James Koussas completed a Bachelor of Science with majors in Mathematics and Statistics at La Trobe University in 2016. He is particularly interested in algebra, analysis and topology. James is planning on pursuing these interests in Honours and in his Vacation Research Project in 2017.
Complex Algebras of Graphs
A complex algebra is an algebra of subsets of a relational structure. These were first studied for groups, and then for various other structures, eventually giving rise to Boolean Algebras with Operators (BAOs). An important tool for the study of BAOs is a categorical duality between BAOs and certain extensions of Stone spaces. The duality is well known in general, but for special classes of BAOs it takes a particularly simple form. It was described in detail for many classes of BAOS, but, somewhat surprisingly, not for BAOs arising from graphs. The project will do that.