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Chin-Yu Hsiao

2008-10-07
14:00:00 - 15:50:00

On the singularities of the Szego projection for ''0,q'' forms

308 , Mathematics Research Center Building (ori. New Math. Bldg.)

In this work we completely study the heat equation method of Menikoff-Sjostrand and apply it to the Kohn Laplacian defined on a compact orientable connected CR manifold. We then get the full asymptotic expansion of the Szego projection for (0,q) forms. This generalizes a result of Boutet de Monvel and Sjostrand for (0,0) forms. Our mail tool is Fourier integral operators with complex valued phase functions of Melin and Sjostrand. We hope that this talk can serve as an introduction to certain micolocal techniques with applications to CR geometry and complex geometry.