MATH 243: Functions of Several Complex Variables
Holomorphic functions in several variables, Hartogs phenomenon, d-bar complex, Cousin problem. Domains of holomorphy. Plurisubharmonic functions and pseudo-convexity. Stein manifolds. Coherent sheaves, Cartan Theorems A&B. Levi problem and its solution. Grauert¿s Oka principle. nPrerequisites:
MATH 215A and experience with manifolds.
Last offered: Winter 2011
| Repeatable
for credit
MATH 244: Riemann Surfaces
Riemann surfaces and holomorphic maps, algebraic curves, maps to projective spaces. Calculus on Riemann surfaces. Elliptic functions and integrals. Riemann-Hurwitz formula. Riemann-Roch theorem, Abel-Jacobi map. Uniformization theorem. Hyperbolic surfaces. (Suitable for advanced undergraduates.) Prerequisites:
MATH 106 or
MATH 116, and familiarity with surfaces equivalent to
MATH 143,
MATH 146, or
MATH 147.
Last offered: Autumn 2017
| Repeatable
for credit
MATH 245A: Topics in Algebraic Geometry
Topics of contemporary interest in algebraic geometry. May be repeated for credit.
Terms: Aut
| Units: 3
| Repeatable
3 times
(up to 9 units total)
Instructors:
Vakil, R. (PI)
MATH 245B: Topics in Algebraic Geometry
May be repeated for credit.
Terms: Win
| Units: 3
| Repeatable
3 times
(up to 9 units total)
Instructors:
Li, J. (PI)
MATH 245C: Topics in Algebraic Geometry
May be repeated for credit.
Last offered: Spring 2017
| Repeatable
for credit
MATH 249A: Topics in number theory
Topics of contemporary interest in number theory. May be repeated for credit.
Terms: Aut
| Units: 3
| Repeatable
3 times
(up to 9 units total)
Instructors:
Taylor, R. (PI)
MATH 249B: Topics in Number Theory
Last offered: Winter 2018
| Repeatable
3 times
(up to 9 units total)
MATH 249C: Topics in Number Theory
Last offered: Spring 2017
| Repeatable
for credit
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: Aut
| Units: 3
Instructors:
Luk, J. (PI)
MATH 256B: Partial Differential Equations
Continuation of 256A.
Terms: Win
| Units: 3
| Repeatable
for credit
Instructors:
Ryzhik, L. (PI)
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