[ TU/e -> CASA -> Mark Peletier -> Lipschitz Lectures 'Variational methods for the analysis of patterns' ]

Lipschitz Lectures 'Variational methods for the analysis of patterns'

Let me first describe the philosophy of the course. The study of patterns has a long history. An important body of pattern analysis comes from bifurcation theory; the books by Hoyle (Pattern Formation, 2006) and Peletier-Troy (Spatial Patterns in Higher-Order Models in Physics and Mechanics, 2001) give an excellent overview of this type of approach (although the book by my father and Bill Troy also uses variational arguments).

I am myself more interested in the variational theory of patterns, for two reasons. The first is that I have a general preference for variational problems; I like the variational structure, the intuition that it gives me, the connections with physics that often accompany such a structure, and the tools that variational systems allow me to use. The second is that the variational structure can allow for stronger statements, such as global characterizations instead of local ones, characterization of stability properties, strong limit characterizations such as by Gamma-convergence, and many more.

For this lecture series I chose for variational tools in pattern formation partly because of this personal preference, but also because it allows us to focus on a specific type of question - understanding pattern techniques that apply to a wide range of variational problems. The focus for this series of lectures will therefore be on variational tools that are well-suited for the analysis of patterns, and which will also serve you well in different problems.

In case you're interested in introductory reading material, here is a short list.

As for required background in mathematical tools: I'm assuming at the moment that most of the students will know most of this material; but to be completely sure, I want to spend some time on the first day (April 20) on the background knowledge, to make sure that you and I are on the same wavelength.

Course plan:

Exercises

Other events: