SEMINAR:
Groups and Combinatorics Seminar
Fri, 21 Jun 2013 15:00 - Blakers Lecture Theatre
Mark Ioppolo, David Raithel, and Daniel Hawtin
This week the seminar will consist of three 20 minute talks, starting at
3pm Friday 21st of June in Blakers Lecture Theatre.
--Talk 1--
Mark Ioppolo
will speak on
Symmetry in coding theory: Constructing error control codes with group
theory
Abstract:
When data is transmitted over a noisy communication channel there is a
possibility that the received message will be different to what the
sender intended. A frequently made assumption in coding theory is that
the probability of an error occurring does not depend on the position of
the error in the codeword, or on the value of the error. The group
theoretic analogue of this assumption is known as neighbour-
transitivity. This talk will introduce the study of neighbour-transitive
codes, focusing on the case where the automorphism group of the code in
question is contained in a group of symplectic matrices.
--Talk 2--
David Raithel
will speak on
Structures of Symmetries
Abstract:
Permutation groups are the tools with which we understand and study
symmetry. For over a century, mathematicians have been endeavouring to
classify classes of permutation groups, which in turn classifies classes
of symmetries. Transitive groups lie at the heart of permutation groups,
and one of the large overarching themes of permutation group theory has
been to characterise transitive groups. In this talk I shall outline
four major structure theorems from as early as 1911 to as recently as
2004. These theorems have proven to be powerful tools which have allowed
group theorists to sledgehammer their way through some otherwise
insurmountable problems.
--Talk 3--
Daniel Hawtin
will speak on
Affine Elusive Codes
Abstract:
An Elusive pair $(C,X)$ is a code-group pair where $X$ fixes the
neighbour set setwise, and contains an automorphism which does not fix
$C$ setwise. This implies that there are multiple codes, each with the
same neighbour set. The concept was introduced by Gillespie and Praeger
in order to discern the correct definition for neighbour transitive
codes. We discuss a family of exmples which are as large as possible, in
some sense, and display properties which previous examples have not.
For more information:
Irene Pivotto
irene.pivotto@uwa.edu.au
Starts : Fri, 21 Jun 2013 15:00
Ends : Fri, 21 Jun 2013 17:00
Last Updated : Tue, 18 Jun 2013 08:22