This page is no longer being updated; please visit my new webpage at NYU

Robert Young

Contact Information

• Address:
  Robert Young
  Courant Institute of Mathematical Sciences
  251 Mercer St.
  New York, NY 10012
  
• Email: rjyoung1729@gmail.com

About Me

Preprints: The Dehn function of SL(n;Z).

We prove that when n>=5, the Dehn function of SL(n;Z) is quadratic. The proof involves decomposing a disc in SL(n;R)/SO(n) into triangles of varying sizes. By mapping these triangles into SL(n;Z) and replacing large elementary matrices by "shortcuts," we obtain words of a particular form, and we use combinatorial techniques to fill these loops.

Most of my papers can be found at the arXiv; here are some slides and notes from talks I've given:

• "The Dehn function of SL(n;Z)", from a talk at Tufts, Oct. 2009.
• Some expository notes on asymptotic cones and filling inequalities, from a talk at "The Isoperimetric Inequality for SL(n,Z)", Sep. 2008.
• "Filling Inequalities in Nilpotent Groups", from a talk at Universite Paris-Sud, Oct. 2007.
• "Scaled Relators and Dehn Functions for Nilpotent Groups", from a talk at the Combinatorial and geometric group theory conference at Vanderbilt, May 2006.
• "Averaged Dehn Functions in Nilpotent Groups", from a talk at the Conference on Geometric and Probabilistic Methods in Group Theory and Dynamical Systems at Texas A&M