CIRCA Seminars

(The links on this page will no longer be maintained. They were correct as of 29th September 2005 when this page was last maintained.)

Archive of Seminars for Academic Year 2004-'05

• 29th September 2004
  Steve Linton (Univ. of St Andrews): How to apply for research grants
  (Slides for this talk are available in HTML and PDF formats.)
• 6th October 2004 (Room 1A)
  Erzsi Dombi (Univ. of St Andrews): Automatic semigroups: Language-theoretic approach
• 20th October 2004 (Pure Mathematics Colloquium)
  George Havas (Univ. of Queensland, Australia): 4-Engel groups are locally nilpotent
• 10th November 2004 (Room 1A)
  Erzsi Dombi (Univ. of St Andrews): Automatic semigroups: Geometric approach
• 1st December 2004
  Andrew Fish (Univ. of Brighton): Reasoning with diagrams for software development

  Abstract

  This will be an overview of some of the work associated to the EPSRC funded RwD project, which is a joint project between the Universities of Brighton and Kent.

  Constraint Diagrams are a diagrammatic notation, designed to express logical statements, especially for use in object oriented systems development. Formalising such a diagrammatic notation is not easy - it requires distinguishing between the concrete syntax (the actual drawing) and an abstract syntax (the information that is "important"), providing formal semantics (mapping to logic) and rules which enable reasoning with the diagrams. Many other issues arise on the way to creating software tools. For instance, given an abstract description of a diagram, how does one generate a "nice-looking" concrete diagram?

  A current trend in the design of software systems involves graphically representing models of the system. The Unified Modelling Language (UML) is an example of such a collection of graphical notations. Currently the only non-graphical notation that is part of the UML is the Object Constraint Language (essentially a textual, stylised form of predicate logic), which is used to express logical statements, such as system invariants or pre- and post-conditions (these specify behaviour of objects in the system). One application of Constraint Diagrams is as a possible alternative to the OCL.

• 15th December 2004 (Room 1A)
  Björn Assmann (Univ. of St Andrews): Polycyclic presentations for matrix groups
• 16th February 2005 (3pm)
  Katrin Gehles (Univ. of Glasgow): Singularities in the centre of an algebra
• 23rd February 2005
  Steve Waton (Univ. of St Andrews): Token passing networks
• 2nd March 2005
  Robert Brignall (Univ. of St Andrews): Finite basis properties of wreath products
• 23rd March 2005 (with Polycyclic Groups Seminar)
  Martyn Quick (Univ. of St Andrews): Introduction to profinite groups

  Abstract

  I will introduce the basic concepts relating to profinite groups, illustrate with some examples, and explain where they occur in the study of infinite groups. (Little prerequisites are needed, though some topology will occur.)

• 20th April 2005
  Jorge André (CAUL, Lisbon): Some results on near permutation semigroups

  Abstract

  A transformation semigroup over a set X with N elements is said to be a near permutation semigroup if it is generated by a group of permutations and by a set of transformations of rank N-1. In this talk I will show some ways of checking whether those specific transformations semigroups belong to various structural classes of semigroups, namely regular and inverse semigroups, just by analysing its generators.

• Monday 9th May 2005
  Vince Vatter (Rutgers): Enumeration schemes for restricted permutations
• 18th May 2005
  Murray Elder (St Andrews): Words in the Grigorchuk group

  Abstract

  In the mid 80's Grigorchuk found a group that could be called the "counterexample to everything" for finitely generated groups. It has intermediate growth, every group element has finite order (a power of 2), its not finitely presented, and the list goes on.

  Grigorchuk is sure to talk about it at Groups St Andrews, so I want to give an introduction to it, and discuss my recent work with Mauricio Gutierrez, where we use a GAP program to examine the nature of geodesic words in the group. Its early days but we are finding some incredibly beautiful structure, and fractal-like behaviour.

  Our work encompasses group theory, automata, computational techniques, and combinatorial insight so has broad appeal for the CIRCA crowd.

• 15th June 2005
  Catarina Carvalho (St Andrews): Finite generation of E-unitary inverse semigroups
• 29th June 2005
  Bob Gray (St Andrews): Subsemigroups and their boundaries