Abstract:

Analysis of Boolean functions (AoBF) applies tools from mathematical analysis, like a discrete variant of the Fourier transform, to study functions defined on the discrete hypercube {0,1}^n. While this setting may seem restricted, one can find applications of AoBF in a wide variety of areas, ranging from social choice and cryptography to percolation theory and quantum computing.

We shall describe the fundamental notions and results of AoBF, many of which were developed at the Hebrew University, and present several applications to diverse areas.

Nathan Keller - Analysis of Boolean Functions and Where to Find It