The course could be held in English, upon proposal of the competent teaching structure.
Knowledge and understanding: To know some basic concepts and results of complex analysis in one variable and of differential geometry. To recognize a real analytic or geometric problem that can be tackled with complex analysis methods. To recognize a geometric problem which is resoluble through differential geometry methods.
Ability to apply knowledge and understanding: To know how to deal with and solve some classical problems of complex analysis in one variable and of differential geometry. To find analytical and geometric applications of complex analysis in one variable and differential geometry
Independent thinking: To know how to find the most appropriate analytical or geometric techniques in solving assigned problems. To address the difficulty of specific problems both in complex analysis of one variable and in differential geometry.
Communication skills: To introduce, orally and in writing, a subject, or a mathematical theory, learned during the course. Being able to present to a non-specialist public the salient aspects of classical theory of analytic functions in one complex variable, of Riemann surfaces, and of curves and surfaces immersed in ordinary space.
Learning ability: to be able to read a graduate degree book in the fields covered by the course. To work independently in literature search. To address the proposed problems by selecting independently the most meaningful ones.
to introduce the basic concepts of complex analysis in one variable;
to introduce the basic concepts of differential geometry.
Walter Rudin, Real and complex analysis, 3rd ed. New York, NY: McGraw-Hill. xiv+416p., 1987.
W. Ballmann, “Introduction to Geometry and Topology”
M.P.Do Carmo, “Differential geometry of curves and surfaces”
M.P. Do Carmo “Riemannian geometry”