I finally sent an email off to Schroeder, who I had expressed an interest in working with before I decided to work with Tropp. He gave me a paper to read and invited me to two of his group meetings– in the first he developed a notion of discrete conformal mappings, and in the second a visitor gave a lecture on an ingenious geometric method for constructing approximate isometries (for applications like texture mapping, or position interpolation in animations). Unfortunately, I could not follow the paper, and the point of it bored me– something about constructing bases for forms on discrete manifolds so exterior differentiation and subdivision commute?– even though a lot of what his group does is right up my alley. Luck of the draw.

I could have inquired after other potential research directions (something like the approximate isometries idea would really capture my interest), but I think that working with Tropp is better in the long run– because the mathematics involved is foundational (in the sense of arising in the posing of many problems), there’s more potential for engaging deep but tractable mathematical problems, and a wider field that I could tap for future avenues of research. I feel the mathematics Schroeder’s group uses is, while slightly more asthetically pleasing to me, somehow less essential.

Anyhow, today I hope to get the final details of my courses for this term settled. Most importantly, when my reading course with Tropp is scheduled, and what I should get started on reading.

Possibly relevant posts:

• Research agenda (5/2/2008)
• A polynomial inequality (and some whining) (6/15/2008)
• Random Matrix studies (4/21/2008)