Education

• Princeton University, Ph.D. in Mathematics, 1990.
• Cambridge University, Certificate of Advanced Study in Math., with honors, 1986.
• Harvard University, A.B. summa cum laude, fourth in class, 1985.

Faculty Positions and Fellowships

• Associate Professor, Department of Mathematics, University of Illinois (Urbana), 2000-
  
  • Faculty Fellow, Department of Theoretical & Applied Mechanics, 2000-
  • Faculty Fellow, National Center for Supercomputing Applications, 2000-2001
  • Acting Director, Center for Process Simulation and Design, May-Dec 2000
• Assistant Professor, Department of Mathematics, University of Illinois (Urbana), 1997-2000
• Assistant Professor, School of Mathematics, University of Minnesota, 1991-1997
• Visiting Assistant Professor, University of Illinois (Urbana), 1996
• Visiting Assistant Professor, Center for GANG, University of Massachusetts (Amherst), 1995
• Mathematical Sciences Research Institute Postdoctoral Fellow, 1993-1994
• Geometry Computing Group Postdoctoral Fellow, 1990-1993
• National Science Foundation Graduate Fellow, 1986-1989
• Henry Fellow at King's College, Cambridge, 1985-1986

Selected Research Publications

• On the Minimum Ropelength of Knots and Links, with Jason Cantarella and Rob Kusner, Inventiones Math., 2002, to appear.
• Cubic Polyhedra, with Chaim Goodman-Strauss, in Discrete Geometry, Dekker, 2002, to appear.
• Approximating Ropelength by Energy Functions, in Physical Knotting, AMS Contemp. Math., 2002, to appear.
• Dynamic Skin Triangulation, with Ho-Lun Cheng, Tamal Dey and Herbert Edelsbrunner, Discrete and Comput. Geom. 25, 2001, pp 525-568.
• Constant Mean Curvature Surfaces with Three Ends, with Karsten Große-Brauckmann and Rob Kusner, Proc. Nat'l Acad. Sci. USA 97:26, 2000, pp 14067-14068.
• New Tetrahedrally Close-Packed Structures, in Proc. Eurofoam 2000 (Delft), pp 111-119.
• Tight Knot Values Deviate from Linear Relations, with Jason Cantarella and Rob Kusner, Nature 392:6673, 1998, pp 237-238.
• Constant Mean Curvature Surfaces with Cylindrical Ends, with Karsten Große-Brauckmann and Rob Kusner, in Mathematical Visualization, Springer, 1998, pp 107-116.
• The Minimax Sphere Eversion, with George Francis et al, in Visualization and Mathematics, Springer, 1997, pp 3-20.
• Using Symmetry Features of the Surface Evolver to Study Foams, with Ken Brakke, in Visualization and Mathematics, Springer, 1997, pp 95-117.
• Möbius Energies for Knots and Links, Surfaces and Submanifolds, with Rob Kusner, in Geometric Topology, International Press, 1996, pp 570-604.
• Sphere Packings Give an Explicit Bound for the Besicovitch Covering Theorem, J. Geometric Analysis 4:2, 1994, pp 219--231.
• Monotonicity Theorems for Two-Phase Solids, with Frank Morgan, Francis Larché, Arch. Rat. Mech. Anal. 124:4, 1994, pp 329-353.
• Computing Hypersurfaces Which Minimize Surface Energy Plus Bulk Energy, in Motion by Mean Curvature and Related Topics, de Gruyter, 1994, pp 186-197.
• Minimizing the Squared Mean Curvature Integral for Surfaces in Space Forms, with Lucas Hsu and Rob Kusner, Experimental Math. 1:3, 1992, pp 191-207.

Published Videos

• The Optiverse, with George Francis and Stuart Levy, in VideoMath Festival at ICM'98, Springer, 1998, 7-minute video.
• Knot Energies, in VideoMath Festival at ICM'98, Springer, 1998, 3-minute video.
• Using Max-Flow/Min-Cut to Find Area-Minimizing Surfaces, in Computational Crystal Growers Workshop, AMS Sel. Lect. Math., 1992, pp 107-110 plus video.
• Crystalline Approximation: Computing Minimum Surfaces via Maximum Flows, in Computing Optimal Geometries, AMS Selected Lectures in Math., 1991, pp 59-62 plus video.
• Computing Soap Films and Crystals, with Fred Almgren, Ken Brakke, Jean Taylor, in Computing Optimal Geometries, 1991, 14-minute video.

Selected Invited Conference Lectures 1997-2002

2002

AMS Central Section (Madison)

2001

Physical Knotting and Unknotting (AMS meeting, Las Vegas); Geometry of Curves and Surfaces (AMS meeting, Columbia)

2000

Multimedia Tools for Mathematics (Lisbon); Mathematics, Art and Culture (Bologna); Geometrie (Oberwolfach) Int'l Soc. of Art and Math (Albany)

1999

Bridges Conference (Kansas); Int'l Soc. of Art and Math (Spain); Differential Geometry (AMS meeting, San Antonio)

1998

Geometry Day (EIU); SIGGRAPH (Orlando)

1997

VisMath'97 (Berlin); SIAM GD'97 (Nashville); Foams and Emulsions (Corsica); PDEs (AMS meeting, Maryland); Computational 3D Topology (MSRI, Berkeley)

Selected Colloquium Lectures at Math Departments

2002

UMass Amherst; U Wisconsin; U Pittsburgh; Texas Tech

1999-2001

U Georgia; Indiana U; WashU StLouis

1996-1998

UIUC; U Iowa; U Arkansas

1993-1995

U Wisconsin; U Minnesota; Florida SU; Northwestern U;

Grant support

• 2000-2003, PI, NSF grant DMS-0071520, Optimal Geometry: Theory and Computation
• 1999-2004, Dept. Educ. grant, Illinois Professional Learners Partnership.
• 1998-2002, Co-PI, NASA grant, Fluid Physics of Foam Evolution and Flow, with Aref and Thoroddsen (UIUC TAM).
• 1998-2001, Co-PI, NSF/DARPA OPAAL grant DMS-9873945, Center for Process Simulation and Design, through UIUC CSE program.
• 1997-2000, PI, NSF grant DMS-97027859, Theory and Computation of Optimal Geometries
• 1997-1999, Arnold O. Beckman Research Award, UIUC Research Board.