MATH 257B: Symplectic Geometry and Topology
Continuation of 257A. May be repeated for credit.
Terms: Win

Units: 3

Repeatable for credit

Grading: Letter or Credit/No Credit
MATH 257C: Symplectic Geometry and Topology
Continuation of 257B. May be repeated for credit.
Terms: not given this year, last offered Spring 2019

Units: 3

Grading: Letter or Credit/No Credit
MATH 258: Topics in Geometric Analysis
May be repeated for credit.
Terms: Win

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: not given this year, last offered Winter 2016

Units: 3

Grading: Letter or Credit/No Credit
MATH 263A: Algebraic Combinatorics and Symmetric Functions
Symmetric function theory unifies large parts of combinatorics. Theorems about permutations, partitions, and graphs now follow in a unified way. Topics: The usual bases (monomial, elementary, complete, and power sums). Schur functions. Representation theory of the symmetric group. LittlewoodRichardson rule, quasisymmetric functions, combinatorial Hopf algebras, introduction to Macdonald polynomials. Throughout, emphasis is placed on applications (e.g. to card shuffling and random matrix theory). Prerequisite: 210A and 210B, or equivalent.
Terms: not given this year, last offered Autumn 2018

Units: 3

Repeatable for credit

Grading: Letter or Credit/No Credit
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, last offered Winter 2016

Units: 3

Repeatable for credit

Grading: Letter or Credit/No Credit
MATH 263C: Topics in Representation Theory
May be repeated for credit.
Terms: Aut

Units: 3

Repeatable for credit

Grading: Letter or Credit/No Credit
Instructors:
Bump, D. (PI)
MATH 269: Topics in symplectic geometry
May be repeated for credit.
Terms: not given this year, last offered Autumn 2018

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: not given this year, last offered Winter 2017

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, last offered Winter 2018

Units: 3

Grading: Letter or Credit/No Credit
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