We will explore two highly symmetric lattices, the E8 lattice and the Leech lattice, which appear in many areas of mathematics. After looking at some closely related Dynkin diagrams, we will derive their associated theta series, which will contain series from the previous talk. Then we will discuss further properties, such as their providing the best lattice packings and providing the best kissing numbers in R^8 and R^24, respectively, as well as connections to sporadic simple groups.
This talk should be accessible to everyone -- elementary analysis and algebra recommended.