Penrose transformation and complex integral geometry

A survey is given of results on the representation of solutions of systems of massless equations in terms of solutions of the Cauchy-Riemann equations on the space of Penrose twisters. A detailed introduction to the theory of twistors is given. The basic integral transform — the Penrose transformation — is investigated by means of complex integral geometry. Other approaches to the theory of twistors are discussed and compared. In addition, the Yang-Mills equation is considered from the point of view of nonlinear Cauchy-Riemann equations.     

Bott periodicity and stable quantum classes

We use Bott periodicity to relate previously defined quantum classes to certain “exotic Chern classes” on $BU$ . This provides an interesting computational and theoretical framework for some Gromov–Witten invariants connected with cohomological field theories. This framework has applications to study of higher dimensional, Hamiltonian rigidity aspects of Hofer geometry of $ \mathbb{CP }^{n}$ , one of which we discuss here.     

Segre hyperboloids and rational subvarieties in Grassmannians

Moscow State University. L'vov Polytechnical Institute. Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 24, No. 1, pp. 69–71, January–March, 1990.     

Siegel domain realization of pseudo-Hermitian symmetric manifolds

For some pseudo-Hermitian symmetric manifolds there are Zariski open subsets which are biholomorphically equivalent to tube domains. These tube domains correspond to homogeneous nonconvex cones.     

Remarks on infinitesimally desarguesian families of curves

Infinitesimally Desarguesian two-parameter families of curves in the plane which are in a sense close to the family of straight lines are discussed. Their properties, examples, and multidimensional generalizations are considered.