Seminar Leader: Lawrence Mouillé

Location: Carnegie 111

Times and presenters: 

Mondays, 10-11am: 

• Eric Cochran, Marie Kramer, Sabrina Traver.

Tuesdays, 10-11am:

• Elana Israel, Nazia Valiyakath, Ralph Xu.

(Feel free to attend either of the sections; just let me know if you don't plan to attend the section you're listed under.)

Schedule: [click here to view]

(To edit the schedule, see the link Lawrence sent in an email email)

Notes:

• Matrix Lie groups, SU(2), and SO(3) - Sabrina Traver

• Connectedness of Lie groups and the identity component - Marie Kramer

• Lie group homomorphisms - Nazia Valiyakath

• The matrix exponential and Lie algebras - Eric Cochran

• Morse functions - Sabrina Traver

• Proof of Fundamental Theorem of Algebra using differential topology - Marie Kramer

• Rotationally symmetric metrics and doubly warped products - Eric Cochran

• Isometries of hyperbolic space - Sabrina Traver

• Bi-invariant metrics on Lie groups - Marie Kramer

• Killing fields - Eric Cochran

• Haar measure and the Peter-Weyl theorem - Sabrina Traver

Suggested topics for presentations: [click here to view]

Suggested sources for presentations:

• B. Hall, Lie groups, Lie Algebras, and Representations, Springer.

• J. Milnor, Topology from the Differential Viewpoint, Princeton University Press.

• J. Lee, Introduction to Smooth Manifolds, Springer.

• V. Guillemin & A. Pollack, Differential Topology, Prentice-Hall.

• M. Spivak, A Comprehensive Introduction to Differential Geometry, Volume I, Publish or Perish.

• M. Do Carmo, Riemannian Geometry, Birkhauser.

• P. Petersen, Riemannian Geometry, Springer.

• J. Milnor, Morse Theory, Princeton University Press.

• J. Cheeger & D. Ebin, Comparison Theorems in Riemannian Geometry, AMS Chelsea Publishing.

Outside Seminars:

• Virtual Seminar on Geometry with Symmetries - see webpage for details and to register.

• Topology/Geometry Zoom Seminar - email organizer Boris Botvinnik (Univ. of Oregon) to be added to the mailing list.

(Image copied from Arun Debray, M392C Notes: Morse Theory, 2018, https://www.math.purdue.edu/~adebray/lecture_notes/m392c_Morse_notes.pdf.)