What's On at UWA

Groups and Combinatorics Seminar

Sukru Yalcinkaya (UWA)

will speak on

Generation of classical groups by good elements

at 1pm on Tuesday 16th of November in MLR2

Abstract: Let G be a classical group and V be the underlying vector space of dimension 2n over a field of size q. Let hi(n,q) be the product of all primitive prime divisors of q^n-1. We consider the elements of order hi(n,q) which act irreducibly on a unique n-dimensional subspace and fix pointwise an n-dimensional subspace of V. We call these elements good elements. I will discuss the probabilistic generation of G by two random conjugate good elements. This is a joint work with Cheryl Praeger and Akos Seress.

Groups and Combinatorics Seminar

John Bamberg (UWA)

will speak on

Perp-systems of Projective Spaces

at 1pm on Tuesday 23 November in MLR2.

Abstract: Perp-systems were introduced by De Clerck, Delanote, Hamilton, and Mathon to construct new partial geometries, and hence, possibly new strongly regular graphs. In a projective space PG(d,q) equipped with a non-degenerate polarity "perp", a perp-system is a set of mutually disjoint r-subspaces of PG(d,q) such that every pair of elements from this set are mutually opposite (disjoint from the "perp" of the other), and it must have the maximum theoretically possible size. By “pair” here, we do not require that the two elements be distinct, so in particular, every element of a perp-system is non-singular with respect to "perp". The only known perp-systems are self-polar maximal arcs of PG(2,q), q even, and Mathon’s sporadic example in PG(5,3). Mathon’s example had no geometric construction, it was simply written down in coordinate form, but it was known that its stabiliser was isomorphic to S_5 and that it was a perp-system with respect to a symplectic, hyperbolic and elliptic polarity. We will give an overview of the geometric background necessary to understand perp-systems and present some recent work of De Clerck and the author which provides a geometric construction of Mathon's perp-system.



All welcome.

Groups and Combinatorics Seminar

Wei Jin (UWA)

will speak on

On distance, geodesic and arc transitivity of graphs

at 1pm in MLR 2 on Tuesday 30th of November

Abstract:

We compare three transitive properties of finite graphs. An s-arc is a vertex sequence (v_0,v_1,...,v_s) such that v_i, v_{i+1} are adjacent and v_{j-1} is not equal to v_{j+1} for each i=0,1,...,s-1 and j=1,2,...,s-1; it is also an s-geodesic if v_0 and v_s are at distance s. For s in {1,2,3}, we give an infinite family of graphs that are transitive on s-arcs and on t-geodesics for all 0< t < diam(Gamma)+1, but intransitive on (s+1)-arcs. We exhibit an infinite family of distance transitive graphs that are not 2-geodesic transitive. Finally we classify all 2-geodesic transitive graphs of prime valency that are not 2-arc transitive: the examples comprise an infinite family of non-bipartite antipodal distance transitive double covers of complete graphs. This is a joint work with Alice Devillers, Caiheng Li and Cheryl Praeger.

All welcome.

Each mathematics teaching context is unique, but whenever the conversation turns to undergraduate education, common themes emerge: minimum standards, engagement, service teaching, the role of small group teaching, and graduate capabilities. The talk title is borrowed from a magazine column called “this works for me”, because it would be most presumptuous to suggest that the strategies to be presented, which have been developed collectively by the mathematicians at La Trobe, are any kind of panacea. I will describe things that we have tried and succeeded with, good ideas that turned out to be not-so-good in practice, and some general principles that we have identified. No-one will be required to write on butcher’s paper during this presentation. The speaker is a senior lecturer in the Department of Mathematics and Statistics at La Trobe University, and Director of Teaching and Learning, School of Engineering and Mathematical Sciences.

Persi Diaconis

Mary Sunseri Professor of Mathematics and Statistics, Stanford University USA

Mathematician, statistician AND magician

will give a public lecture entitled

The search for randomness

on Wednesday 8th of December 2010

What does it mean to say something is "random"? Persi Diaconis will take a close look at some of our most primitive images of random phenomena: tossing a coin, shuffling cards, and rolling a roulette wheel. While all these processes can achieve randomness, usually we are lazy. A bit of math and experiment shows that things are not so random after all.

