My main research interests lie in geometry and analysis, particularly in questions concerning fractal sets and measures. Fractals are intricate and often beautiful mathematical objects which exhibit complexity over a wide range of scales. They often arise naturally through dynamical processes, for example from conformal or non-conformal iterated function systems. I am especially interested in the rate of decay of the Fourier transforms of stationary measures for such systems; this is the subject of my MSCA fellowship ‘Fourier Decay for Nonlinear Fractal Measures.’ Another strand of my research explores different notions of dimension, such as the intermediate dimensions, which provide refined information about the global and local scaling properties of sets and measures. I enjoy finding connections between these topics and other areas of mathematics such as number theory, probability, and dynamical systems.
More information is available on my personal website https://amlan-banaji.github.io
