Research

For many years I described myself as a computational geometer—my research focused on the design and analysis of algorithms and data structures to manipulate geometric objects (points, lines, curves, spheres, polyhedra, and so on). Over the last few years, the main focus of my work has shifted to computational topology, focusing mostly on algorithmic questions involving graphs embedded on surfaces. Specific problem areas I have worked on include basic questions in combinatorial geometry and topology; analysis of realistic geometric inputs; geometric range searching; algorithms for continuously changing data; and applications of geometric algorithms to computer graphics, computer vision, robotics, spatial and temporal databases, and mesh generation.

Most of my research has been supported by the National Science Foundation, under several different grants — an NSF Mathematical Sciences Research Postdoctoral Fellowship, a CAREER award (CCR-0093348), two ITR grants (DMR-0121695 and CCR-0219594), and an MSPA grant (DMS-0528086). I was also supported by a Sloan Research Fellowship.

My stuff

My local colleagues

My global colleagues

Me again

Here's a picture of me working in Barbados. The small folded-up piece of paper (a chain of right isosceles triangles joined along their short sides, or an unfolded paper football) and the larger multicolored toy (a chain of quarter circles joined end to end) can be moved in precisely the same ways. So in some sense, these two objects are "the same". I'm admiring the isomorphism, which is a fancy mathematical way of saying "staring off into space". My hair and my glasses are both smaller now, but alas, not my eyebrows.

I came in late to Jeff Erickson's 8:30 pm talk on "Lower Bounds in Computational Geometry." Jeff's a CS grad student at Berkeley, and when I emailed Yarvin to ask if he knew this guy Jeff who did theoretical computational geometry, he responded, "Theoretical computational geometry makes me ill."

Jeff Erickson (jeffe@cs.uiuc.edu) 21 Jan 2009