Skip to content

# GAN

## Seminar

### Dimension of Self-similar Measures and Additive Combinatorics

Hochman, M (Hebrew University of Jerusalem)
Wednesday 02 July 2014, 10:00-10:50

Seminar Room 1, Newton Institute

#### Abstract

I will discuss recent progress on the problem of computing the dimension of a self-similar set or measure in $\mathbb{R}$ in the presence of non-trivial overlaps. It is thought that unless the overlaps are "exact" (an essentially algebraic condition), the dimension achieves the trivial upper bound. I will present a weakened version of this that confirms the conjecture in some special cases. A key ingredient is a theorem in additive combinatorics that describes in a statistical sense the structure of measures whose convolution has roughly the same entropy at small scales as the original measure. As time permits, I will also discuss the situation in $\mathbb{R}^d$.

#### Video

The video for this talk should appear here if JavaScript is enabled.
If it doesn't, something may have gone wrong with our embedded player.
We'll get it fixed as soon as possible.

#### Comments

Start the discussion!

Back to top ∧