A basic operation in calculus of variations is the Euler-Lagrange variational derivative, whose kernel determines the extremals of functionals. There exists a natural resolution of this operator, called the variational complex. In this talk, I shall explain how to use tools from the theory of vertex algebras to explicitly construct the variational complex. This also provides a very convenient language for classifying and constructing integrable Hamiltonian evolution equations.

Last time I introduced the variational complex of an algebra of differential functions and gave a sketchy definition of a vertex algebra. This week I will make this notion more precise and explain how to apply it to the calculus of variations.

The aim of psychology in general, and of cognitive psychology in particular, is to construct theoretical accounts of mental processes based on observed changes in performance on one or more cognitive tasks. The fundamental problem faced by the researcher is that these mental processes are not directly observable but must be inferred from changes in performance between different experimental conditions. This inference is further complicated by the fact that performance measures may only be monotonically related to the underlying psychological constructs. State-trace analysis provides an approach to this problem which has gained increasing interest in recent years. In this talk, I explain state-trace analysis and discuss the set of mathematical issues that flow from it. Principal among these are the challenges of statistical inference and an unexpected connection to the mathematics of oriented matroids.

In the modern information era, managers (e.g. winemakers) recognize the competitive opportunities represented by decision-support tools which can provide a significant cost savings & revenue increases for their businesses. Wineries make daily decisions on the processing of grapes, from harvest time (prediction of maturity of grapes, scheduling of equipment and labour, capacity planning, scheduling of crushers) through tank farm activities (planning and scheduling of wine and juice transfers on the tank farm) to packaging processes (bottling and storage activities). As such operation is quite complex, the whole area is loaded with interesting OR-related issues. These include the issues of global vs. local optimization, relationship between prediction and optimization, operating in dynamic environments, strategic vs. tactical optimization, and multi-objective optimization & trade-off analysis. During the talk we address the above issues; a few real-world applications will be shown and discussed to emphasize some of the presented material.

Research into two-dimensional laminar fluid mixing has enjoyed a renaissance in the last decade since the realisation that the Thurston–Nielsen theory of surface homeomorphisms can assist in designing efficient "topologically chaotic" batch mixers. In this talk I will survey some tools used in topological fluid kinematics, including braid groups, train-tracks, dynamical systems and topological index formulae. I will then make some speculations about topological chaos in three dimensions.

I will describe a family of algebras of tangles (which give rise to link invariants following the methods of Reshetikhin-Turaev and Jones) and describe some aspects of their structure and their representation theory. The main goal will be to explain how to use universal Verma modules for the symplectic group to compute the representation theory of affine BMW (Birman-Murakami-Wenzl) algebras.

This title is taken from the novel of Hermann Hesse. In joint work with A. Kleshchev, we were amused to discover a glass bead game for constructing representations of quiver Hecke algebras (algebras recently defined by Khovanov-Lauda and Rouquier whose representation theory categorifies quantum groups of Kac-Moody Lie algebras). In fact, the glass bead game is tantalizingly simple, and may soon be marketed in your local toy store. I will explain how this game works, and some of the fascinating numerology that appears in the scoring of the plays.