2017 - Pertti Mattila (University of Helsinki)

Hausdorff dimension, Kakeya problems and projections
Viernes, 9 de junio de 2017, Sala 520, 11:30 h.
Departamento de Matemáticas
Módulo 17 de la Facultad de Ciencias (UAM)

Abstract: A Kakeya (or Besicovitch) set is a set of Lebesgue measure zero in a Euclidean space containing a unit line segment in all directions. The Kakeya conjecture asks whether these must have full Hausdorff dimension. This is known in the plane and open in higher dimensions. It is related to many questions of modern Fourier analysis. In the talk I shall discuss its relations to questions how Hausdorff dimension is transformed under projections.