MATH 248A: Algebraic Number Theory
Structure theory and Galois theory of local and global fields, finiteness theorems for class numbers and units, adelic techniques. Prerequisites:
MATH 210A,B.
| Repeatable
2 times
(up to 6 units total)
MATH 249A: Topics in number theory
| Repeatable
3 times
(up to 9 units total)
MATH 257A: Symplectic Geometry and Topology
Linear symplectic geometry and linear Hamiltonian systems. Symplectic manifolds and their Lagrangian submanifolds, local properties. Symplectic geometry and mechanics. Contact geometry and contact manifolds. Relations between symplectic and contact manifolds. Hamiltonian systems with symmetries. Momentum map and its properties. May be repeated for credit.
| Repeatable
2 times
(up to 6 units total)
MATH 257B: Symplectic Geometry and Topology
Continuation of 257A. May be repeated for credit.
| Repeatable
2 times
(up to 6 units total)
MATH 259: mirror symmetry
| Repeatable
3 times
(up to 9 units total)
MATH 261A: Functional Analysis
Geometry of linear topological spaces. Linear operators and functionals. Spectral theory. Calculus for vector-valued functions. Operational calculus. Banach algebras. Special topics in functional analysis. May be repeated for credit.
| Repeatable
2 times
(up to 6 units total)
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.
MATH 264: Infinite Dimensional Lie Algebra
| Repeatable
for credit
MATH 266: Computational Signal Processing and Wavelets
Theoretical and computational aspects of signal processing. Topics: time-frequency transforms; wavelet bases and wavelet packets; linear and nonlinear multiresolution approximations; estimation and restoration of signals; signal compression. May be repeated for credit.
MATH 270: Geometry and Topology of Complex Manifolds
Complex manifolds, Kahler manifolds, curvature, Hodge theory, Lefschetz theorem, Kahler-Einstein equation, Hermitian-Einstein equations, deformation of complex structures. May be repeated for credit.
| Repeatable
for credit
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