Aniruddha Sudarshan, Temple University
Selmer groups are used to study ranks of ellptic curves. Selmer groups are defined to be a subgroup of a certain first cohomology group whose elements satisfy some local conditions. For any integer m, we define the m-Selmer group using the Kummer maps. We then stick to the case when m=2, and perform a 2-descent to prove the Weak Mordell-Weil theorem for certain elliptic curves. If time permits, we talk about Selmer groups of twists of elliptic curves.