# LECTURE NOTES

##
- Lecture 1
  History. Examples. Definitions. **** not written yet **

- Lecture 2
  Getting the Lie algebra from the group.

- Lecture 3
  The exponential map: from the algebra back to the group.

- Lecture 3 A
  Loose end: the bracket in the matrix case

- Lecture 4
  Functorial equivalence. Simply connected Lie groups.

- Lecture 5
  The three adjoint actions.

- Lecture 6
  Differential of the exponential map ( 1/19 and 1/24)..

- Lecture 6A
  Characterizing connected Abelian Lie groups ( 1/19)..

- Lecture 7
  universal covers. fundamental group. ( Andrew Marshall speaks )..

- Lecture 8?
  Characterizing simply connected Nilpotent Lie groups ( 1/31 ?)..

- Lecture 9
  universal cover of a Lie group is Lie

- Lecture 9A
  Exponentiating algebra homomorphisms to the group; subalgebra-subgroup theorem. ( 1/31 ?)..

- Lecture 11
  `Chapter 2': goal : get to Cartan's classification of compact Lie groups.

- Lecture 11 + N
  the dual perspective. preparation for Koiller's lecture of Feb 23
- G2 and rolling
  a ROUGH draft of a paper w Gil Bor

- Geometry on Lie Groups; Maximal Torus proof.
  last TeXed lecture