Ma 191c-sec3:  The Dirac Operator and the Atiyah-Singer Index Theorem

ANNOUNCEMENTS

Registration for Spring term opens Thursday, February 23, 2016.

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COURSE DESCRIPTION

This course presents the heat equation proof of the Atiyah-Singer index theorem. The following topics will be covered: spin geometry, Dirac operator, pseudodifferential calculus, Fredholm operators, the heat kernel method for computing the Seeley-de Witt coefficients and the index of an elliptic operator on a closed manifold, the McKean-Singer index formula, the Hodge decomposition theorem, characteristic classes, the harmonic oscillator, Mehler's formula, and the Atiyah-Singer index theorem.


PREREQUISITES

Acquaintance with manifolds, exterior derivative, Riemannian metrics, and the spectral theorem for compact self-adjoint operators on a Hilbert space, will be very useful.


SCHEDULE

Tuesday and Thursday, 2:30 - 3:55 p.m., 159 Sloan.


INSTRUCTORS

Farzad Fathizadeh
OLGA TAUSSKY AND JOHN TODD INSTRUCTOR IN MATHEMATICS
Sloan 358
626-395-4355
farzadf@caltech.edu


TA's

There is no TA for this course.


OFFICE HOURS

Friday 4 to 5 p.m., Sloan 358.


POLICIES

Grades

Based on final presentation and class attendance. Suggested references for choosing the topic of the final presentation will be posted at the bottom of this page.

Homework Policy

There is no homework for this course.


TOPICS COVERED

Please refer to the Course Description.


TEXTBOOKS


LECTURE NOTES

Date Description
   
   
   

HOMEWORK

Due Date Homework Solutions

EXAMS

 


PAPERS FOR PRESENTATIONS