Formal groups of elliptic curves

In this two talk series, we will start by recalling elliptic curves and give the explicit construction of the formal group associated to an elliptic curve. While the construction is explicit, it does not make it clear if the construction is a special case of something more general. We will then describe the formal group of a specific Lie group as motivation for the notion of a formal group, and show the analogy with the case of elliptic curves. After that (most likely in the second talk) we will describe the general abstract construction of the formal group associated to an algebraic group (which includes elliptic curves), and then explain how the explicit construction of the formal group of an elliptic curve described earlier is a special case of this more general construction. Finally, we will explain how a perhaps better way of looking at a formal group is via the formal group scheme associated to an elliptic curve. We will assume background in basic algebraic geometry (e.g., local rings of varieties), but nothing beyond that. The talk is mostly expository in nature, and there will be some interesting algebraic geometry during the talk.