Research

Roughly speaking, I am interested in studying geometric structures which can be determined by differential equations on manifolds. For instance, you could look for constant mean curvature embeddings of a surface in three-space, or for complete constant scalar curvature metrics on a subdomain of a sphere. In both of these problems the geometry and analysis play off each other in beautiful ways. Also, to analyze the problems one must do analysis on noncompact manifolds.

CV: in postscript format or in pdf format.

Research summary: in postscript format or in pdf format. Teaching statement: in postscript format or in pdf format.

Thesis: in postscript format or in pdf format. This is gluing construction which glues together two CMC surfaces with Delaunay-type ends, along ends with matching asymptotics. Not that you'll read it, but you can look at the pictures.

A paper: postscript format or pdf format. End to end gluing for constant scalar curvature metrics, Indiana University Mathematics Journal Vol. 52 (2003) pages 703-726. This is essentially the same as the gluing construction in my thesis, but done in the context of the singular Yamabe problem.

Preprint: joint work with Nick Korevaar and Rob Kusner. in postscript format or pdf format. Shows nondegeneracy for many CMC surfaces and bounds the dimension of the space of L^2 Jacobi fields for even more CMC surfaces. We're excited about this paper.

Some Mathematical Links:

• The Geometry, Analysis, Numerics and Graphics Program: They have a lot of neat pictures of minimal and constant mean curvature surfaces. Also, they have several faculty who work on problems closely related to those I think about.
• The minimal surfaces group at Granada does great work and has a fantastic list of links and preprints on their site.
• Math Preprints This is a great resource for math articles. Anything that gets posted here stays forever, so you can download preprint versions of papers going back to 1994 (or so). And all the Annals articles get posted here.
• Mathscinet has references and reviews to articles going back to the early 1900's
• Dan Pollack was my advisor. Ok, he still gives me advice; but it's a less formal arrangement now.

Teaching

Math 2280 people go here.

Here are links to some previous courses:

• PDE for engineers, Fall 2003
• Topics in Geometry: the Yamabe Problem, Spring 2003
• Trigonometry, Fall 2002
• Linear Algebra, Spring 2002

Miscellaneous

Math Circle notes: notes for a series of three lectures on fractals, geared towards motivated high school students. Lecture 1. Lectures 2 and 3. Nick Korevaar wrote the supporting MAPLE code.

Constant mean curvature surfaces. These are lecture notes for a series of 4 lectures Nick, Nat, Andrejs and I gave on constant mean curvature during a minicourse in the summer of 2002.

The requisite list of links which have nothing to do with math.

• My sister collaborates with a group of artists called Pacce.
• I am a co-founder and member of the board of directors of the Salt Lake City Bicycle Collective. We do all sorts of bike-related stuff, like teaching kids how to repair bikes, and providing valet parking for bikes. We're just all around bicycle freaks.
• Critical Mass! Or try Michael Bluejay's Critical Mass Hub. The local page is here. Critical mass is a bunch of people riding their bikes in car traffic at rush hour. It takes place the last working Friday of every month, starting at 5:30ish at the Gallivan center. Join us be; it's fun. Flyers:
  • mammoth flyer in postscript format or in pdf format.
  • springtime flyer in postscript format or in pdf format.
  • pterodactyl flyer in postscript format or in pdf format.
  The revolution will not be motorized!
• More bike links here.
• the Ultimate Players Association. In case you need to know, the local Ultimate hotline number here is (801) 488-1177. The local Ultimate page is here.
• Repent! at the Coffee Messiah. My friend Opus owns and operates the lovely-est little coffee house in Seattle, at the corner of Denny and Olive.
• Record labels: Aum Fidelity, Tzadik, Okka Disk, Eremite and Kranky. Most of these are tiny labels. For instance, when I ordered some music from Aum Fidelity the president of the label sent it himself. Tzadik is John Zorn's label and releases a fair amount of archival stuff (i.e. whatever of Zorn's back-catalogue which he wants to rescue from being out of print).
• Comic strips: Apples and Orbifolds, Bob the Angry Flower, Cat and Girl and Ted Rall
• McSweeney's