MATH 245B: Topics in Algebraic Geometry: Dessin d'Enfants
Grothendieck's theory of dessin d'enfants, a study of graphs on surfaces and their connection with the absolute Galois group of the rational numbers. Belyi's theorem, representations of the absolute Galois group as automorphisms of profinite groups, Grothendieck-Teichmuller theory, quadratic differentials, and the combinatorics of moduli spaces of surfaces. May be repeated for credit.
| Repeatable
3 times
(up to 9 units total)
MATH 247: Topics in Group Theory
Topics include the Burnside basis theorem, classification of p-groups, regular and powerful groups, Sylow theorems, the Frattini argument, nilpotent groups, solvable groups, theorems of P. Hall, group cohomology, and the Schur-Zassenhaus theorem. The classical groups and introduction to the classification of finite simple groups and its applications. May be repeated for credit.
| Repeatable
for credit
MATH 248A: Algebraic Number Theory
Structure theory and Galois theory of local and global fields, finiteness theorems for class numbers and units, adelic techniques. Prerequisites:
MATH 210A,B.
| Repeatable
2 times
(up to 6 units total)
MATH 249B: Topics in Number Theory: Class Field Theory
Classification of abelian extensions of local and global fields; classical, adelic, and cohomological formulations; applications to L-functions. May be repeated for credit.
| Repeatable
3 times
(up to 9 units total)
MATH 250: Topics in Algebra
MATH 254: Geometric Methods in the Theory of Ordinary Differential Equations
Topics may include: structural stability and perturbation theory of dynamical systems; hyperbolic theory; first order PDE; normal forms, bifurcation theory; Hamiltonian systems, their geometry and applications. May be repeated for credit.
| Repeatable
for 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.
| Repeatable
2 times
(up to 6 units total)
MATH 257B: Symplectic Geometry and Topology
Continuation of 257A. May be repeated for credit.
| Repeatable
2 times
(up to 6 units total)
MATH 261A: Functional Analysis
Geometry of linear topological spaces. Linear operators and functionals. Spectral theory. Calculus for vector-valued functions. Operational calculus. Banach algebras. Special topics in functional analysis. May be repeated for credit.
| Repeatable
2 times
(up to 6 units total)
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