The assignments will deal with some results or examples from the course left for the students to work on, or with interesting subjects related, although not directly, to the main core of the course. There will be a final assignment at the end of the course, which will be marked, graded and will count towards the final pass/fail grade.

There is no formal submission of the assignments but you are expected to work on them.

• Assignment 1: linear symplectic structures.

• Assignment 2: linear complex structures and more.

• Assignment 3: the exterior algebra and generalized linear algebra.

• Assignment 4: more generalized linear algebra.

• Assignment 5: linear generalized complex structures and generalized transformations.

• Assignment 6: annihilators of forms and the Clifford algebra.

• Assignment 7: the pairing on differential forms.

• Assignment 8: linear generalized complex structures.

• Assignment 9: symmetries of the Courant bracket and examples.

• Assignment 10: the Nijenhuis tensor and an interpolation between complex and symplectic structures.

• Final assignment, to be submitted electronically before Monday 6th Aug 7pm.