MATH 273B: QUANTUM MECHANICS II
Terms: not given this year

Units: 3

Grading: Letter or Credit/No Credit
MATH 280: Evolution Equations in Differential Geometry
Terms: Win

Units: 3

Repeatable for credit

Grading: Letter or Credit/No Credit
Instructors:
Bamler, R. (PI)
MATH 282A: Low Dimensional Topology
The theory of surfaces and 3manifolds. 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 3manifolds: triangulations, Heegaard splittings, Dehn surgery. Loop theorem, sphere theorem, incompressible surfaces. Geometric structures, particularly hyperbolic structures on surfaces and 3manifolds. May be repeated for credit up to 6 total units.
Terms: Spr

Units: 3

Repeatable for credit

Grading: Letter or Credit/No Credit
Instructors:
Mirzakhani, M. (PI)
MATH 282B: Homotopy Theory
Homotopy groups, fibrations, spectral sequences, simplicial methods, DoldThom theorem, models for loop spaces, homotopy limits and colimits, stable homotopy theory. May be repeated for credit up to 6 total units.
Terms: Win

Units: 3

Repeatable for credit

Grading: Letter or Credit/No Credit
Instructors:
Galatius, S. (PI)
MATH 282C: Fiber Bundles and Cobordism
Possible topics: principal bundles, vector bundles, classifying spaces. Connections on bundles, curvature. Topology of gauge groups and gauge equivalence classes of connections. Characteristic classes and Ktheory, including Bott periodicity, algebraic Ktheory, and indices of elliptic operators. Spectral sequences of AtiyahHirzebruch, Serre, and Adams. Cobordism theory, PontryaginThom theorem, calculation of unoriented and complex cobordism. May be repeated for credit up to 6 total units.
Terms: Spr

Units: 3

Repeatable for credit

Grading: Letter or Credit/No Credit
Instructors:
Carlsson, G. (PI)
MATH 283: Topics in Algebraic and Geometric Topology
May be repeated for credit.
Terms: not given this year

Units: 3

Repeatable for credit

Grading: Letter or Credit/No Credit
MATH 283A: Topics in Topology
Terms: not given this year

Units: 3

Grading: Letter or Credit/No Credit
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.
Terms: Win

Units: 3

Repeatable for credit

Grading: Letter or Credit/No Credit
Instructors:
Kerckhoff, S. (PI)
MATH 284A: Geometry and Topology in Dimension 3
The Poincare conjecture and the uniformization of 3manifolds. May be repeated for credit.
Terms: not given this year

Units: 3

Repeatable for credit

Grading: Letter or Credit/No Credit
MATH 284B: Geometry and Topology in Dimension 3
The Poincare conjecture and the uniformization of 3manifolds. May be repeated for credit.
Terms: not given this year

Units: 3

Repeatable for credit

Grading: Letter or Credit/No Credit
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