Abstracts of plenary talks
Abstract: The notion of $(\infty, 1)$-category has generated much interest recently due to the fact that it brings together key ideas in homotopy theory as well as category theory. Several models for $(\infty, 1)$-categories have been defined and shown to be equivalent, and they are all being used in different areas of algebra and topology. More recently, there has been interest in more general $(\infty, n)$-categories, especially with Lurie's recent work on the Cobordism Hypothesis. Comparison of different definitions is still work in progress by several authors. In this talk, we will go over some of the models for $(\infty, 1)$-categories and discuss some of the methods for inductively generalizing them to models for $(\infty, n)$-categories.
Abstract: Radar imaging is a technology that has been developed, very successfully, within the engineering community during the last 50 years. Radar systems on satellites now make beautiful images of regions of our earth and of other planets such as Venus. One of the key components of this impressive technology is mathematics, and many of the open problems are mathematical ones. This lecture will explain, from first principles, some of the basics of radar and the mathematics involved in producing high-resolution radar images.
Abstract: A higher-order function is a function for which the input or output is another function (in mathematics sometimes called a "functional"). In computing, higher-order functions occur e.g. when a function depends on an "oracle", and in physics, when a system interacts with a "black box". In this talk, I will discuss the lambda calculus as a mathematical approach to higher-order functions, and ways in which one might combine higher-order functions with quantum computation. I will argue that many (perhaps all) of the interesting phenomena of quantum information theory actually take place at higher-order functions, although that is not often how they are presented.