List of exercises, TODOs, and things to read before the next meeting.

• Adjoint to exterior derivative: two proofs
• Formula for rough Laplacian
• Weitzenböck formula in an arbitrary orthonormal frame
• Work out the curvature terms in the Weitzenböck formula
• Derive the claimed Bochner formula from the Weitzenböck formula: recall we did $\Delta |\mathrm{d}\sigma|^2 = -\nabla_i \nabla_i \langle \mathrm{d}\sigma,\mathrm{d}\sigma\rangle$ …; do it again without assuming the connection vanishes at the point in question
• Read do Carmo ch. 5, 9, prepare proof of second variation formula for harmonic maps