MATH 245B: Topics in Algebraic Geometry
May be repeated for credit.
Terms: Win

Units: 3

Repeatable for credit

Grading: Letter or Credit/No Credit
Instructors:
Vakil, R. (PI)
MATH 245C: Topics in Algebraic Geometry
May be repeated for credit.
Terms: not given this year, last offered Spring 2017

Units: 3

Repeatable for credit

Grading: Letter or Credit/No Credit
MATH 246: Topics in number theory: Lfunctions
The Riemann Zeta function and Dirichlet Lfunctions, zerofree regions and vertical distribution of the zeros, primes in arithmetic progressions, the class number problem, Hecke Lfunctions and Tate's thesis, Artin Lfunctions and the Chebotarev density theorem, Modular forms and Maass forms.nnPrerequisites: Algebraic Number Theory.
Terms: not given this year, last offered Spring 2016

Units: 3

Repeatable for credit

Grading: Letter or Credit/No Credit
MATH 248: Introduction to Ergodic Theory
Topics may include 1) subadditive and multiplicative ergodic theorems, 2) notions of mixing, weak mixing, spectral theory, 3) metric and topological entropy of dynamical systems, 4) measures of maximal entropy. Prerequisites: Solid background in "Measure and Integration" (
Math 205A) and some functional analysis, including Riesz representation theorem and HahnBanach theorem (
Math 205B).
Terms: not given this year, last offered Autumn 2014

Units: 3

Repeatable for credit

Grading: Letter or Credit/No Credit
MATH 249A: Topics in number theory
Topics of contemporary interest in number theory. 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 249B: Topics in Number Theory
Terms: Win

Units: 3

Repeatable for credit

Grading: Letter or Credit/No Credit
Instructors:
Taylor, R. (PI)
MATH 249C: Topics in Number Theory
Terms: Spr

Units: 3

Repeatable for credit

Grading: Letter or Credit/No Credit
Instructors:
Tsai, C. (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 GiorgiNashMoser theory for elliptic equations; nonlinear equations such as the minimal surface equation, geometric flow problems, and nonlinear hyperbolic equations.
Terms: Spr

Units: 3

Grading: Letter or Credit/No Credit
Instructors:
Luk, J. (PI)
MATH 256B: Partial Differential Equations
Continuation of 256A.
Terms: not given this year, last offered Winter 2019

Units: 3

Repeatable for credit

Grading: Letter or Credit/No Credit
MATH 257A: Symplectic Geometry and Topology
Linear symplectic geometry and linear Hamiltonian systems. Symplectic manifolds and their Lagrangian submanifolds, local properties. Symplectic geometry and mechanics. Contact geometry and contact manifolds. Relations between symplectic and contact manifolds. Hamiltonian systems with symmetries. Momentum map and its properties. May be repeated for credit.
Terms: Aut

Units: 3

Repeatable for credit

Grading: Letter or Credit/No Credit
Instructors:
Varolgunes, U. (PI)
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