Sofia Lindqvist (Oxford): Even moments of random multiplicative functions
Abstract: We give an asymptotic formula for the even moments of a sum of multiplicative Steinhaus or Rademacher random variables. This is obtained by expressing the sum as a multiple contour integral from which the asymptotic behaviour can be extracted. The result was obtained independently by Harper, Nikeghbali, and Radziwill by using a result of La Breteche. We also give an asymptotic relationship between the Steinhaus even moments and the even moments of a truncated characteristic polynomial of a unitary matrix, which extends earlier work of Conrey and Gamburd. The talk is based on joint work with Winston Heap.
Guhan Harikumar (UCL): Darmon cycles and the Kohnen-Shintani lifting
Abstract: We will first recall the theory of Darmon cycles due to V. Rotger and M. Seveso. These are a higher weight analogue of Stark-Heegner points. Then, we will show how these Darmon cycles are related to (a p-adic family of) half-integral weight modular forms. The relation follows by the p-adic interpolation of a well known formula of Waldspurger.