William Troiani is a Master of Science (Mathematics and Statistics) student at the School of Mathematics and Statistics at the University of Melbourne. In particular, William is part of the Pure Mathematics stream. His interests lie in the interplay between Pure Mathematics and Computer Science. Specifically, his research interests revolve around select areas of Category Theory (such as Symmetric Closed Monoidal Categories), as well as Linear Logic and its connections to Linear Algebra. By studying such areas, William hopes to contribute towards our understanding of computation; what exactly is computation? Why is it worth thinking about?
One possible approach to this, is to examine already existing connections between Mathematical Logic, and programming languages such as the λ-Calculus (the Curry-Howard correspondence provides a concrete example of such a connection). It is through these areas of Mathematics, Logic, and Computer Science, that William hopes to push our Mathematical understanding of computer programs as formal objects, which in a world where the sophistication of modern technology is rapidly advancing, is an important task.
Programming in Three Dimensions
What is computation? The pioneering work of Godel, Turing and Church in the 1930s organised the theory of computation around several different, but equivalent, definitions of the mathematical objects that we now call “computer programs”. Recent developments in mathematics, computer science and physics are leading to a re-imagining of the nature these objects. For example: programs and their execution are often presented using string diagrams and transformations of diagrams, either for λ-terms in Church’s approach to computation or in related approaches like linear logic, an abstract functional programming language introduced by Girard.