Institut Mittag-Leffler - Junior Fellows - Interactions between fractal geometry, harmonic analysis, and dynamical systems

Interactions between fractal geometry, harmonic analysis, and dynamical systems

The purpose of the semester is to unite experts working at the interfaces between fractal geometry, harmonic analysis, and dynamical systems. These areas have become increasingly intertwined in the 2000s. Some of the most striking recent progress in each of fields has resulted from surprising input from the two others. The three main aims of the semester are to discover further connections between the fields, to facilitate experts in one field to rapidly gain a deeper understanding of the other two, and to provide junior mathematicians a unique opportunity gain experience in all three areas, early-on in their careers.

Examples of specific topics covered by the semester include (i) problems in continuum incidence geometry related to Kakeya sets, distance sets, and projections, sum-product theory, and finding patterns in fractal sets, (ii) connections between these problems with Fourier restriction and decoupling theory, fractal uncertainty principles in quantum chaos, and Fourier decay problems for dynamically defined fractal measures, (iii) the theory of effective equidistribution of random walks on groups.

The scientific programme of the semester will contain two week-long workshops, and several weekly seminars.

About Institut Mittag-Leffler

Institut Mittag-Leffler is an international centre for research and postdoctoral training in mathematical sciences. It was founded in 1916 by Professor Gösta Mittag-Leffler and his wife Signe, who donated their magnificent villa, with its first-class library, for the purpose of creating the institute that bears their name.

The institute, the oldest mathematical research institute in the world, operates under the auspices of the Royal Swedish Academy of Sciences but enjoys great autonomy. 

The premises of Institut Mittag-Leffler encompasses several buildings on a park-like estate. The main building, originally the home of Gösta and Signe, is a beautifully preserved villa in the art nouveau style. In addition to the library, the building houses a lecture room and offices for staff and participants.

Our Mission

The mission of Institut Mittag-Leffler is to support international top-level research in mathematics, with special attention to the development of mathematical research in Nordic countries. It also has a responsibility to serve as a contact and link between mathematicians in the Nordic countries as well as the international research community.

Activities

Major activities of the institute include research programs, conferences, workshops and summer schools. 

Publications

The institute is responsible for publishing two research journals: Acta Mathematica and Arkiv för matematik.

• Acta Mathematica was founded by Gösta Mittag-Leffler in 1882 and is one of the most prestigious mathematics research journals in the world.
• Arkiv för matematik was founded 1903 and since then became a high quality research journal.