MATH 261A: Functional Analysis
Geometry of linear topological spaces. Linear operators and functionals. Spectral theory. Calculus for vectorvalued functions. Operational calculus. Banach algebras. Special topics in functional analysis. May be repeated for credit.
Terms: not given this year

Units: 3

Repeatable for credit

Grading: Letter or Credit/No Credit
MATH 262: Applied Fourier Analysis and Elements of Modern Signal Processing (CME 372)
Introduction to the mathematics of the Fourier transform and how it arises in a number of imaging problems. Mathematical topics include the Fourier transform, the Plancherel theorem, Fourier series, the Shannon sampling theorem, the discrete Fourier transform, and the spectral representation of stationary stochastic processes. Computational topics include fast Fourier transforms (FFT) and nonuniform FFTs. Applications include Fourier imaging (the theory of diffraction, computed tomography, and magnetic resonance imaging) and the theory of compressive sensing.
Terms: Win

Units: 3

Grading: Letter or Credit/No Credit
Instructors:
Candes, E. (PI)
MATH 263B: Quantum Groups and the YangBaxter Equation
Two classes of phenomena in mathematical physics, namely the solvable lattice models in statistical physics and Heisenberg spin chains lead to the same identity, namely the YangBaxter equation. Quasitriangular Hopf algebras (quantum groups), "braided monoidal category," such as Kuperberg's proof of the alternating sign conjecture, deformations of the Weyl character formula, and knot invariants such as the Jones polynomial. May be repeated for credit.
Terms: Spr

Units: 3

Repeatable for credit

Grading: Letter or Credit/No Credit
Instructors:
Bump, D. (PI)
MATH 264: Infinite Dimensional Lie Algebra
Terms: not given this year

Units: 3

Repeatable for credit

Grading: Letter or Credit/No Credit
MATH 266: Computational Signal Processing and Wavelets
Theoretical and computational aspects of signal processing. Topics: timefrequency transforms; wavelet bases and wavelet packets; linear and nonlinear multiresolution approximations; estimation and restoration of signals; signal compression. May be repeated for credit.
Terms: not given this year

Units: 3

Grading: Letter or Credit/No Credit
MATH 269: Topics in symplectic geometry
May be repeated for credit.
Terms: Spr

Units: 3

Repeatable for credit

Grading: Letter or Credit/No Credit
Instructors:
Eliashberg, Y. (PI)
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: not given this year

Units: 3

Repeatable for credit

Grading: Letter or Credit/No Credit
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: not given this year

Units: 3

Repeatable for credit

Grading: Letter or Credit/No Credit
MATH 273A: Quantum Mechanics I
Terms: not given this year

Units: 3

Grading: Letter or Credit/No Credit
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