Hardwired... to Szarek and Ball

I shall present an extension of Szarek’s optimal Khinchin inequality (1976) for distributions close to the Rademacher one when all the weights are uniformly bounded by a 1/√2 fraction of their total l_2 mass; similarly for Ball’s cube slicing inequality (1986). The underpinning to such estimates is the Fourier-analytic approach going back to Haagerup (1981). Based on joint work with Eskenazis and Nayar.