Matthew Badger
University of Washington
Department of Mathematics
Box #354350
Seattle, WA 98195-4350

Office: C-109 Padelford
E-mail: mbadger at math.washington.edu

Autumn 09 Office Hours
M	By Appointment
T	By Appointment
W	By Appointment
H	By Appointment
F	By Appointment

Office hours are held
in PDL C-109

Fourth Year Graduate Student

Mathematics

I am a fourth year graduate student at the University of Washington, studying geometric measure theory (GMT).

My thesis advisor is Tatiana Toro.

Here is a random fact from GMT. "Tangent measures to tangent measures are tangent measures": if ν ∈ Tan(μ, x) and y ∈ spt(ν), then Tan(ν, y) ⊂ Tan(μ,x) for μ-a.e. x ∈ Rⁿ.

[Curriculum Vitae]

Teaching

Autumn 2009

Currently taking a break from teaching... I have an Inverse Problems and Partial Differential Equations RTG Fellowship this quarter.

Previous Quarters

Autumn 2008 - Spring 2009: Real Analysis (TA)
Summer 2008: Math 308B - Matrix Algebra with Applications
Autumn 2007 - Spring 2008: Fund. Concepts of Analysis (TA)
Autumn 2006: Math 124 AB / Math 124 BA - Calculus 1 (TA)

Research

I am currently using tools from geometric measure theory to study blow-ups of harmonic measure on non-tangentially accessible (NTA) domains in higher dimensions.

Here is a related picture. There are homogeneous harmonic polynomials of degree 3, e.g.

x²(y-z) + y²(z-x) + z²(x-y) - xyz

whose zero sets divide the 2-sphere into two components.

Preprints

Harmonic polynomials and tangent measures of harmonic measure (arXiv:0910.2591): We show that on an NTA domain if each tangent measure to harmonic measure at a point is a polynomial harmonic measure then the associated polynomials are homogeneous. Geometric information for solutions of a two-phase free boundary problem studied by Kenig and Toro is derived.

Presentations

Slides on some recent results I obtained are available:

Tangent Measures and Harmonic Polynomials: Short talk on June 19, 2009 at CRM. (PDF)

Miscellaneous

Bee Sting: North American history in Ontario County, NY
Division Algebras over the Real Numbers: Final project for Math 2501 at Pitt: after introducing the quaternions and octonions, we classify the associative, normed and alternative real division algebras. (PDF)
Sage <link to>: Open Source Mathematics Software

Date of Freshest Content: October 14, 2009