Benjamin Young

• Postdoc in Random Matrix Theory
• Mathematical Sciences Research Institute
• benyoung at math dot msri dot org

Research

I study enumerative and algebraic combinatorics. Loosely speaking, this means that I use algebraic methods to count things. The "things", for me, are usually objects like tilings of plane regions, various types of partitions of an integer, discrete surfaces, and so forth. I have a particular fondness for questions which have some application outside of my field.

Preprints of my papers are available on the arXiv.

Here is my CV in PDF format.

Gallery

I'm convinced that it's always a good idea to spend as much time and energy as you need to visualize a problem, so I make a lot of pictures and models.

Here are some pictures that I have made. I often prefer to write programs that generate pictures. I use a variety of tools to make my pictures, nearly all of which are free software: this includes POV-Ray, perl, the GIMP, imagemagick and LaTeX. For pictures simple enough to draw by hand, I use xfig or inkscape. Very occasionally, I use a camera (although I nearly always need help with it).

• Height functions of domino tilings on Aztec Diamonds: Order 51 Order 201
• A pyramid partition, viewed from above, looks like a domino tiling of the plane.
• If you redraw a length-infinity pyramid partition slightly, you get two 3D Young diagrams which share a common asymptotic shape.
• Cutting a box along the planes x=y, y=z, x=z and measuring the volumes of the pieces. (A permutation problem of Knuth, in dimension 3).
• If you cut a tube on an angle and unroll it , you get a sine wave. I noticed this when I was a high school student; in retrospect, it was one of the first mathematical facts I discovered for myself.