# 2021-03-26

## 20:00

• What is a Dirichlet character?

• A Dirichlet character is equivalent to a group homomorphism \begin{align*} \chi:(\mathbb{Z} / N)^{\times} \rightarrow \mathbb{C}^{\times} .\end{align*}
• What is a Dirichlet L function?

• Definition of a Dirichlet $$L{\hbox{-}}$$function:

\begin{align*} L(s ; \chi):=\sum_{n=1}^{\infty} \frac{\chi(n)}{n^{s}} =\prod_{p} \qty{ 1-\chi(p) p^{-s} }^{-1} .\end{align*}

• How is a Bernoulii number defined? Generalized Bernoulli numbers:

• What is the conductor of a Dirichlet character?

• What is the J-homomorphism?

• How is it defined in terms of loop space?

• How is it defined in terms of framed cobordism? What is a framing?

• How is it defined in terms ofThom space? What is a Thom space?

• What is a complex oriented cohomology theory?

• What is a uniformizer?

• Uniformizer $$\pi$$: can think of this as a generator of a maximal ideal.