Benjamin Young

I work in algebaic combinatorics. My Ph.D. work was in the combinatorics of the dimer model, plane partitions and related areas. Lately, I have been working more with reduced words and areas related to Schubert calculus. I like to study problems with links to algebraic geometry, modern discrete probability, or other areas of mathematics, and I like solving problems.

These are links to preprints of my articles, each accompanied by a nice, (somewhat) representative picture.

If you prefer, you can simply look at a list of my preprints on the arxiv, the usual way.

	Rank 2 sheaces on toric 3-folds: classical and virtual counts Amin Gholampour, Martijn Kool, Benjamin Young Preprint.
	Nearly radial Neumann eigenfunctions on symmetric domains Nilima Nigam, Bartłomiej Siudeja, Benjamin Young Preprint.
	Intersection cohomology of the symmetric reciprocal plane Nicholas Proudfoot, Max Wakefield, Benjamin Young. To appear, Journal of Algebraic Combinatorics Preprint.
	A Markov growth process for Macdonald's distribution on reduced words Benjamin Young Preprint.
	Coxeter-Knuth graphs and a signed Little map for type B reduced words Sara Billey, Zachary Hamaker, Austin Roberts, Benjamin Young. Electronic Journal of Combinatorics 21.4 (2014): P4.6.
	Coupling Functions for Domino tilings of Aztec diamonds Sunil Chhita, Benjamin Young. Advances in Mathematics 259 (2014): 173-251.
	Asymptotic domino statistics in the Aztec diamond Sunil Chhita, Benjamin Young The Annals of Applied Probability 25.3 (2015): 1232-1278.
	Relating Edelman-Greene insertion to the Little map Zachary Hamaker, Benjamin Young Journal of Algebraic Combinatorics 40.3 (2014): 693-710.
	Correlations for the Novak process Eric Nordenstam, Benjamin Young FPSAC 2012
	Domino shuffling on Novak half-hexagons and Aztec half-diamonds Eric Nordenstam, Benjamin Young Electronic Journal of Combinatorics, 18(1), P181.
	The Orbifold Topological Vertex Jim Bryan, Charles Cadman, Ben Young Advances in Mathematics 229.1 (2012): 531-595.
	Domino shuffling for the Del Pezzo 3 lattice Cyndie Cottrell, Benjamin Young Preprint.
	A solution to one of Knuth's permutation problems Benjamin Young Comptes Rendus Mathematique 348.13 (2010): 713-716.
	Squishing dimers on the hexagon lattice Benjamin Young Electronic Journal of Combinatorics 16 (2009): R86.
	Generating functions for colored 3D Young diagrams and the Donaldson-Thomas invariants of orbifolds Benjamin Young, appendix by Jim Bryan. Part of my Ph.D. thesis. Duke Mathematical Journal, 152.1 (2010), 115-153.
	Computing a pyramid partition generating function with dimer shuffling Benjamin Young. Part of my Ph.D. thesis. Journal of Combinatorial Theory Series A, 116.2 (2007), 334-350.

Here is my curriculum vitae in pdf form.

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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.

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