Marc Levine 

Title: Motivic tubular neighborhoods and exponential maps

Abstract:  An algebraic version of of the tubular neighborhood construction
for differentiable manifolds is possible in one of the Morel-Voevodsky
homotopy categories.  An algebraic version of the punctured tubular
neighborhood is also possible, after a stabilization process. This latter
construction leads to a stable algebraic version of the exponential map on
the punctured normal bundle of an immersion. We apply this to give a
provisional definition of the stable motivic cohomology of the moduli space
of smooth curves.