This short and intensive advanced undergraduate level course starts with the understanding of light as an electromagnetic wave. Optical phenomena in nature and technology and the underlying concepts are explored using mathematical ideas and tools, experimental demonstrations, and computer simulations. Problem-solving and discussion sessions are interwoven with the lectures. The physical ideas and mathematical models lead to least action and phase space in classical physics and wave functions in quantum physics.

This will be a reading course in algebraic topology, emphasizing the homotopy theoretic point of view. The main topics will be higher homotopy groups, (generalized) homology and cohomology, characteristic classes, and computational tools like spectral sequences. We will aim to cover Chapters 1 - 3 of the book "Homotopical Topology" by Anatoly Fomenko and Dmitry Fuchs. There will be no lectures; the students will read the material on their own. There will be weekly online office hours, during which students can interact with the instructor.