graph isomorphism). Such a graph is said to have the Cayley Isomorphism, or CI, property.
Furthermore, there are some groups G for which every Cayley graph Cay(G;S) has the CI property; these groups are said to have the CI property. The Cayley Isomorphism problem is the problem of determining which graphs, and which groups, have the CI property.
In this talk, I will discuss the motivation and background of the CI
problem (which stems from a 1977 paper by Laszlo Babai), and survey
some of the results that have been obtained on this problem.
Traditionally, the problem has been confined to finite Cayley graphs.
Towards the end of the talk, I will discuss the extension of this
problem to infinite graphs, and some results I have obtained on
locally finite graphs in joint work with Babai.
All welcome

Friday 11 
14:15  SEMINAR  DECRA Information Seminar : Guidance on applying for an ARC Discovery Early Career Researcher Award

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The Research Development Office will be presenting a seminar regarding the rules and how to write a winning application for an ARC Discovery Early Career Researcher Award.

Tuesday 15 
12:00  SEMINAR  Groups and Combinatorics Seminar: Does every Cayley graph have a hamiltonian cycle?

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Groups and Combinatorics Seminar
Dave Morris (University of Lethbridge, Canada)
will speak on
Does every Cayley graph have a hamiltonian cycle?
at 12 noon in MLR2 on Tuesday 15th of March
Abstract: It was conjectured 40 years ago that every connected Cayley graph has a hamiltonian cycle, but there is very little evidence for such a broad claim. The talk will describe some of the progress that has been made, and present a few of the many open problems. Almost all of the talk will be understandable to anyone familiar with the fundamentals of graph theory and group theory.
All welcome

Tuesday 22 
12:00  SEMINAR  Groups and Combinatorics Seminar: Normal coverings of finite symmetric and alternating groups

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Groups and Combinatorics Seminar
Daniela Bubboloni (University of Firenze)
will speak on
Normal coverings of finite symmetric and alternating groups
at 12 noon on Tuesday 22nd of March in MLR2
Abstract: In this talk we consider the symmetric and alternating finite groups G=S_n, A_n and investigate the minimum number gamma(G) of maximal subgroups H_i, i=1 ... k of G such that each element in G lies in some Gconjugate of H_i. The number gamma(G) lies between a*phi(n) and b*n for certain constants a, b, where phi(n) is the Euler phifunction and depends on the arithmetical complexity of n. In the case where n is divisible by at most two primes, we determine the exact value for gamma(S_n) when n is odd and for gamma(A_n) when n is even.
All welcome

Tuesday 29 
12:00  SEMINAR  Groups and Combinatorics Seminar: A duality for mixed abelian groups

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Groups and Combinatorics Seminar
Phill Shultz (UWA) will speak on
A duality for mixed abelian groups
at 12 noon on Tuesday 29th of March in MLR2
Abstract: An abelian group is mixed if it contains nonzero elements of finite and of infinite order, and well mixed if it is not the direct sum of a torsion and a torsionfree group. The classification of well mixed groups is an intractable problem.
In this seminar, I will use a duality to describe the structure of well mixed groups G satisfying two finiteness conditions:
1. G has finite rank, that is, G contains a maximal free subgroup of finite dimension;
2. G is selfsmall, that is, the image of every homomorphism from G into an infinite direct sum of copies of G is contained in the direct sum of finitely many of these copies.
All welcome


April 2011

Tuesday 05 
12:00  SEMINAR  Groups and Combinatorics Seminar: On the lambdadesign conjecture

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Groups and Combinatorics Seminar
Akos Seress (UWA)
will speak on
On the lambdadesign conjecture
at 12 noon in MLR2 on Tuesday 5th of April.
Abstract:
A lambdadesign is a set system consisting of v sets on a velement
underlying set so that any two distinct members intersect in exactly
lambda points and not all sets are of the same size.
Ryser and Woodall's lambdadesign conjecture states that all lambdadesigns
can be obtained from symmetric designs a certain blockcomplementation
procedure. We report about recent efforts toward the solution of this
conjecture.
All welcome


May 2011

Tuesday 03 
12:00  SEMINAR  Groups and Combinatorics Seminar: On the vanishing graph of finite groups

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Groups and Combinatorics Seminar
Pablo Spiga (UWA)
will speak
On the vanishing graph of finite groups
at 12 noon Tuesday 3rd of May in MLR2
Abstract: In this talk, we investigate a graph Gamma encoding some information on the zeros of the irreducible complex characters of a finite group G. (We say that the element g of G is a zero, if there exists an irreducible complex character $ hi$ with $ hi(g)=0$.) This graph Gamma is called "the vanishing graph" of G. The vertices of Gamma are the primes p such that G contains a zero whose order is divisible by p. Moreover, the edges of Gamma are the pairs {p,q} such that G contains a
zero whose order is divisible by pq.
Clearly, Gamma is a subgraph of the prime graph. In this talk, we study
the density of the graph Gamma and we show how some geometrical
properties of Gamma generalise two classical character theory results
of Thompson and of ItoMichler.

