Hong Kong Geometry Colloquium

June 4, 2005 (Saturday)

Room 517, Meng Wah Complex, HKU

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Professor Yum-Tong Siu

William Elwood Byerly Professor, Harvard U., USA and

C.V. Starr Visiting Professor, HKU

Application of algebraic geometric techniques to estimates of partial differential equations

Abstract

Conditions for the solvability and the regularity of partial differential equations are usually pointwise, such as conditions for ellipticity and subellipticity. In this talk we will discuss a new method involving algebraic-geometric techniques of ideals and modules which handles situations when pointwise conditions fail but the failure does not occur in an integrable manner. Integrability here is taken in the sense of integrating a distribution of tangent subspaces in the theorem of Frobenius involving Lie-bracket conditions.