Ingrid Daubechies, Princeton University, The interplay between analysis and algorithms.

Eleny Ionel, University of Wisconsin, Embedded curves and Gromov-Witten invariants.

Bruce A. Kleiner, University of Michigan, Ann Arbor, Perelman's work on Ricci flow.

Robert K. Lazarsfeld, University of Michigan, How polynomials vanish: Singularities, integrals, and ideals, Part III: Global applications of multiplier ideals.

Robert K. Lazarsfeld, University of Michigan, How polynomials vanish: Singularities, integrals, and ideals, Part II: The local theory of multiplier ideals.

Robert K. Lazarsfeld, University of Michigan, How polynomials vanish: Singularities, integrals, and ideals, Part I: How many times does a polynomial vanish at a point?

Gunther Uhlmann, University of Washington, Travel time tomography, boundary rigidity, and the Dirichlet-to-Neumann map.

Avi Wigderson, Institute for Advanced Study, The power and weakness of randomness (when you are short on time).

Steven M. Zelditch, Johns Hopkins University, Random Complex Geometry, or How to count universes in string theory.

Georgia Benkart, University of Wisconsin, Madison, Square ice is very nice, but can you put a match to it?

Erik D. Demaine, Massachusetts Institute of Technology, Origami, linkages, and polyhedra: Folding with algorithms.

Fernando Q. Gouv\^ea, Colby College, What are p-adic numbers and what are they for?

Steven G. Krantz, Washington University in St. Louis, Symmetry in complex analysis.

Ravi D. Vakil, Stanford University, Given four lines in space, how many other lines meet all four?: The geometry, topology, and combinatorics behind linear algebra.

Robin J. Wilson, The Open University, Victorian combinatorics.