Number Theory Seminar

The classical Diophantine problem of determining which integers can be written as a sum of two rational cubes has a long history; it includes works of Sylvester, Selmer, Satgé, Leiman and the recent work of Alpöge-Bhargava-Shnidman-Burungale-Skinner. In this talk, we will use Selmer groups of elliptic curves and integral binary cubic forms to study some cases of the rational cube sum problem. This talk is based on joint works with D. Majumdar, P. Shingavekar and B. Sury.