Math 257A Home Page (Driver, W15)


Lecture Notes

Math 257A (Driver, winter 2015) Topics in Differential Geometry

Frobenius Integrability, Curvature, and Pseudo-differential operators


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Instructor: Bruce Driver (, AP&M 5260, 534-2648.

Office Hours: TBA

Meeting times: Lectures are on MWF 10:00a - 10:50a in AP&M 5829

Textbook: There is no official text book for this course. However, there will likely be posted lecture notes on the course web-site.  Other references will be supplied as the course progresses.

Lecture Notes -- Updated 3/13/2015
For related material on embedded sub-manifolds, see the first four chapter of the notes:  Curved Wiener Space Analysis.

Prerequisites:  The bare minimum is a standard undergraduate course in real analysis. It would be helpful to have taken Math 250A and to know a little measure theory – the latter is not absolutely necessary.


Course Description: This will not be a topics course on only one subject. Rather we will concentrate on perhaps 4 or 5 different topics throughout the quarter.  The main goal is to introduce you to some hands on computations involving differential geometry while at the same time covering some topics that are often not covered in detail in Math 250.   Some topics that we might cover are;

  1. ODE Review.

  2. Frobeneous’ integrability theorem and its relationship to curvature.

  3. Densities and integration theory on manifolds and Lie groups.

  4. An introduction to some nilpotent Lie groups which arise in the theory of rough path analysis and regularity structures.

  5. Riemannian geometry in the context of embedded submanifolds.

  6. The basics of Hamiltonian mechanics.

  7. Some calculus of Pseudo-differential operators on manifolds.


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Last modified on Friday, 02 January 2015 11:18 AM.