My talk will be related to the stable intersections of dynamically defined Cantor sets (as well as to the finding intervals in their sums). In the famous work of Morreira and Yoccoz it is shown that for a generic pair of dynamically defined Cantor sets with sum of their Hausdorff dimensions greater than one, their intersection (provided that they do intersect) is stable under small perturbations.
However, it would be nice to be able to check this for a particular couple of sets, and up to this moment the only explicitly checkable sufficient condition that is known is that the product of the thicknesses is greater than one.
I will present an approach to finding such a sufficient condition (eventually, in a computer-assisted way) that can be hopefully used to attack the conjecture that claims that F(2)+F(4) contains an interval (that is currently open).
My talk will be based on a joint project will A. Gorodetski, A. Gordenko and E. Nesterova.