printer friendly pageMATH 235C: Topics in Markov Chains
Classical functional inequalities (Nash, Faber-Krahn, log-Sobolev inequalities), comparison of Dirichlet forms. Random walks and isoperimetry of amenable groups (with a focus on solvable groups). Entropy, harmonic functions, and Poisson boundary (following Kaimanovich-Vershik theory).
Last offered: Spring 2016
| Repeatable
for credit
(up to 99 units total)
MATH 236: Introduction to Stochastic Differential Equations
Brownian motion, stochastic integrals, and diffusions as solutions of stochastic differential equations. Functionals of diffusions and their connection with partial differential equations. Random walk approximation of diffusions. Prerequisite: 136 or equivalent and differential equations.
Terms: Win
| Units: 3
Instructors:
Papanicolaou, G. (PI)
MATH 238: Mathematical Finance (STATS 250)
Stochastic models of financial markets. Forward and futures contracts. European options and equivalent martingale measures. Hedging strategies and management of risk. Term structure models and interest rate derivatives. Optimal stopping and American options. Corequisites:
MATH 236 and 227 or equivalent.
Terms: Win
| Units: 3
Instructors:
Papanicolaou, G. (PI)
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.
Terms: Aut
| Units: 3
| Repeatable
for credit
Instructors:
Mazzeo, R. (PI)
MATH 245A: Topics in Algebraic Geometry
Topics of contemporary interest in algebraic geometry. May be repeated for credit.
| Repeatable
3 times
(up to 9 units total)
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:
Soundararajan, K. (PI)
MATH 249B: Topics in Number Theory
Terms: Win
| Units: 3
| Repeatable
3 times
(up to 9 units total)
Instructors:
Tsai, C. (PI)
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