Title: A stability result for the semisum of sets in R^n
Speaker: Alessio Figalli
Speaker Info: University of Texas at Austin
Brief Description:
Special Note: Please note the unusual date and time

Given a Borel A is R^n of positive measure, one can consider its semisum S=(A+A)/2. It is clear that S contains A, and it is not difficult to prove that they have the same measure if and only if A is equal to his convex hull minus a set of measure zero. We now wonder whether this statement is stable: if the measure of S is close to the one of A, is A close to his convex hull? When n=1, one can approximate A with finite unions of intervals to translate the problem to Z, and in the discrete setting this question becomes a well studied problem in additive combinatorics, usually known as Freiman's Theorem. In this talk I'll review some results in the one-dimensional discrete setting, and show how to answer to this problem in arbitrary dimension. Also, if time permits, I'll discuss some extensions where one considers the semisum of two different sets.
Date: Friday, April 05, 2013
Time: 4:00pm
Where: Lunt 105
Contact Person: Valentino Tosatti
Contact email: tosatti@math.northwestern.edu
Contact Phone:
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