Multivariable algorithmics seeks to develop algorithms and complexity theory in a theory taking account of the parameters associated with the input data. This area has seen enormous progress in the last 25 years. I will look at the development, achievements, and challenges associated with the area in a general talk.
Rod Downey works in the theory of computation, computational complexity and most recently, algorithmic randomness. The last seeks to reconcile statistical notions with those of algorithmic information theory. The former seeks to try to develop complexity theory to be attuned to real computation by exploiting the multivariant nature of data. He has won numerous awards for his work in logic and his work in theoretical computer science. These include the inaugural MacLaurin Fellowship, the Hamilton Prize of the Royal Society of NZ, and the ASL Shoenfield Prize in Logic. He has been an organizer for several Dagstuhl meetings, including ones on parameterized complexity (which he co-invented with Mike Fellows) and one on computation on infinite structures. He was the first New Zealand based mathematician to give an invited lecture at the International Congress of Mathematicians, in its 100+ year history, and is only the second New Zealand based computer scientist to become a Fellow of Association for Computing Machinery. He has given invited addresses an numerous conferences including the International Congress of Logic Methodology and Philosophy of Science, and the IEEE Conference on Computational Complexity, is an editor of several journals, and author of around 200 journal papers, and several books.