Ainsley Pullen is a fourth year undergraduate student studying maths and philosophy at the University of Queensland (UQ). Her research interests are topology and algebra with a view towards algorithms. She has been able to pursue research in these areas as a part of the Advanced Study Program in Science at UQ. In 2013/4 she undertook a project in computational topology attempting to find a fast unknot recognition algorithm. Her current research is on quiver representations.
Ainsley presented an introduction to this topic for a non-specialist audience at this year’s Undergraduate Science Research Conference at UQ. Last year she also attended the Ludwig Maximilian University (LMU) Summer School on Mathematical Philosophy in Munich.
Aside from research a lot of her time at uni is spent organising events for the maths student society and filling the coke machine which pays for their events. This year she was able to help run AMSI’s Women in Mathematics event which is held in conjunction with the Winter School.
Indecomposables Of Quiver Representations In The Category Of Finitely Generated Abelian Groups
Quiver representations are abstract algebraic objects which are constructed by identifying vector spaces and maps between them with the nodes and arrows of a directed graph respectively. Quiver representations have applications through a related field of persistent homology, which studies the ___life-span__ of features such as holes within evolving shapes. Traditionally, these homology groups have coefficients from a field, which gives the vector spaces for our representations, and the life-span of a topological feature is encoded in the indecomposable of the quiver representation. However you can also consider the homology group with coefficien