We develop, analyze and implement numerical algorithms to solve optimization problems of the form min f(x) where x is a point on a smooth manifold. To this end, we first study differential and Riemannian geometry (with a focus dictated by computational con ...
Quantum computing has received wide-spread attention lately due the possibility of a near-term breakthrough of quantum supremacy. This course acts as an introduction to the area of quantum computing. After the course, the students will have an basic unders ...
This course will provide an introduction to model category theory, which is an abstract framework for generalizing homotopy theory beyond topological spaces and continuous maps. We will study numerous examples of model categories and their applications in ...
The topics addressed in this course are the structure theory of reductive algebraic groups, their associated Lie algebras, the related finite groups of Lie type, and the representation theory of all of these objects. ...