SPECIAL SUMMER DIFFERENTIAL GEOMETRY SEMINARS

                           Monday, August 24
                          Wednesday, August 26
                             Padelford C-36
                                3:45 pm

           Deformation of CR structures and the Rumin complex

                             Takao Akahori
                (Himeji Institute of Technology, Japan)


One of the main applications of the theory of CR manifolds is in the
study of deformations of isolated singularities of complex analytic
varieties, by considering how changes in the analytic structure of the
singularity are reflected by changes in the CR structure on the boundary
of a small neighborhood of it (the ``link'' of the singularity).  A main
feature of the theory is the construction of a ``versal family'' of CR
structures on the link, which is a family of CR structures containing a
representative for each deformation, and which is minimal in a certain
sense.  Building on the pioneering work of Kuranishi, in the late 1980's
the speaker constructed such a versal family for each compact, strongly
pseudoconvex CR manifold of real dimension greater than 5.

Now, inspired by the Rumin complex (a new analytic approach to deRham
cohomology on contact manifolds introduced several years by Michel
Rumin), the speaker has succeeded in constructing a versal family of CR
structures on a strongly pseudoconvex CR manifold of real dimension 5.

The first of these two talks will explain the well known deformation
theory of CR structures.  The second talk will explain how to modify the
Rumin complex to obtain a versal family in dimension 5.

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For more information about this seminar, visit the DG/PDE Seminar Web
page (from the Math Department home page, https://www.math.washington.edu,
follow the link Seminars, Colloquia, and Conferences).

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