Knowledge and ability to understand. At the end of the course, the student will have to possess a robust knowledge of basic elements of abstract measure theory and BV spaces and he will have to be able to understand how these mathematical tools come into play for the resolution of problems of geometric character, using the approach classified under the label geometric measure theory.
Ability to apply knowledge and understanding. Thanks both to examples carried out in the classroom and proofs left as an exercise, the student will learn both to handle the theoretical tools presented in the course with awareness and familiarity, and to apply them to a concrete context of geometric problems mainly related to the existence of minimal surfaces. Furthermore, he must be fully aware of the pivotal examples on which general and abstract constructions are modeled.
Autonomy of judgment. The student must be able to evaluate the consistency and correctness of proofs, constructing and developing logical arguments with a clear identification of assumptions and conclusions. Furthermore, he will have to be able to evaluate the likelihood of general results stemmed from model cases or analogies with he already knows.
Communication skills. The student must be able to communicate in a clear and precise manner, appropriate for a mathematician in an advanced stage of training, mathematical contents related to the program of the course. Lectures and the direct confrontation with the teacher will favor the acquisition of a specific appropriate scientific language.
Learning ability. At the end of the course, the student will be able to autonomously deepen his knowledge in the areas covered, starting from the basic and fundamental knowledge provided by the course itself. He will be able to consult specialist texts in an autonomous way, even outside the topics covered in detail during the lessons, even written in English, in order to effectively address complex problems inherent to these topics, possibly as part of master's degree theses.