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Lecture Schedule for Differential Geometry 2

Introduction

The lectures are based on Jost's book "Riemannian Geometry and Geometric Analysis" References are to sections in that book.

January

Week 1

  • 05/01 Mon: Manifolds and Tangent Spaces (1.1, 1.2)
  • 07/01 Wed: no lecture
  • 09/01 Fri: Submanifolds (1.3)

Week 2

  • 12/01 Mon: Riemannian metrics (1.4)
  • 14/01 Wed: Existence of geodesics (1.5)
  • 16/01 Fri: Heat flow and geodesics (1.6)

Week 3

  • 19/01 Mon: No meeting - Martin Luther King day
  • 21/01 Wed: Geodesics on complete manifolds (1.7)
  • 23/01 Fri: Vector Bundles (1.8)

Week 4

  • 26/01 Mon: Vector Fields and Lie Algebras (1.9)
  • 28/01 Wed: Lie Groups (1.10)
  • 30/01 Fri: Spin Structures (1.11)

February

Week 5

  • 02/02 Mon: Spin II
  • 04/02 Wed: Laplace Operator (2.1)
  • 06/02 Fri: Harmonic Forms and deRham cohomology (2.2)

Week 6

  • 09/02 Mon: Heat flow and Harmonic forms (2.4)
  • 11/02 Wed: Connections on Vector Bundles (3.1)
  • 13/02 Fri: Levi-Civita connection (3.3)

Week 7

  • 16/02 Mon: Yang Mills Functional (3.2)
  • 18/02 Wed: Yang-Mills II
  • 20/02 Fri: Yang-Mills III

Week 8

  • 23/02 Mon: Yang-Mills IV
  • 25/02 Wed: The Dirac operator (3.4)
  • 27/02 Fri: Variation of Energy (4.1), midterm evaluation (essay or oral exam) problem set 1

March

Week 9

  • 02/03 Mon: Jacobi Fields (4.2)
  • 04/03 Wed: Manifolds of Constant Curvature and Projective Spaces (4.4) (5.1)
  • 06/03 Fri: Kaehler Manifolds (5.2)

Spring Recess, March 8-15

Week 10

  • 16/03 Mon: Symmetric Spaces I (5.3)
  • 18/03 Wed: Symmetric Spaces II (5.3,5.4)
  • 20/03 Fri: Symmetric Spaces III (5.4,5.5)

Week 11

  • 23/03 Mon: Symmetric Spaces IV (5.5)
  • 25/03 Wed: Symmetric Spaces problem set 2
  • 27/03 Fri: Symmetric Spaces

April

Week 12

  • 30/03 Mon: Symmetric Spaces SL(n)/SO(n)
  • 01/04 Wed: Symmetric Spaces SL(n)/SO(n)
  • 03/04 Fri: Morse Theory

Week 13

  • 06/04 Mon: Morse Theory
  • 08/04 Wed: Morse Theory
  • 10/04 Fri: Morse Theory

Week 14

  • 13/04 Mon: Morse Theory
  • 15/04 Wed: Morse Theory
  • 17/04 Fri: Morse Theory final evaluation (essay, or oral exam)

Week 15

  • 20/04 Mon: Seiberg-Witten 1 final problem set due
  • 22/04 Wed: Seiberg-Witten 2
  • 24/04 Fri: Dirac harmonic maps (9.3)