March 2011

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

Friday 30 
13:00  SEMINAR  Groups and Combinatorics Seminar: The concept of pdeficiency and its applications

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Groups and Combinatorics Seminar
Anitha Thillaisundaram (Cambridge)
will speak on
The concept of pdeficiency and its applications.
at 1pm on Friday 30th September in MLR2
Abstract: We use SchlagePuchta's concept of pdeficiency and Lackenby's
property of plargeness to show that a group having a finite presentation
with pdeficiency greater than 1 is large. What about when pdeficiency is
exactly one? We also generalise a result of Grigorchuk on Coxeter groups to
odd primes.
All welcome.


October 2011

Wednesday 05 
The Postgraduate and Honours Expo showcases a host of opportunities for further study, including honours and postgraduate coursework and research possibilities.
Discover the courses each faculty has to offer, learn about postgraduate scholarships, attend information sessions and talk to staff, honours and postgraduate students.
For more information about the Expo along with details on the presentations being held throughout the evening please go uwa.edu.au/postgradexpo

Friday 07 
13:00  SEMINAR  Groups and Combinatorics Seminar: On the diameter of permutation groups

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Groups and Combinatorics Seminar
Akos Seress (UWA)
will speak
On the diameter of permutation groups
at 1pm Friday 7th of October in MLR2
Abstract: Joint work with H. Helfgott.
Given a finite group G and a set A of generators, the diameter diam(Gamma(G,A)) of the Cayley graph Gamma(G,A) is the smallest number x such that every element of G can be expressed as a word of length at most x in A and the inverse of A. We are concerned with the diameter under the worstcase generators: diam(G):= max(diam(Gamma(G,A))).
It has long been conjectured that the diameter of the symmetric group of degree n is polynomially bounded in n, but the best previously known upper bound was exponential in the square root of n (Babai, Seress, 1988). We give a quasipolynomial upper bound for diam(Sym(n)). The same bound applies to the alternating groups.
This addresses a key open case of Babai's conjecture that the diameter of all nonabelian finite simple groups G is bounded by a polylogarithmic function of the group order. The first class of groups for which the conjecture was verified was PSL(2,p), p prime (Helfgott, 2008). This has been generalised to all simple groups of Lie type of bounded rank (Pyber, Szabo, 2011 and Breuillard, Green, Tao, 2011); the unboundedrank cases are likely to raise combinatorial problems of the type studied in this paper.
By a theorem of Babai, Seress (1992), our result implies a quasipolynomial upper bound on the diameter of all transitive permutation groups of degree n.
Our approach combines ideas on growth in groups (as in (Helfgott, 2008), (Helfgott, 2011)) with an adaptation of older techniques on permutation groups  most notably (Babai, 1982) and (Pyber, 1993)  to sets of permutations.

Friday 14 
13:00  SEMINAR  Groups and Combinatorics Seminar: The spread of a finite group

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Groups and Combinatorics Seminar
Simon Guest (UWA)
will speak on
The spread of a finite group
at 1pm on Friday 14th of October in MLR2
Abstract: Let G be a finite group. We say that G has spread at least k if for any k distinct nontrivial elements x_1, ... , x_k in G, there exists y in G such that x_i and y generate G for each i. If G does not have spread at least 1 then G is said to have spread 0. Using elementary methods we can prove that if G has a nontrivial normal subgroup N such that G/N is noncyclic then G must have spread 0. It has been conjectured by Guralnick and Kantor that the converse is true. They can prove that the converse holds in many cases. We will discuss some recent joint work with Tim Burness involving the remaining cases.

Friday 21 
13:00  SEMINAR  Groups and Combinatorics Seminar: Transferring Proportions of Invertible Matrices to the Full Matrix Algebra M(n,q)

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Groups and Combinatorics Seminar

Brian Corr
"Transferring Proportions of Invertible Matrices to the Full Matrix Algebra M(n,q)"
Friday 21st October (2011), 1pm, MLR2
Abstract:
Many questions in Computational Group Theory revolve around the counting of objects inside groups and other structures. Monte Carlo and Las Vegas algorithms depend on a random search for objects with desirable properties, and knowing how abundant these objects are is the key to knowing how long our search should take.
The Quokka Theory of Niemeyer and Praeger is a powerful tool for counting desirable matrices in subgroups of the General Linear Group GL(n,q), but it depends on the invertibility of the matrices. We present a new theory which allows us, under certain conditions, to transfer results about subsets of GL(n,q) into results about subsets of the full matrix algebra M(n,q), and present an application of how this applies to results obtained through Quokka Theory.


November 2011

Thursday 03 
10:00  EVENT  Teaching and Learning Mathematics in the Australian Curriculum : As part of UWA's Year of Mathematics, this event is a forum to discuss the teaching and learning of Mathematics in the Australian Curriculum.

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Early Childhood, Primary and Secondary teachers are invited to share this event.
Professor Ramagge is a member of the ACARA Mathematics Advisory Panel and of the Educational Advisory Committee of the Australian Mathematical Sciences Institute.
She has helped to develop support materials for teachers that are available free to all Australian Schools as part of The Improving Mathematics Education in Schools project funded by the Australian Government.
RSVP ONLINE
Cost: free
Registrations are essential.
Places are limited!
Register online at www.education.uwa.edu.au/mathsevent
All registrations received on,or before, September 30 will be in the draw to win an iPad.


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