Date:
Tue, 16/12/202514:00-15:00
Location:
Ross 70
Speaker: Amir Algom (University of Haifa at Oranim)
Title: Recent Progress on Fourier Decay and L^2-flattening
Abstract: The study of Fourier decay for stationary measures is a classical problem, tracing back to Erdős’s 1939 work on Bernoulli convolutions. Over the years, ideas from number theory, smooth dynamics, and arithmetic combinatorics have led to substantial progress, yet several fundamental questions remain open. I will discuss recent progress in this area, including that a sufficiently regular image of a self-similar measure on R can exhibit polynomial Fourier decay, even when the original measure has no decay at all. A key tool used here is L^2-flattening. This notion has remarkable applications, yet fully determining which measures satisfy it remains open; I will report on progress in this direction as well.
Based on joint works with F. Rodríguez Hertz, Z. Wang, M. Wu, O. Khalil, T. Orponen, and others.
Title: Recent Progress on Fourier Decay and L^2-flattening
Abstract: The study of Fourier decay for stationary measures is a classical problem, tracing back to Erdős’s 1939 work on Bernoulli convolutions. Over the years, ideas from number theory, smooth dynamics, and arithmetic combinatorics have led to substantial progress, yet several fundamental questions remain open. I will discuss recent progress in this area, including that a sufficiently regular image of a self-similar measure on R can exhibit polynomial Fourier decay, even when the original measure has no decay at all. A key tool used here is L^2-flattening. This notion has remarkable applications, yet fully determining which measures satisfy it remains open; I will report on progress in this direction as well.
Based on joint works with F. Rodríguez Hertz, Z. Wang, M. Wu, O. Khalil, T. Orponen, and others.