Lectures

Week 1

• 25/08 Mon: Introduction
• 27/08 Wed: Frenet curves, torsion, curvature, global theory of curves (K2)
• 29/08 Fri: curves II Unique Existence of Solutions to ODE

September

Week 2

• 03/09 Wed: curves III
• 05/09 Fri: surfaces, Gauss-Bonnet, Gauss map (P10) (K3) (K3B) (K4F)

Week 3

• 08/09 Mon: surfaces II
• 10/09 Wed: surfaces III
• 12/09 Fri: Gauss's theorema egregium (K4C)

Week 4

• 15/09 Mon: intrinsic geometry and covariant derivatives (K4A,K4B)
• 17/09 Wed: L10: hyperbolic space (P2) (K3.44)
• 19/09 Fri: conformal geometry (P8)

Week 5

• 22/09 Mon: L12: Riemann surfaces, moduli spaces (P8)
• 24/09 Wed: Riemann surfaces II
• 26/09 Fri: minimal surfaces, Kelvin problem (P10.5) (K3D)

October

Week 6

• 29/09 Mon: L15: minimal surfaces II
• 01/10 Wed: computers and differential geometry optiverse video optiverse commentary surface evolver minimal surface gallery boy's surface
• 03/10 Fri: the group of rotations and quaternions (P11) (K7D)

Higher Dimensions

Week 7

• 06/10 Mon: No meeting
• 08/10 Wed: manifold (P12) (K5A) (M1)
• 10/10 Fri: manifold II --FIRST ESSAY DUE

Week 8

• 14/10 Tue: L20: Riemannian manifolds, tangent and cotangent spaces (P12) (K5C)
• 15/10 Wed: vector fields, 1-forms, (P2) (P14.7) (K5D) (M22)
• 17/10 Fri: differential forms, tensor products, exterior square, Stokes theorem

Week 9

• 20/10 Mon: differential forms II
• 22/10 Wed: review, covariant derivative, Riemannian curvature tensor
• 24/10 Fri: Riemannian curvature, sectional, Ricci, scalar curvature, torsion, Riemannian connections (P14.4) (K5D) (K6B) (K6C) (M24)

Week 10

• 27/10 Mon: curvature II
• 29/10 Wed: curvature III
• 31/10 Fri: geodesics, exponential map, parallel transport (P14) (K4B) (M23) (M24)

November

Week 11

• 03/11 Mon: geodesics II
• 05/11 Wed: Lie derivative (P14.6) (K5D) (M16)
• 07/11 Fri: Lie groups (P13) (M4) --SECOND ESSAY DUE

Week 12

• 10/11 Mon: Lie groups II
• 12/11 Wed: Lie groups III
• 14/11 Fri: Lie gropus IV

Week 13

• 17/11 Mon: De Rham cohomology, and Poincare duality (P12.5) (M11) (M12) (M13)
• 19/11 Wed: De Rham II
• 21/11 Fri: De Rham III
• 24/11 Mon: De Rham IV

December

Week 14

• 01/12 Mon: classification of surfaces
• 03/12 Wed: Poincare conjecture
• 05/12 Fri: triangulating a manifold --THIRD ESSAY DUE

Week 15

• 08/12 Mon: Whitney embedding
• 10/12 Wed: holonomy
• 12/12 Fri: general relativity (P18 P19) (K8B)