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

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 oral examination consists of two parts:

1) presentation of a brief seminar (aprroximately 20 minutes)  on a topic previously agreed upon

2) questions on the program. 

Further, the final grade will also be based on the discussions that have taken place during the problem sessions.

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 main purpose of the oral examination is

1. as far as the seminar is concerned, to evaluate the student's ability to organize and expose the material, and the ability to present it in a clear and precise way; 

2. as far as the questions on the program, , to evaluate the student's competence on the various topics and the ability to apply the theory to the most relevant examples.

As far as The blackboard discussion of the exercises assigned as homework, this part is voluntary and consists in presenting the  he arguments used in solving the proposed problems, including the difficulties encountered. Every contribution to the discussions during the problem sessions will be evaluated positively.

FURTHER INFORMATION

Ask the professor for other information not included in the teaching schedule