My research interest is in low-dimensional topology, geometry, combinatorial and geometric group theory, and computational complexity. In recent years most of my research has been on triangulations of 3-manifolds, decision problems, algorithms and complexity. I am normal but maybe on occassion only almost normal; however, in the latter case, a small tweak in either direction and I will become normal.

 

 

Available Papers

Finding planar surfaces in knot- and link-manifolds. Preprint, (2006), 44 pages. (with J. Hyam Rubinstein and Eric Sedgwick)
Layered-triangulations of 3-manifolds. Preprint, (2006), 96 pages. (with J. Hyam Rubinstein)
0-efficient triangulations of three-manifolds. J. Differential Geometry, 65 (2003), 61-168. (with J. Hyam Rubinstein)
Decision problems in the space of Dehn fillings. TOPOLOGY, 42 (2003), 845-906. (with E. Sedgwick)
Algorithms for essential surfaces in 3-manifold. Contemporary Mathematics, Vol 314, 2002, 107-124. (with David Letscher and Hyam Rubinstein)

 

 

Publications

Following is a list of publications. Copies may be requested from the author.

Download Publication List (PDF format)

 

Course Notes

MATH 697. TOPICS IN TOPOLOGY. (U MICH, Winter 2006)

CAUTION: These notes were written several years ago; in teaching MATH 697, I have decided to make MAJOR revisions to the style of presentation, the content and the order of material. Thus these notes will be undergoing revision - he said, hopefully.

Set 1. Basic Notions (Preliminary)
Set 2. Shrinking and Barrier Surfaces: Existence of Normal Surfaces
Set 4. Parametrizations of Normal and Almost Normal Surfaces

 

Here are transparencies of some of the presentations I have given over the past few years.

HOMEOMORPHISM PROBLEM (For Topologists) (December 8, 2006 - Columbia University) (October 28, 2006 - Lehigh-Lafayette)
BLOW-UPS OF IDEAL TRIANGULATIONS (December 5, 2006 - Rutgers University)
TRIANGULATIONS OF 3-MANIFOLDS (November 16, 2006 - Princeton University)
PEKING SUMMER SCHOOL LECTURES (July 10-24, 2005 - Beijing, China)
PLANAR SURFACES AND THE WORD PROBLEM (July 1999, University of Melbourne)
EFFICIENT TRIANGULATIONS (March 2002, Calvin College)
HOMEOMORPHISM PROBLEM (General Audience) (March 2004, Florida State University)

 

American Math Society

OSU Graduate Mathematics Program

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