Complex Analysis
- Research
- Research areas that are currently active include the
interconnected fields of Riemann surfaces, Kleinian groups (of Mobius
transformations), and Teichmuller theory. Equally important are
studies in potential theory, Brownian motion, fractals, and harmonic
measure as they relate to the study of Kleinian groups.
- Coursework
- Graduate students take a standard one-semester introduction to
functions of a complex variable, Complex Analysis I; MAT 542. Topics
include complex numbers, continuity and differentiability of functions
of a complex variable, complex integration, Cauchy's Theorem and the
Cauchy Integral Formula, Mobius transformations, Schwarz' Lemma, and
the Riemann Mapping Theorem. Complex Variables II; MAT 543, offered
in the fall semester, varies between treatments of several complex
variables and other topics. For more advanced students, there is a
Topics in Complex Analysis course offered each fall, which in recent
years covered topics including Hardy spaces and function theory on the
unit disk (Chapters 1-3 of Bounded Analytic Functions by
Garnett).
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