MATH 263B: Crystal Bases: Representations and Combinatorics
Crystal Bases are combinatorial analogs of representation theorynof Lie groups. We will explore different aspects of thesenanalogies and develop rigorous purely combinatorial foundations.
Terms: not given this year

Units: 3

Repeatable for credit

Grading: Letter or Credit/No Credit
MATH 263C: Topics in Representation Theory
May be repeated for credit.
Terms: not given this year

Units: 3

Repeatable for credit

Grading: Letter or Credit/No Credit
MATH 269: Topics in symplectic geometry
May be repeated for credit.
Terms: not given this year

Units: 3

Repeatable for credit

Grading: Letter or Credit/No Credit
MATH 270: Geometry and Topology of Complex Manifolds
Complex manifolds, Kahler manifolds, curvature, Hodge theory, Lefschetz theorem, KahlerEinstein equation, HermitianEinstein equations, deformation of complex structures. May be repeated for credit.
Terms: Win

Units: 3

Repeatable for credit

Grading: Letter or Credit/No Credit
Instructors:
Eliashberg, Y. (PI)
MATH 271: The HPrinciple
The language of jets. Thom transversality theorem. Holonomic approximation theorem. Applications: immersion theory and its generaliazations. Differential relations and Gromov's hprinciple for open manifolds. Applications to symplectic geometry. Microflexibility. Mappings with simple singularities and their applications. Method of convex integration. NashKuiper C^1isometric embedding theorem.
Terms: not given this year

Units: 3

Grading: Letter or Credit/No Credit
MATH 272: Topics in Partial Differential Equations
Terms: Spr

Units: 3

Repeatable for credit

Grading: Letter or Credit/No Credit
Instructors:
Ryzhik, L. (PI)
MATH 273: Topics in Mathematical Physics (STATS 359)
Covers a list of topics in mathematical physics. The specific topics may vary from year to year, depending on the instructor's discretion. Background in graduate level probability theory and analysis is desirable.
Terms: Spr

Units: 3

Grading: Letter or Credit/No Credit
Instructors:
Chatterjee, S. (PI)
MATH 280: Evolution Equations in Differential Geometry
Terms: not given this year

Units: 3

Repeatable for credit

Grading: Letter or Credit/No Credit
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: Win

Units: 3

Repeatable for credit

Grading: Letter or Credit/No Credit
Instructors:
Wright, A. (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: Spr

Units: 3

Repeatable for credit

Grading: Letter or Credit/No Credit
Instructors:
Perlmutter, N. (PI)
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