printer friendly pageMATH 245A: Topics in Algebraic Geometry: Moduli Theory
Topics in the study of moduli spaces: Basic of algebraic surfaces, Hodge structure of surfaces, moduli of K3 surfaces, cycles and rational curves in K3 surfaces, Torelli for K3 surfaces.
Terms: Win
| Units: 3
| Repeatable
3 times
(up to 9 units total)
Instructors:
Li, J. (PI)
MATH 249A: Topics in number theory
Terms: Aut
| Units: 3
| Repeatable
3 times
(up to 9 units total)
Instructors:
Soundararajan, K. (PI)
MATH 249B: Topics in Number Theory
Terms: Win
| Units: 3
| Repeatable
3 times
(up to 9 units total)
Instructors:
Venkatesh, A. (PI)
MATH 249C: Topics in Number Theory
Terms: Spr
| Units: 3
| Repeatable
for credit
Instructors:
Conrad, B. (PI)
MATH 256A: Partial Differential Equations
The theory of linear and nonlinear partial differential equations, beginning with linear theory involving use of Fourier transform and Sobolev spaces. Topics: Schauder and L2 estimates for elliptic and parabolic equations; De Giorgi-Nash-Moser theory for elliptic equations; nonlinear equations such as the minimal surface equation, geometric flow problems, and nonlinear hyperbolic equations.
Terms: Spr
| Units: 3
Instructors:
Vasy, A. (PI)
MATH 256B: Partial Differential Equations
Continuation of 256A.
Terms: Win
| Units: 3
| Repeatable
for credit
Instructors:
Vasy, A. (PI)
MATH 257C: Symplectic Geometry and Topology
Continuation of 257B. May be repeated for credit.
Terms: Win
| Units: 3
Instructors:
Ionel, E. (PI)
MATH 258: Topics in Geometric Analysis
May be repeated for credit.
Terms: Spr
| Units: 3
| Repeatable
for credit
Instructors:
Wang, Y. (PI)
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
Instructors:
Candes, E. (PI)
MATH 263A: Infinite-dimensional Lie Algebras
Basics of Kac-Moody Lie algebras, which include both finite dimensional semisimple Lie algebras and their infinite-dimensional analogs, up to the Kac-Weyl character formula and Macdonald identities, and the Boson-Fermion correspondence. May be repeated for credit. Prerequisite: 210 or equivalent.
Terms: Win
| Units: 3
| Repeatable
for credit
Instructors:
Bump, D. (PI)
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