18 Feb 2011; IMS (UiTø), room U1=A228. Friday 12:15-14:00.

Boris Kruglikov

"Symmetries of almost complex structures"

Generically an almost complex structure has no symmetries at all. However there exist interesting symmetric structures different from integrable complex structures. We describe how to guarantee that the pseudogroup of local symmetries is small (finite-dimensional).

It will be indicated that a large symmetry pseudogroup (infinite-dimensional) is a signature of some integrable structure, like a pseudoholomorphic foliation. We are mostly concerned with almost complex structures in dimensions 4 and 6, while briefly discuss the higher dimensions.

The whole story can be understood as search of point symmetries of (nontrivial) Cauchy-Riemann equations. I will describe the most symmetric models of these. The exposition will not depend on familiarity with the subject.