Seminar

# How I could not solve the Besicovitch/Kakeya problem (yet)

#### Fractal Geometry and Dynamics

#### 20 September 14:00 - 14:50

#### Tamas Keleti - Eötvös Loránd University

By a Besicovitch set in R^n we mean a set that contains a unit line segment in every direction. The Kakeya conjecture states that such a set must have Minkowski and Hausdorff dimension n. We will see how different hoped results would imply some versions of this conjecture. All of these hoped results we can prove only for cases which are not relevant in the original problem (but interesting in itself). I personally believe only in the Minkowski version of the conjecture. A possible way to disprove the Hausdorff version would be to show that a typical (in Baire category sense) Besicovitch set is a counter-example. It turns out that if a counter-example exists then it is typical. I will also mention some similar type of results in which the category argument gives examples of minimal Hausdorff dimension.

Organizers

Kenneth Falconer

University of St Andrews

Maarit Järvenpää

University of Oulu

Antti Kupiainen

University of Helsinki

Francois Ledrappier

University of Notre Dame

Pertti Mattila

University of Helsinki