Title: Pretentious characters and the Polya-Vinogradov theorem

Abstract: In a recent paper, Granville and Soundararajan proved that a primitive character sum can be large if and only if the character 'pretends' to be like a primitive character of small conductor and opposite parity. From this characterization they were able to deduce a number of new results, including an improvement of the Polya-Vinogradov inequality for characters of bounded odd order. In this talk I will discuss their work and demonstrate how their characterization can be applied to improve Polya-Vinogradov for characters to smooth moduli.