The Dehn function of SL(n,Z)

Geometry & Topology
Event time: 
Tuesday, November 10, 2009 - 8:10am to Monday, November 9, 2009 - 7:00pm
215 LOM
Robert Young
Speaker affiliation: 
Event description: 

The Dehn function is a group invariant which connects geometric and
combinatorial group theory; it measures both the difficulty of the
word problem and the area necessary to fill a closed curve in an
associated space with a disc. The behavior of the Dehn function for
high-rank lattices in high-rank symmetric spaces has long been an open
question; one particularly interesting case is SL(n,Z). Thurston
conjectured that SL(n,Z) has a quadratic Dehn function when n>=4. This
differs from the behavior for n=2 (when the Dehn function is linear)
and for n=3 (when it is exponential). I have proven that it is
quadratic when n>=5, and in this talk, I will discuss some of the
background of the problem and sketch a proof that it is at most
quartic when n >= 5.