This is a study of Singularities of affine equidistants, especially an extrinsic geometry of surfaces in 4-space. Investigation of
the invariant geometry of surfaces in four space by the fields of reflection maps (continued research of P. Giblin, S. Janeczko,
M. Ruas). Constructions of tetrahedral chains accessible to the modelling of DNA or other long bio-particles. Study of differential
forms on polyhedral structures (S. T. Yau).
The talk by S.T. Yau
Title: Kohn-Rossi cohomology and nonexistence of CR morphisms between compact strongly pseudoconvex CR manifolds
Abstract: One of a fundamental questions in CR geometry ask: Given two strongly pseudoconvex CR manifolds X_1 and X_2 of
dimension n-1, determine whether there is a non-constant CR morphism between them. In this lecture we use Kohn-Rossi
cohomology to show the non-existence of non-constant CR morphism between such two CR manifolds. Specifically, we show that
there is no non-constant CR morphism from X_1 to X_2 if dimH^(p,q)_(KR) (X_1) < dimH^(p,q)_(KR) (X_2) for any (p,q) with 0 < q <n-1.