Tuesday 10 
12:00  SEMINAR  Groups and Combinatorics Seminar: The automorphisms of McCulloughMiller space

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Groups and Combinatorics Seminar
Adam Piggott (Bucknell University)
will speak on
The automorphisms of McCulloughMiller space
at 12 noon 10th of May in MLR2
Abstract: McCulloughMiller's space X=X(W) is a topological model for the outer automorphism group of a free product of groups W. We will discuss the question of just how good a model it is. In particular, we consider circumstances under which Aut(X) is precisely Out(W).
All welcome

Tuesday 17 
12:00  SEMINAR  Groups and Combinatorics Seminar: FinInG: A GAP package for Finite Incidence Geometry

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Groups and Combinatorics Seminar
John Bamberg (UWA)
will speak on
FinInG: A GAP package for Finite Incidence Geometry
at 12 noon on Tuesday 17th of May in MLR2
Abstract: FinInG is a GAPpackage under development for computation in finite incidence geometry, based on the computer algebra package GAP (Groups, Algorithms and Programming). The algebraic power of GAP is employed, particularly in its facility with matrix and permutation groups. The aim of the package FinInG is to provide users with the basic tools to work in various areas of finite incidence geometry from the realms of projective spaces to the flat lands of generalised polygons. In this talk we will give some examples and explain some of the main features of the package.
All welcome

Tuesday 24 
12:00  SEMINAR  Groups and Combinatorics Seminar: Primitive generalised quadrangles

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Groups and Combinatorics Seminar
Michael Giudici (UWA)
will speak on
Primitive generalised quadrangles
at 12 noon Tuesday 25th of May in MLR2
Abstract: A generalised quadrangle is an incidence structure of points and lines such that the bipartite incidence graph has diameter 4 and girth 8. The classical examples are the low dimensional polar spaces associated with the classical groups PSp(4,q), PSU(4,q) and PSU(5,q). In this talk I will discuss recent work with John Bamberg, Joy Morris, Gordon Royle and Pablo Spiga aimed at characterising the classical examples in terms of the action of their automorphism group on points and lines.
All welcome

Tuesday 31 
12:00  SEMINAR  Groups and Combinatorics Seminar: Fat elements in quasisimple groups of Lie type

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Groups and Combinatorics Seminar
Sabina Pannek (UWA/Aachen)
will speak on
Fat elements in quasisimple groups of Lie type
at 12 noon on Tuesday 31st of May in MLR2
Abstract:
We call an element of the general linear group GL(d,q) fat, or more
precisely a fat(d,q;e)element, if it leaves invariant and acts
irreducibly on a subspace of dimension e > d/2 > 1. Equivalently, g in
GL(d,q) is a fat(d,q;e)element if the characteristic polynomial for g
has an irreducible factor over GF(q) of degree e > d/2 > 1.
We wish to classify irreducible subgroups G of GL(d,q) which contain
fat elements and are quasisimple, that is where G is a covering group
of an alternating group, a covering group of a sporadic simple group,
or a quasisimple group of Lie type. In my talk, I will discuss recent
results in the latter case of G being a quasisimple group of Lie
type.


