Graduate Student / Postdoc Seminar

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Quantification of Analyticity and Geometric Measure of Nodal Set

Speaker: Fanghua Lin, Courant Institute

Location: Warren Weaver Hall 1302

Date: Friday, March 23, 2018, 1 p.m.

Synopsis:

 It is well-known that the geometric measure and the topology of nodal sets of polynomials can be controlled in terms of its degree and
number of variables. One can generalize these statements to locally uniformly analytic functions; and these are studied in the classical algebriac (analytic) geometry. In this talk, we describe some approaches to these issues for solutions of elliptic (parabolic) equations under almost minimal smoothness assumptions. Some of the key ingredients are: quantification of analyticity (unique continuation) and growth of solutions, covering arguments from geometric measure theory and stability theorems.