Math 257A (Driver, winter 2015) Topics in
Differential Geometry
Frobenius Integrability, Curvature, and Pseudo-differential operators
(http://math.ucsd.edu/~driver/257A-Winter2015/index.htm)
Instructor: Bruce Driver (bdriver@math.ucsd.edu),
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;
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ODE Review.
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Frobeneous’ integrability theorem and its relationship to curvature.
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Densities and integration theory on manifolds and Lie groups.
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An introduction to some nilpotent Lie groups which arise in the theory of rough path analysis and regularity structures.
-
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The basics of Hamiltonian mechanics.
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