The Fourier transform and Hausdorff dimension delivered by Pertti Mattila.
The theme of the course is some interplay between Fourier analysis and geometric measure theory. I begin by explaining some relations between Fourier transforms of measures and Hausdorff dimension of sets. Then I give applications to some geometric problems on Hausdorff dimension such as dimension estimates on projections, intersections and distance sets. Another somewhat separate, but anyway related, topic is questions on Besicovitch (or Kakeya) sets and their relations to modern Fourier analysis, in particular Fourier restriction problems. I discuss how estimates on Hausdorff dimension of Besicovitch sets are related to restriction estimates and I at least survey the best known dimension estimates on Besicovitch sets.
The lectures will be based on the book
P. Mattila: Fourier analysis and Hausdorff dimension, Cambridge University Press, 2015
There will be introductory talks aimed at students and non-specialists on Thursday's evening (31 March). There will be five sessions (Friday morning, Friday afternoon, Saturday morning, Saturday afternoon, Sunday morning), each starting with the course Pertti Mattila and followed by talks of other participants.
All lectures will take place at the Mathematical Institute of the Polish Academy of Sciences in Warsaw (www.impan.pl)
There will be no conference fee, but we do ask people to register in advance. It is probable that we will be able to cover the accommodation of some number of participants (with the strong emphasis of young people and researchers without financial support of their organizations).
For the registration contact
Wandering seminar is an initiative, which aims at integrating ergodic theory and dynamical systems research groups in Poland. The idea is to organise mini-conferences/workshops a few times each year. These meeting are to be devoted to actual research topics in our area. Contrary to what the title suggest, this should be a recurring event, which only wanders geographically across Polish universities with dynamical systems research groups.