Responsible: Onirban Islam

Wave phenomena are omnipresent, from the propagation of sound and light to quantum fields. Waves are described mathematically by second-order partial differential equations, which are examined in detail in the lecture. The theory is developed on curved spacetimes in order to deal with applications in general relativity, for instance. After a chapter on fundamentals, the exact content of which depends on the prior knowledge of the audience, there is a chapter on linear and then one on non-linear wave equations. The existence, uniqueness and stability of solutions are discussed. Other topics include finite propagation speed, singularity propagation and the Huygens property.

In the first-week rudimentary materials on differential operators and Lorentzian geometry will be discussed by Rebecca Roero  as a preparation.

Schedule:
Lecture: Tuesdays 12:15-13:45 and Fridays 14:00-15:30
Tutorial: Fridays 12:00-13:30;

Place: Institute for Mathematics, Campus Golm, House 9:
Lecture: Tuesday Room 2.05.1.06 & Friday Room 2.09.0.13
Tutorial: Friday 2.09.0.14 

Literature:
Lecture notes on Geometric Wave Equations by Christian Bär