Youming Qiao (University of Technology Sydney) Friday 29 September, 12-1pm, Place: Carslaw 375 Title: Improved lower bound on the number of finite p-groups. Abstract: The number of finite p-groups of order p^k is known to be upper bounded by p^(2k^3/27+O(5k/2)) (Newman and Seeley), and lower bounded by p^(2k^3/27-4k^2/9) (G. Higman, 1960). In this talk I will describe how to obtain an improved lower bound p^(2k^3/27-O(k)). Interestingly, the key idea is inspired by a result from random graph theory (Babai-Erdos-Selkow, 1980). This is based on a joint work with Yinan Li at UTS.