One of the most interesting things about several complex variables ("scv") is how geometry interacts with analysis. In one variable, there is hardly any geometry involved, but in scv: different domains (even topologically identical ones) have different holomorphic functions living on them, zero sets of holomorphic functions are surfaces which bend and twist in space (instead of just isolated points), the "canonical'' kernels associated to a domain (e.g., the Bergman and Szego kernels) are not truly canonical, but depend on the curvature of the boundary of the domain, and so on.

However, one of the most difficult things, for beginners, about working in scv is that it takes awhile to get to the frontier: methods from PDE, algebraic geometry and harmonic analysis are all routinely used in scv and mastering some of these methods takes time. In this working group, we will not develop scv as in a graduate course, but pick a couple of interesting objects and do some computations with them, for example the Bergman kernel. These objects are the focus of current research in the filed, but we will look at toy versions of research problems, by assuming a high degree of symmetry, and be able to do computations with them. A background course in complex analysis in one variable, and a desire to learn more complex analysis, are the only prerequistes for this working group.

To sign up for this working group, enroll for 3 credits in 693 (McNeal), call number 12626-7