SEMINAR.....
Event Title : "Polynomial approximation, Polynamial convexity and CR singularities"
Speaker : Dr. Gautam Bharali
Affiliation : University of Michigan
Subject Area : Mathematics
Date : March 28, 2005
Time : 4.00 pm
Venue : Lecture Hall I, Depat of Mathematics
Abstract : We consider the following question: given a closed disc D in the complex plane, and a continuous complex valued function F, when is the uniform algebra generated by Z and F(z) equal to the class of continuous functions on D? when F is smooth, the graph of F is a smooth surface S in C^2. The answer to the above question is complicated by the presence of points P in S at which the tangent plane T_p(S) is a complex subspace of the ambient tangent space(C^2)_p. Such points are called CR singularities. In this talk, we will address some of the complications posed by CR singularities. To this end, we will also present a functional-analytic result that answers the initial question for certain non-smooth functions F