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.

# The Dehn function of SL(n,Z)

Event time:

Tuesday, November 10, 2009 - 8:10am to Monday, November 9, 2009 - 7:00pm

Location:

215 LOM

Speaker:

Robert Young

Speaker affiliation:

IHES

Event description: