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
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.
Teaching
Winter 2010
Starting in January, I will be teaching...
Math 308K - Matrix Algebra and Its Applications
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 harmonic measure on non-tangentially accessible (NTA) domains in dimensions three and higher.
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)
