University of Washington Department of Mathematics Matthew Alan Badger
Matthew at Canandaigua Lake

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

Winter 10 Office Hours
M By Appointment
T 11:00 - 12:00
W By Appointment
H By Appointment
F 10:20 - 11:20

Office hours are held
in PDL C-109

Fourth Year Graduate Student

Mathematics

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

My thesis advisor is Tatiana Toro.

Here is a random (and useful!) 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

Winter 2010

Starting in January, I will be teaching...

     Math 308K - Matrix Algebra and Its Applications

Previous Quarters

Research

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

Intersecting Varieties

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 Bee
North American history in Ontario County, NY
Sage <link to>
Open Source Mathematics Software
Date of Freshest Content: January 4, 2010