printer friendly pageMATH 271: The H-Principle
The language of jets. Thom transversality theorem. Holonomic approximation theorem. Applications: immersion theory and its generaliazations. Differential relations and Gromov's h-principle for open manifolds. Applications to symplectic geometry. Microflexibility. Mappings with simple singularities and their applications. Method of convex integration. Nash-Kuiper C^1-isometric embedding theorem.
MATH 272: Topics in Partial Differential Equations
| Repeatable
for credit
MATH 273A: Quantum Mechanics I
MATH 273B: QUANTUM MECHANICS II
MATH 283: Topics in Algebraic and Geometric Topology
May be repeated for credit.
| Repeatable
for credit
MATH 283A: Topics in Topology
MATH 284A: Geometry and Topology in Dimension 3
The Poincare conjecture and the uniformization of 3-manifolds. May be repeated for credit.
| Repeatable
for credit
MATH 284B: Geometry and Topology in Dimension 3
The Poincare conjecture and the uniformization of 3-manifolds. May be repeated for credit.
| Repeatable
for credit
MATH 287: Introduction to optimal transportation
This will be an introductory course on Optimal Transportation theory. We will study Monge's problem, Kantorovich's problem, c-concave functions (also in the Riemannian setting), Wasserstein distance and geodesics (including a PDE formulation), applications to inequalities in convex analysis, as well as other topics, time permitting.
MATH 292A: Set Theory (PHIL 352A)
The basics of axiomatic set theory; the systems of Zermelo-Fraenkel and Bernays-Gödel. Topics: cardinal and ordinal numbers, the cumulative hierarchy and the role of the axiom of choice. Models of set theory, including the constructible sets and models constructed by the method of forcing. Consistency and independence results for the axiom of choice, the continuum hypothesis, and other unsettled mathematical and set-theoretical problems. Prerequisites: PHIL151 and
MATH 161, or equivalents.
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