Dear all, 

Hope to see you, 

Iddo. 

--

Title: Tangents and Local Set Approximation
Speaker: Matthew Badger (University of Connecticut) 
Time: Friday, September 26, 2014 at 3:30 pm
Place: MSB 109A
Abstract: One way to interpret derivatives that we teach to our calculus students is 
that a derivative m=f′(x) exists exactly when `zooming in' on the graph of the 
function at (x,f(x)) transforms the graph into a tangent line with slope m. When 
graphs of differentiable functions are replaced by arbitrary closed sets in Euclidean 
space, there is a similar story: `zooming in' on a closed set along a sequence of 
scales produces a `tangent set'. In the first part of the talk, I will describe a nice 
topology on the space of nonempty closed subsets of Euclidean space that lets us 
make a rigorous definition of tangent sets. (For geometers: tangent sets are 
distinct from, but related to Gromov-Hausdorff limits of pointed metric spaces.) In 
the second part of the talk, I will discuss some recent applications of tangent sets 
to problems in geometric measure theory and partial differential equations. This is 
joint work with Stephen Lewis, who recently finished his PhD at the University of 
Washington and is now a postdoc at the University of Minnesota. I will try to make 
the talk accessible to graduate students and faculty who are interested in analysis 
and nearby fields.