Gabriele Benedetti
Summary: This was the first of three parts on a course about advanced topics in the analysis of functions of one complex variable. We had 8 sessions of roughly 3 hours each. Each session comprised an interactive lecture to advance in the theory and a discussion part where students were subdivided into three pairs and each pair was asked to work on a different exercise. Students could get my help, if needed, and in the end each group presented to the others their solution. The topics we discussed during the course were: recap of isolated singularities of holomorphic functions, residue theorem, logarithmic derivative, sequences and series of meromorphic functions with applications to partial fraction decompositions, infinite products of functions with applications to the study of the zeta and gamma function. The students were given a link to complete lecture notes, reference to the literature and three set of exercises corresponding to the three chapters of my part. The students were extremely engaged and motivated: they participated actively in the lectures and asked many questions. Those with a weaker background in complex analysis managed to fill in the gaps in their preparation also helped by the other students. By the end of the two weeks, I had the impression that the students learned a lot and could identify the key concepts of this first part. The assessment (most likely a written assignment) will be carried out after all three parts of the course are over.