What's On at UWA

Brian Corr (UWA)

will speak on

Analysis and Implementation: the Two 'Editions' of a Matrix Group Algorithm

at 3pm Friday January the 10th in Blakers Lecture Theatre.

Abstract :

The quality of an algorithm in computational mathematics is represented by two separate, yet equally important measures: the theoretical analyses which measure the runtime's growth for large input, and the implementations whose runtimes we can measure in seconds. This leads to different aspects of algorithm design being prioritised in different settings, and often two very different algorithms are produced: one is described in a journal article analysing the worst-case complexity, and a very different procedure is implemented in practice.

In this talk I present the motivation, overall structure, and details of a reduction algorithm for specific irreducible modules of a classical group G, and discuss issues specific to the implementation of the algorithm in the Magma computer algebra system.

This is joint work with Cheryl Praeger and Akos Seress, with special thanks to Eamonn O'Brien.

Alice Devillers (UWA)

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Graphs and transitivity on 2-geodesics

at 3pm Friday January the 17th in Blakers Lecture Theatre.

Abstract :

Joint work with Wei Jin, Cai Heng Li, Cheryl Praeger, Akos Seress.

An s-geodesic in a graph is a shortest path connecting two vertices at distance s. We say that a graph is locally transitive on s-geodsics if the stabiliser of any vertex is transitive on the s-geodesics starting at that vertex. Being locally transitive on s-geodesic is not a monotone property: if an automorphism group G of a graph is locally transitive on s-geodesics, it does not follow that G is locally transitive on shorter geodesics. For instance, (local) transitivity on 2-geodesics does not imply local transitivity on arcs (1-geodesics).

In this talk, I will first show a nice characterisation of all graphs that are locally transitive on 2-geodesics, but not locally transitive on 1-geodesics.

Then I will describe graphs that are (locally) transitive on 2-geodesics and on arcs, in terms of their local structure.

Irene Pivotto (UWA)

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An introduction to IPE

at 3pm Friday January the 24th in Blakers Lecture Theatre.

Abstract:

IPE is a drawing editor for creating figures in PDF or EPS format, which can then be inserted into LaTeX documents. I will show the basic features of IPE, as well as some of the more advanced ones.

André Nies (University of Auckland)

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Groups and first-order logic

at 3pm Friday January the 31st in Blakers Lecture Theatre.

Abstract :

We study the expressive power of first-order logic for groups. A finitely generated group is called quasi-finitely axiomatizable if a single sentence characterizes it within the class of finitely generated groups. I showed in 2005 that, for instance, the Heisenberg group is quasi-finitely axiomatizable. Recent work of Lasserre provides new examples, such as the Thompson groups.

A group is homogeneous if the orbit of every tuple under the action of automorphisms is described by its first-order properties. I proved (J. Algebra, 2003) that the free group F_2 has this property. Recent work of Perrin and Sklinos (Duke Math. J. 2013) extends this to F_n for larger n.

Phill Schultz (UWA)

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Row echelon matrices, flags and Grassmannians

at 3pm Friday February the 7th in Blakers Lecture Theatre.

Abstract:

There is a well trodden path from finite dimensional vector spaces to algebraic geometry. How much progress along this path is possible if fields are replaced by rings?

The aim of this course is to introduce you to basic statistics. It will cover descriptive statistics (means and standard deviations); data exploration; basic categorical data analysis; simple linear regression and basic analysis of variance (ANOVA). The statistical package SPSS will be used to illustrate the ideas demonstrated. The course will be held in a computer laboratory allowing participants to immediately apply the material covered through a series of practical examples.

Dugald MacPherson (University of Leeds)

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Metrically homogeneous graphs

at 3pm Friday February the 21st in Blakers Lecture Theatre.

Abstract:

A `homogeneous structure' is a countably infinite relational structure M (e.g. graph, k-uniform hypergraph, digraph,...) with the property that every isomorphism between finite induced substructures of M extends to an automorphism of M. These are constructed by an amalgamation method developed by Fraisse (and independently Jonsson) in the 1950s. There are classification results, often very hard, in restricted contexts (e.g. graphs, partial orders, digraphs, totally ordered graphs) but in general classification seems out of reach.

I will discuss an attempt to classify `metrically homogeneous graphs', that is, countably infinite graphs M which become homogeneous when enriched by binary `distance relations' corresponding to graph-distance in M. This notion generalises distance transitivity for countably infinite graphs. Cherlin has produced a `catalogue' of metrically homogeneous graph and conjectures that it is complete. In joint work in progress with Amato and Cherlin, we verify the conjecture for metrically homogeneous graphs of diameter at most three.

Eric Swartz (UWA)

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Subgroup covering numbers of symmetric groups

at 3pm Friday February the 28th in Weatherburn Lecture Theatre.

Abstract:

Let G be a group. The subgroup covering number of G is defined to be the least integer m such that G is equal to the set theoretic union of m proper subgroups of G. In 2005, Maroti determined the subgroup covering number for the symmetric group S_n, when n > 9 is odd, and he provided bounds for sufficiently large even values of n. I will discuss these previous results, joint work with Luise-Charlotte Kappe and Daniela Nikolova towards filling in the gap for small values of n, and ongoing work to determine the exact value for large even values of n.

