MATH 210C: Lie Theory
Topics in Lie groups, Lie algebras, and/or representation theory. Prerequisite:
math 210B. May be repeated for credit.
Terms: Spr

Units: 3

Repeatable for credit

Grading: Letter or Credit/No Credit
Instructors:
Venkatesh, A. (PI)
MATH 215A: Complex Analysis, Geometry, and Topology
Analytic functions, complex integration, Cauchy's theorem, residue theorem, argument principle, conformal mappings, Riemann mapping theorem, Picard's theorem, elliptic functions, analytic continuation and Riemann surfaces.
Terms: Aut

Units: 3

Grading: Letter or Credit/No Credit
Instructors:
Ryzhik, L. (PI)
MATH 216A: Introduction to Algebraic Geometry
Algebraic curves, algebraic varieties, sheaves, cohomology, RiemannRoch theorem. Classification of algebraic surfaces, moduli spaces, deformation theory and obstruction theory, the notion of schemes. May be repeated for credit. Prerequisites: 210ABC or equivalent.
Terms: Aut

Units: 3

Repeatable for credit

Grading: Letter or Credit/No Credit
Instructors:
Li, Z. (PI)
MATH 216B: Introduction to Algebraic Geometry
Continuation of 216A. May be repeated for credit.
Terms: Win

Units: 3

Repeatable for credit

Grading: Letter or Credit/No Credit
Instructors:
Vakil, R. (PI)
MATH 216C: Introduction to Algebraic Geometry
Continuation of 216B. May be repeated for credit.
Terms: Spr

Units: 3

Repeatable for credit

Grading: Letter or Credit/No Credit
Instructors:
Vakil, R. (PI)
MATH 217A: Differential Geometry
Smooth manifolds and submanifolds, tensors and forms, Lie and exterior derivative, DeRham cohomology, distributions and the Frobenius theorem, vector bundles, connection theory, parallel transport and curvature, affine connections, geodesics and the exponential map, connections on the principal frame bundle. Prerequisite: 215C or equivalent.
Terms: Spr

Units: 3

Grading: Letter or Credit/No Credit
Instructors:
Mazzeo, R. (PI)
MATH 220: Partial Differential Equations of Applied Mathematics (CME 303)
Firstorder partial differential equations; method of characteristics; weak solutions; elliptic, parabolic, and hyperbolic equations; Fourier transform; Fourier series; and eigenvalue problems. Prerequisite: foundation in multivariable calculus and ordinary differential equations.
Terms: Aut

Units: 3

Grading: Letter or Credit/No Credit
Instructors:
Ryzhik, L. (PI)
MATH 221A: Mathematical Methods of Imaging (CME 321A)
Image denoising and deblurring with optimization and partial differential equations methods. Imaging functionals based on total variation and l1 minimization. Fast algorithms and their implementation.
Terms: Win

Units: 3

Grading: Letter or Credit/No Credit
Instructors:
Ryzhik, L. (PI)
MATH 221B: Mathematical Methods of Imaging (CME 321B)
Array imaging using Kirchhoff migration and beamforming, resolution theory for broad and narrow band array imaging in homogeneous media, topics in highfrequency, variable background imaging with velocity estimation, interferometric imaging methods, the role of noise and inhomogeneities, and variational problems that arise in optimizing the performance of array imaging algorithms.
Terms: Spr

Units: 3

Grading: Letter or Credit/No Credit
Instructors:
Papanicolaou, G. (PI)
MATH 222: Computational Methods for Fronts, Interfaces, and Waves
Highorder methods for multidimensional systems of conservation laws and HamiltonJacobi equations (central schemes, discontinuous Galerkin methods, relaxation methods). Level set methods and fast marching methods. Computation of multivalued solutions. Multiscale analysis, including waveletbased methods. Boundary schemes (perfectly matched layers). Examples from (but not limited to) geometrical optics, transport equations, reactiondiffusion equations, imaging, and signal processing.
Terms: not given this year

Units: 3

Grading: Letter or Credit/No Credit
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