CODE 61683 ACADEMIC YEAR 2025/2026 CREDITS 6 cfu anno 1 MATEMATICA 11907 (LM-40 R) - GENOVA 6 cfu anno 2 MATEMATICA 9011 (LM-40) - GENOVA SCIENTIFIC DISCIPLINARY SECTOR MAT/05 LANGUAGE Italian (English on demand) TEACHING LOCATION GENOVA SEMESTER 2° Semester OVERVIEW In this course the fundamental notions relative to abstract harmonic analysis will be presented, namely the basics of unitary representations of locally compact topological groups, emphasizing the analytic aspects and working on some important examples. The lectures will be delivered in Italian AIMS AND CONTENT LEARNING OUTCOMES The course aims to provide an introduction to Abstract Harmonic Analysis, that is, to the theory of unitary representations of locally compact topological groups. AIMS AND LEARNING OUTCOMES The objective is to introduce the main analytic problems addressed by representation theory, and to develop general techniques relative to integration on homogeneous spaces PREREQUISITES Basic notions of Functional Analysis will be used throughout TEACHING METHODS Traditional. The problems’ sessions consist of a blackboard discussion with the students of the proposed exercises SYLLABUS/CONTENT The course is divided into four chapters: Topological groups: integration on the group and on its homogeneous spaces Generalities on unitary rappresentations Compact groups Induced rappresentations RECOMMENDED READING/BIBLIOGRAPHY - G. Folland, An Introduction to Abstract Harmonic Analysis, CRC press. TEACHERS AND EXAM BOARD FILIPPO DE MARI CASARETO DAL VERME Ricevimento: Weekly office hours, typically 2-hours per week, will be communicated. Meetings upon E-mail requests will also be considered compatibly with the teacher's availability. LESSONS LESSONS START In agreement with the academic calendar, approved by the “Consiglio di Corsi di Studi” Class schedule The timetable for this course is available here: Portale EasyAcademy EXAMS EXAM DESCRIPTION The final grade is based on the discussions that have taken place during the problem sessions and on the oral examination Students with certified inabilities or special needs are kindly invited to contact the teacher at the beginning of the course in order to agree on the suitable adjustments that respect both the objectives of the course and the individual needs ASSESSMENT METHODS The blackboard discussion of the exercises assigned as homework is voluntary and consists in presenting the arguments used in solving the proposed problems, including the difficulties encountered. The main purpose of the oral examination is to evaluate the students' ability to apply the theory developed in class to the main examples. In the oral examination, the degree of understandin and the ability to explain and connect the various concepts are evaluated.
