model predictive control, Moving Horizon Estimation, Economic MPC, Distributed MPC

This course covers recent advances is building digital representations of humans for a variety of practical applications. The focus is on building realistic models of real humans, using measurements, and on numerical simulation of humans using finite element methods and other techniques.
The course will include aspects of 3D computer graphics (using Python) and numerical methods that may be attractive to applied mathematics graduate students and advanced undergraduates.

This course will give students an overview of Non-Newtonian Fluid Dynamics, and discuss two approaches to building constitutive models for complex fluids: continuum modeling and kinetic-microstructural modeling. In addition, it will provide an introduction to multiphase complex fluids and to numerical models and algorithms for computing complex fluid flows.

Evolution is the unifying theme in biology. Evolutionary processes are responsible for the emergence of the rich variety of species across the planet. Cooperation represents one of the key organizing principles in evolution, and the history of life and of societies could not have unfolded without the repeated cooperative integration of lower level units into higher level entities. Evolutionary theories have attracted increasing attention from other behavioural disciplines including sociology and economics. This has led to the notion of cultural evolution aiming at a better understanding of human cooperation including the emergence of social norms.
This course provides an introduction into mathematical models of evolution and the theory of games. Modelling techniques that are covered include: stochastic dynamics of invasion and fixation of mutants in finite populations; evolutionary game theory and frequency dependent selection; adaptive dynamics and the process of diversification and speciation through evolutionary branching; as well as modelling the dynamics in spatially structured populations.

This is a graduate course designed to introduce tensors (or multi-dimensional arrays) and their uses in statistics and machine learning. In particular, we will illustrate fundamental theoretical properties of several types of tensor decompositions, including CP-decomposition, nonnegative matrix and tensor decomposition, Tucker decomposition as well as tensor network decompositions arising from physics. We will see how these naturally come up in hidden variable models, Gaussian mixture models, directed and undirected graphical models, blind source separation, independent component analysis, and quantum physics. We will discuss algorithms for computing such decompositions, and will exhibit open problems.