Summary
Modern data science, quantum computation, and high-dimensional probability rely on mathematical tools for understanding functions of many yes/no variables and their continuous analogues. This project studies such functions on the discrete cube and in Gaussian space, where approximation, learning, randomness, and boundary structure can be analyzed precisely. The work addresses basic questions about how much information is needed to learn a low-complexity function, how well complicated functions can be approximated by simple polynomials, and how the shape of a high-dimensional set controls its b
