GAUSS Seminar

Maitreyo Bhattacharjee

 The partition function p(n), which counts the number of distinct ways ofrepresenting n as a sum of positive integers, is a major object of study inNumber Theory. Though easy to compute for lower values of n, no closed-form expression for p(n) is known. It was Ramanujan, who first observedthat p(n) has modular arithmetic patterns. In 1944, while still anundergraduate at Cambridge, Dyson introduced the concept of “rank” of apartition. The theory gained a further impetus with the discovery ofRamanujan’s Lost Notebook in the Spring of 1976. In this talk, we wouldfocus on the early history of partitions, including the famous work of Hardyand Ramanujan(1918), various famous identities related to p(n), the theory ofranks, cranks, congruences, and some applications. No formal backgroundin Analytic Number Theory will be assumed.

Event Date: 
September 13, 2023 - 4:30pm to 5:20pm
Online (See URL)
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