About the speaker: At 14 Persi Diaconis had finished high school when he was invited by Dai Vernon, the greatest magician in the US, to go on tour with him. Diaconis dropped out of school and left home without telling his parents. At 16 he struck out on his own as a magician and did well doing magic, inventing tricks, giving lessons and living a very colorful life. When he came across a book on probability that he couldn't read he decided to enrol in a mathematics degree. He graduated two and a half years later. He has been at Stanford since he completed his PhD in 1974.

"The way I do magic is very similar to mathematics. Inventing a magic trick and inventing a theorem are very, very similar activities . . . One difference between magic and mathematics is the competition. The competition in mathematics is a lot stiffer than in magic."

Persi Diaconis, who is one of the world’s most famous mathematicians, is well known for his talks on popular mathematics to non-specialist audiences. Come and enjoy an evening with him. Enquiries 9332 2900 or [email protected].

He will be visiting Perth as an invited speaker at the Australian Statistics Conference and OZCOTS, the Australian Conference on Teaching Statistics (www.promaco.com.au/2010/asc/).

Groups and Combinatorics Seminar

Seyed Hassan Alavi (UWA)

will speak on

Triple factorisations: Geometric and group theoretic approaches

at 1pm in MLR 2 on Tuesday 14th of December

Abstract: Triple factorisations of groups G of the form G=ABA, for subgroups A and B, are fundamental in the study of Lie type groups as well as in geometry. In this talk, we first introduce and develop a general framework for studying triple factorisations, especially nondegenerate ones where G eq AB. We identify two necessary and sufficient conditions to obtain a triple factorisation in terms of the G-actions on the A-cosets and the B-cosets. We more importantly present a rationale for further study of primitive triple factorisations G=ABA in which A is maximal and both A and B are core-free.

Geometrically, triple factorisations correspond to flag-transitive collinearly connected point-line geometries in which `each pair of points lies on at least one line'. Geometries satisfying the dual condition, where each pair of lines meets in at least one point, are called concurrently connected. In this talk, we also introduce new point-line incidence geometries which arise from studying triple factorisations G=ABA and G=BAB of general linear groups G=GL(V) with A parabolic and B either parabolic, or the stabiliser of a decomposition V=V_1 plus V_2. These investigations give rise to various important examples of flag-transitive collinearly (respectively, concurrently) connected spaces. As duality is important in geometry, we also present the conditions under which these rank 2 geometries satisfy one, both or neither of connectivity properties.

This is a practice talk for an upcoming conference.

Groups and Combinatorics Seminar

Brendan McKay ( School of Computer Science, Australian National University)

will speak on

Subgraphs of Random Graphs with Specified Degrees

at 11am Friday 14th of January in MLR2.

Abstract: If a graph is chosen uniformly at random from all the graphs with a given degree sequence, what can be said about its subgraphs? The same can be asked of bipartite graphs, equivalently 0-1 matrices. These questions have been studied by many people. In this paper we provide a partial survey of the field, with emphasis on two general techniques: the method of switchings and the multidimensional saddle-point method.

All welcome.

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.

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.

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.

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

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.

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

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 G-conjugate 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 phi-function 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

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 non-zero elements of finite and of infinite order, and well mixed if it is not the direct sum of a torsion and a torsion-free 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 self-small, 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

Groups and Combinatorics Seminar

Akos Seress (UWA)

will speak on

On the lambda-design conjecture

at 12 noon in MLR2 on Tuesday 5th of April.

Abstract:

A lambda-design is a set system consisting of v sets on a v-element 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 lambda-design conjecture states that all lambda-designs can be obtained from symmetric designs a certain block-complementation procedure. We report about recent efforts toward the solution of this conjecture.

All welcome

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 Ito-Michler.

Groups and Combinatorics Seminar

Adam Piggott (Bucknell University)

will speak on

The automorphisms of McCullough-Miller space

at 12 noon 10th of May in MLR2

Abstract: McCullough-Miller'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

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 GAP-package 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

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