A mathematical gallery

Many of the subjects I've worked on can be illustrated with nice pictures. Below is a collection of mathematical images related to papers I've written. See the references at the bottom for links to the relevant papers and additional information. Additional galleries can be found in these pages:

1. A random square Young tableau of order 25, shown on the left as a discrete stepped surface. The smooth surface on the right is the limit shape of such random Young tableaux. The coloring scheme highlights the level curves of both surfaces. [References]
2. The half-way permutation of a random sorting network with 2000 particles. [References and movies]
3. A random domino tiling of the Aztec diamond of order 50. [References]
4. A random Erdos-Szekeres permutation of order 50, and the limit shape of such permutations, an algebraic curve of degree 4. [References]
5. Connectivity patterns in loop percolation on a cylinder. [References]
6. A fully packed loop configuration of order 8. [References]
7. Bootstrap percolation (picture by Alexander Holroyd). [References]
8. A tesselation of the hyperbolic plane by quadrilaterals. This is related to a natural dynamical system associated with Pythagorean triples. [References]
9. Limit shapes of bumping routes in the Robinson-Schensted correspondence. [References]


1. Random square Young tableaux

2. Random sorting networks

3. Domino tilings

4. Erdos-Szekeres permutations

5-6. Connectivity patterns in loop percolation, fully packed loops

7. Bootstrap percolation

8. Tesselation of the hyperbolic plane by quadrilaterals

9. Bumping routes in the Robinson-Schensted correspondence