Complex Dynamics, Geometric Function Theory, and a Fixed Point Theorem
A basic complex variables course contains few results belonging to the body of knowledge known as "Geometric function theory". Arguably, the most popular is the simple, yet far reaching, Schwarz lemma. The student working on this project is required to complete successfully the Complex Variables course offered at UNO, then read an upper level material (a select collection of notes elaborated by the adviser for this project), in order to be able to read and understand the paper:
Matache, Valentin, A fixed point theorem for analytic functions. Fixed Point Theory Appl. 2005, no. 1, 87–91.
In the second phase of this project , the student taking it, is supposed to produce, under guidance, refinements and further developments of the results in the above paper.