Speaker: Qihang Sun (UIUC)
Title: Asymptotics in partitions: circle method and Kloosterman sums
Abstract: In 1917, Hardy and Ramanujan established an asymptotic formula for the integer partition function $p(n)$. Rademacher later proved that this formula converges to $p(n)$ when summed to infinity. The concept of rank for partitions was introduced by Dyson to explain Ramanujan's congruences. Since then, the asymptotic properties of these rank functions and their connections with modular forms have become a vast area of research. In this talk, we will explore the recent progresses related to the rank of partitions, delving into both the circle method and Kloosterman sums.
