The Burnside groups and small cancellation theory

In a pair of recent papers (one to appear and one forthcoming), the author develops a general version of small cancellation theory applicable in higher dimensions, and then applies this theory to the Burnside groups of sufficiently large exponent. The present article gives a brief introduction to the methods and techniques involved in the proofs. Many of the ideas originate with the recent work of A. Yu. Olshanskii and S. V. Ivanov. Some familiarity with their work on the Burnside problem is assumed.