June 2011

Tuesday 14 
Groups and Combinatorics Seminar
There will be three 25 minute talks on Tuesday 14th of June in MLR2 starting at 10:30 am.
10:30am:
Sylvia Ozols (Adelaide)
will speak on
The BruckBose Construction
11am:
Wei Jin (UWA)
will speak
On distance, geodesic and arc transitivity of graphs
11:30am
Carmen Amarra (UWA)
will speak on
Quotientcomplete arctransitive graphs
Abstract 1:
The BruckBose representation of a projective plane is a tool both for examining objects of any even dimensional projective space in the more familiar setting of a projective plane, and for 'magnifying' objects in certain projective planes by looking at them in a higher dimensional space. In this talk we will go through some finite projective geometry background, including Baer subplanes and partitions of odd dimensional projective spaces. We will define the BruckBose construction and get a general understanding of how it works.
Abstract 2:
We compare three transitivity properties of finite graphs, namely, for a positive integer s, sdistance transitivity, sgeodesic transitivity and sarc transitivity. It is known that if a finite graph is sarc transitive but not (s+1)arc transitive then s<8 and s not equal to 6. We show that there are infinitely many geodesic transitive graphs with this property for each of these values of s, and that these graphs can have arbitrarily large diameter if and only if 0< s<4. Moreover, for a prime p we prove that there exists a graph of valency p that is 2geodesic transitive but not 2arc transitive if and only if p = 1 (mod 4), and for each such prime there is a unique graph with this property: it is an antipodal double cover of the complete graph K_{p+1} and is geodesic transitive with automorphism group PSL(2,p) x Z_2. This is joint work with A. Devillers, C.H. Li and C. E. Praeger.
Abstract 3:
A graph Gamma is Gquotientcomplete (for some G in Aut(Gamma)) if it has at least one nontrivial Gnormal quotient which is a complete graph, and each of its other nontrivial Gnormal quotients is either a complete graph or an empty graph. We define the parameter k to be the number of Gnormal quotients of Gamma which are complete, and in this talk we consider the family of quotientcomplete graphs with k>2. We construct all the graphs Gamma; in this family together with the corresponding automorphism groups G, and give upper bounds for k in terms of the order of Gamma.


August 2011

Wednesday 03 
11:00  SEMINAR  Groups and Combinatorics Seminar: Perfect State Transfer

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Groups and Combinatorics Seminar
Murray Smith (UWA)
will speak on
Perfect State Transfer
at 11am Wednesday 3rd of August in MLR2
Abstract: In quantum information systems, it is desirable to transfer the quantum state of one qubit to another with high fidelity. This is known as perfect state transfer, and can be modelled as a graph theoretic problem. In this talk I will offer an introduction to the topic with types of graphs that can permit PST, specifically integral circulant graphs. I will also discuss my time spent at the University of Waterloo under the direction of Dr. Chris Godsil, and recent developments in characterising graphs with PST.
All welcome

Sunday 14 
UWA opens up the whole campus to the public.
Come and find out about the courses on offer, valuable research, community programs, and facilities...all mixed with a day full of lots of fun activities for everyone!


September 2011

Friday 09 
13:00  SEMINAR  Groups and Combinatorics Seminar: Algorithmic Generalisations of Small Cancellation Theory

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Groups and Combinatorics Seminar

Max Neunhöffer
(University of St Andrews)
"Algorithmic Generalisations of Small Cancellation Theory"
Friday 9th September (2011), 1pm, MLR2
Abstract:
In this talk I will report on joint work in progress with Stephen
Linton, Richard Parker and Colva RoneyDougal. We want to generalise
classical small cancellation theory (SCT) in an algorithmic direction.
SCT used to be a fixed set of conditions to test on a finite
presentation of a group. If these conditions are fulfilled, SCT proves
that the group is infinite, wordhyperbolic and provides a solution to
the word problem.
I will describe our ideas to generalise this beyond recognition.
In the end, the computer will analyse a finite presentation of a group
or other algebraic structure and come up with a SCTlike proof showing
that the algebraic structure is infinite and providing a solution to
the word problem.

Friday 16 
13:00  SEMINAR  Groups and Combinatorics Seminar:Generation and random generation: from simple groups to maximal subgroups

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Groups and Combinatorics Seminar
Tim Burness (University of Southampton)
will speak on
Generation and random generation: from simple groups to maximal subgroups
at 1pm on Friday 16th of September in MLR2
Abstract: Problems concerning the generation of finite simple groups have been studied since the early days of group theory in the 19th century. In this talk I will survey some of the main results and open problems in this area, and I will present some new results on the generation of maximal subgroups of simple groups. Applications and related open problems will also be discussed. This is joint work with Martin Liebeck and Aner Shalev.
All welcome

Friday 23 
13:00  SEMINAR  Groups and Combinatorics Seminar: Locally sdistance transitive graphs with a regular star normal quotient

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Groups and Combinatorics Seminar
Alice Devillers (UWA)
will speak on
Locally sdistance transitive graphs with a regular star normal quotient
at 1pm Friday 23rd of September in MLR2
Abstract: During the study of locally sdistance transitive graphs
(DevillersGiudiciLiPraeger), it was found that an important case is
the case of graphs with a star quotient. These graphs are bipartite,
with a normal subgroup transitive on one bipart but not on the other.
With Cheryl Praeger we studied in particular the case where the star has
at least 3 branches, and the normal subgroup acts regularly on one
bipart. I will explain our main result. Warning: there will be proofs.
All welcome


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