ADVANCED TOPICS IN COMPLEX ANALYSIS

MATH 722

The basic theory of functions of one complex variable including Cauchy formula, singularities and residues, meromorphic functions, conformal mappings, harmonic functions, approximation and the nonhomogeneous d-bar equation. Requires knowledge of undergraduate analysis (e.g. the sequenceMATH 521and522).

MATH 623

Elementary functions of a complex variable; conformal mapping; complex integrals; the calculus of residues.

MATH 821

Topics in partial differential equations and real analysis.

MATH 863

Geometry of several complex variables; algebraic groups, abelian varieties; topological aspects of algebraic geometry, including sheaf theory and homology theory; advanced theory of local rings; intersection theory of algebraic varieties.

MATH 826

Topics in functional analysis and differential equations.