Abstract: Wave turbulence theory is a vast subject, and its goal is to formulate for us a multiscale picture of wave interactions.
Phenomena involving interactions of waves happen at different scales and in different media: from gravitational waves to the waves on the surface of the ocean, from our milk and coffee in the morning to infinitesimal particles that behave like wave packets in quantum physics. These phenomena are difficult to study in a rigorous mathematical manner, but because of this challenge, mathematicians have developed interdisciplinary approaches that are powerful and beautiful.
During these lectures I will describe some of these approaches and I will outline along the way questions that remain open in spite of the great progress already made.
This is the first of three lectures. This lecture will be followed by a reception in Bevier Commons.