Analysis Seminar

Title: (Special Time)The Structure of the Singular Set of a Two-Phase Free Boundary Problem for Harmonic Measure
Speaker: Max Engelstein
Speaker Info: University of Chicago
Brief Description:
Special Note: Special Time

We study the stratification, structure and dimension of the singular set of a two-phase free boundary problem for harmonic measure. However, in our setting, the usual ingredients (e.g. monotonicity formulas, the uniqueness of blowups etc) are unavailable. Instead, we study the (pseudo-)tangent sets using techniques from geometric measure theory. Two key tools are Lojasiewicz inequalities for harmonic polynomials and the quantitative stratification results of Cheeger, Naber and Valtorta. This is joint work with Matthew Badger (UConn) and Tatiana Toro (UW-Seattle).
Date: Monday, November 30, 2015
Time: 3:00pm
Where: Lunt 105
Contact Person: Prof. Aaron Naber
Contact email: anaber@math.northwestern.edu
Contact Phone: 847-491-5580
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