Interactions between fractal geometry, harmonic analysis, and dynamical systems
September 2 - December 11, 2026
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.
Workshop 1: September 21 — September 25
Workshop 2: November 16 — November 20
RECORDED SEMINARS: