No class on March 7.

We will have an extra session on Tuesday, March 20, at 5:00.

Class Meetings: W 4:00-7:00, RLM 9.166

Discusion/Office Hours: Mondays, 2:30-4:00, RLM 9.162

For more details, see the First Day Handout

Chapter/Topic | Students | Date |
---|---|---|

2. Connections and characteristic classes | Riccardo Pedrotti | January 24 |

George Torres | ||

3. Clifford algebras and Dirac operators | Ivan Tulli | January 31 |

Ricky Wedeen | ||

4. Spin groups | Arun Debray | February 7 |

Sebastian Schulz | ||

5. Analytic properties of Dirac operators | Kendric Schafers | February 14 |

Gillian Grindstaff | ||

6. Hodge theory | Adrian Clough | February 21 |

Rok Gregoric | ||

Qianyu Hao | ||

7. Heat and wave equations | Cameron Darwin | February 28 |

Ravi Mohan | ||

8. Traces and eigenvalue asymptotics | Kenny Schefers | March 21 |

Ivan Tulli | ||

9. Some non-compact manifolds | Sebastian Schulz | March 28 |

Arun Debray | ||

10. The Lefschetz formula | George Torres | April 4 |

Riccardo Pedrotti | ||

11. The index problem | Ricky Wedeen | April 11 |

Rok Gregoric | ||

12. The Getzler calculus and the local index theorem | Cameron Darwin | April 25 |

Ravi Mohan | ||

13. Applications of the index theorem | Ivan Tulli | May 2 |

Kenny Schefers | ||

14. Witten's approach to Morse theory | Gillian Grindstaff | May 7 (1:00, RLM 10.176) |

Ricky Wedeen |

Problem Set #2

Problem Set #3

Short essay on Atiyah-Singer index theorem by Higson-Roe (from Princeton Companion)

Announcement by Atiyah-Singer of index theorem

On elliptic equations by Gelfand

Proof of the spectral theorem for compact self-adjoint operators

An inequality important for the analysis of the Dirac operator and associated heat and wave operators

Mark Kac's article "Can you hear the shape of a drum?"

Atiyah-Bott papers (Part 1, Part 2) on the Lefschetz formula

Some Atiyah-Singer papers (Part 1, Part 3) on the index theorem

Getzler's papers (1 and 2) on the index theorem.

Witten paper on Morse theory and supersymmetry

Two papers by Bott (Paper 1, Paper 2) on Morse theory.