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Yum-Tong Siu 
2009-06-29 
15:30 - 16:30
101 , Mathematics Research Center Building (ori. New Math. Bldg.)

A new interface between analysis and algebraic geometry is the notion of multiplier ideal sheaves. They identify the location and the extent of failure of estimates in partial differential equations and describe the degeneracy from instability in geometric analysis. They have been applied to such algebraic geometric problems as the Fujita conjecture, the deformational invariance of plurigenera, and the analytic proof of the finite generation of the canonical ring. They have also opened up a new avenue of applying algebraic geometric methods to solvability and regularity problems of partial differential equations. This lecture is a survey to introduce to a general mathematical audience the method of multiplier ideal sheaves and its applications to analysis and algebraic geometry.