Michael Hallam recently completed a Bachelor of Mathematical Sciences (Advanced) at Adelaide University, majoring in pure mathematics. In 2016 he will begin a Master of Philosophy at Adelaide University, studying Seiberg-Witten invariants and their applications. He has not always been interested in maths – in fact he resented being forced to slog through pages and pages of boring, repetitive calculations in primary school maths class. It wasn’t until reaching year 12 in high school that he began to appreciate the beauty and elegance of mathematics, and ever since then he has been hooked on learning new maths and challenging himself to understand unfamiliar concepts. Michael’s interests are in pure maths – particularly topology and analysis, but pretty much anything pure can grab his attention. He is excited to begin researching and aspires to a long and fruitful career in mathematics.
Internal Hom-Objects In The Category Of Topological Spaces
The areas of research are category theory and topology. It is known that internal hom-objects can fail to exist in the category of topological spaces. After reading and understanding the relevant theory behind this, the main goal of the project is to develop a series of examples which illustrate this phenomenon, and in particular to classify the different ways in which this failure can occur. A secondary research goal of the project is to understand how the notion of compactness arises naturally from the internal hom-object problem for topological spaces.