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 273A: Quantum Mechanics I
MATH 273B: QUANTUM MECHANICS II
MATH 280: Evolution Equations in Differential Geometry
| Repeatable
for credit
MATH 282A: Low Dimensional Topology
The theory of surfaces and 3-manifolds. Curves on surfaces, the classification of diffeomorphisms of surfaces, and Teichmuller space. The mapping class group and the braid group. Knot theory, including knot invariants. Decomposition of 3-manifolds: triangulations, Heegaard splittings, Dehn surgery. Loop theorem, sphere theorem, incompressible surfaces. Geometric structures, particularly hyperbolic structures on surfaces and 3-manifolds. May be repeated for credit up to 6 total units.
| Repeatable
2 times
(up to 6 units total)
MATH 283: Topics in Algebraic and Geometric Topology
May be repeated for credit.
| Repeatable
for credit
MATH 283A: Topics in Topology
MATH 284: Topics in Geometric Topology
Incompressible surfaces, irreducible manifolds, prime decomposition, Morse theory, Heegaard diagrams, Heegaard splittings, the Thurston norm, sutured manifold theory, Heegaard Floer homology, sutured Floer homology.
| Repeatable
for credit
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
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