New to the club this year? Want to meet some of the other new people, some older people, and do some computer stuff? At 5pm this Friday, all Freshers and new members should come on up to the loft (just above the clubroom; see your fresher guide) to break the ice on your UCC experience. There'll be a few short presentations and introductions on how to make the most of all the services the club supplies, including a basic introduction to Linux. As an added incentive, all first time members get FREE pizza!

Binzhou Xia (Peking University)

will speak on

Factorizations of almost simple groups with a soluble factor

at 3pm Friday March the 7th in Weatherburn Lecture Theatre.

Abstract:

Factorizations of almost simple groups arise in many contexts. I will talk about the factorizations with one factor soluble, including construction of examples in classical groups and the classification result.

Come along and hear from Teach for Australia about their 2-year graduate program. This session will deliver information about the program, the application process, and an opportunity to ask an alumnus about what the experience was like.

"Our award-winning leadership program affords an accelerated two years of unprecedented personal growth and a Masters level of professional training. Come along to ask an alumnus why Australia's most outstanding young leaders are choosing our associate experience to rapidly advance their careers and make an impact on educational inequity".

All disciplines (particularly Science and Maths Graduates) outside of education are encouraged to attend and find out more.

UCC's AGM, for the election of express purpose of electing the eight new committee members for 2014: president, vice president, treasurer, secretary, three ordinary commmittee members (OCMs), and one fresher representative (fresher rep).

Send all nominations and agenda items to [email protected]. The current agenda can be found at http://wiki.ucc.asn.au/AGM2014Agenda.

If you don't know where the Council Meeting Room is, join the group leaving the clubroom just before 1pm, on Tuesday, 11th of March.

Hope to see lots of people there!

John Bamberg (UWA)

will speak on

The brilliant career of Frédéric Vanhove

at 3pm Friday March the 14th in Weatherburn Lecture Theatre.

Pablo Spiga (Universita' di Milano-Bicocca)

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Have we ever tried to count Cayley graphs?

at 3pm Friday March the 21st in Weatherburn Lecture Theatre.

Abstract:

In this talk we give some elementary upper bounds on the number of finite Cayley graphs. The asymptotic number of Cayley graphs is much harder to pin down and we give a brief outline of the main technique and the main ingredients needed for this counting. On the way we leave some problems on oriented Cayley graphs and tournaments.

In the week beginning 24 March 2014, iVEC will offer the following short courses on supercomputing topics:

Introduction to iVEC: 1:00 – 2:00pm Mon 24th March

Introduction to Linux: 3:00 – 4:00pm Mon 24th March

Introduction to Supercomputing: 10:00am – 4:00pm Tues 25th March

Developing with MPI and OpenMP: 10:00am – 4:00pm Wed 26th March

Debugging with DDT: 10am – 12:00 noon Thurs 27th March

Introduction to Optimisation and Profiling: 1:00 – 4:00pm Thurs 27 March

Courses are delivered in a face to face classroom style. Attendees are encouraged to bring and work on their own laptops. Staff from the Supercomputing Team will be facilitating so you can meet and chat with them.

Free parking available on-site.

Courses are free of charge and open to all, however places are limited.

Light refreshments and lunch will be provided on each day (no lunch on Monday).

Register online at http://www.ivec.org/ai1ec_event/ivec-supercomputing-training-february-2014-2/?instance_id=

Michael Zieve (University of Michigan)

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Primitive groups, diophantine equations, and functional equations

at 3pm Friday March the 28th in Weatherburn Lecture Theatre.

Abstract:

I will explain how results about primitive groups play a crucial role in proving results about diophantine equations and functional equations. A sample application is that, for any polynomial f(X) with rational coefficients, the function Q-->Q defined by c --> f(c) is (<=6)-to-1 over all but finitely many values.

Cai-Heng Li (UWA)

will speak on

Edge transitive dessins d'enfant

at 3pm Friday April the 4th in Weatherburn Lecture Theatre.

Abstract:

A 2-cell embedding of a bipartite graph in an orientable surface is called a dessin d'enfant. Thus a dessin d'enfant is an orientable bipartite map. I will present an explicit representation of an edge transitive dessin in terms of a group with two distinguished generators, and apply it to study the dessin.

There will be presentations by international visitors, games, prizes, a photo booth, treats on offer and lots and lots of information about exchange and study abroad opportunities for UWA students.

Come along to Profectus UWA's Inaugral 2014 AGM on Tuesday April 8. If you are passionate about business and entrepreneurship be sure to drop by at 1pm to learn more about our agenda. We will answer any questions you have about Profectus and events being held this semester!!!

Steven Noble (Brunel University)

will speak on

Graphs are to matroids what ribbon graphs are to ...?

at 3pm Friday April the 11th in Weatherburn Lecture Theatre.

Abstract:

Much of the combinatorial structure of an abstract connected graph is encoded in its set of spanning trees. These form one of the canonical examples of the bases of a matroid. Ribbon graphs contain extra topological information on the embedding of the underlying abstract graph in a surface. The structures playing the role of spanning trees are the subgraphs having one boundary component. The combinatorial structure which they form is a delta-matroid, which roughly speaking is like a matroid except that the bases do not need to have the same size. We will discuss three classes of delta-matroids, some natural operations on ribbon graphs which correspond to natural operations on delta-matroids, give an excluded minor theorem for one of the classes of delta-matroids and, time-permitting describe the Bollobas-Riordan polynomial which forms one way of generalizing the Tutte polynomial to ribbon graphs.