Speaker: Ryan Budney
 
Title: A basic family of embedding spaces.

Abstract: When studying any phenomena, a standard practice 
is to focus on some of the simplest objects that exhibit a 
non-trivial behavior. If one can get a sufficient 
understanding of them, then one inductively moves on to 
increasingly more complicated objects.  In the case of, say, 
isotopy classes of PL embeddings, this quickly leads one to 
the study of codimension 2 embeddings of spheres in spheres.  
This talk will be about spaces of smooth embeddings. In a 
sense, the most basic objects turn out to be the spaces of 
`long' embeddings of a Euclidean space in another Euclidean 
space, and the corresponding pseudoisotopy embedding spaces.   
I will show how, using work of Goodwillie, Sinha, Scannell,
Turchin and Vassiliev one can compute the first non-trivial 
homotopy groups of these spaces and give a quadrisecant 
interpretation of the answer.