## EVENT DETAILS AND ABSTRACT

**Colloquium**
**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**

**Abstract:**

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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