0522200040 DIPARTIMENTO DI MATEMATICA EQF7 MATHEMATICS 2022/2023

 YEAR OF COURSE 2 YEAR OF DIDACTIC SYSTEM 2018 SPRING SEMESTER
SSD CFU HOURS ACTIVITY TYPE OF ACTIVITY MAT/03 6 48 LESSONS SUPPLEMENTARY COMPULSORY SUBJECTS
 CHIARA ESPOSITO T ALFONSO GIUSEPPE TORTORELLA
ExamDate
GEOMETRIA SUPERIORE12/06/2023 - 09:00
GEOMETRIA SUPERIORE03/07/2023 - 09:00
Objectives
THE AIM OF THE COURSE CONSISTS IN GIVING THE STUDENT BASICS OF LIE THEORY.
IN PARTICULAR THERE WILL BE DISCUSSED BASIC NOTIONS OF LIE GROUPS AND LIE ALGEBRAS.
THIS COURSE SITS IN AN INTERSECTION BETWEEN DIFFERENTIAL GEOMETRY AND ALGEBRA

GLI OBIETTIVI PRINCIPALI DELL’INSEGNAMENTO “GEOMETRIA SUPERIORE” SONO DESCRITTI COME SEGUE.

KNOWLEDGE AND UNDERSTANDING:

THE GOAL OF TEACHING WILL BE REACHING A GOOD MASTERING IN THE USE OF TECHNIQUES RELATIVE TO LIE THEORY AND RELATED TOPICS.
IN ORDER TO OBTAIN SUCH A GOAL, THE COURSE WILL BE STRUCTURED IN LECTURES AND TUTORIALS IN WHICH STUDENTS NEED TO DISCUSS THE EXERCISES.

APPLYING KNOWLEDGE AND UNDERSTANDING:

THE STUDENT WILL NEED TO GET A DEEP KNOWLEDGE OF THE DISCUSSED NOTIONS AND A GOOD ABILITY IN SOLVING PROBLEMS WHICH ARE USEFUL IN MATH AND PHYSICS.
ONE OF THE OBJECTIVES OF THE COURSE CONSISTS IN MAKING THE STUDENT AUTONOMOUS AS MUCH AS POSSIBLE
AND THE ABILITY TO RECOGNIZE CRUCIAL IDEAS AND TOPICS.
THE STUDENT WILL BE ABLE TO EXPOSE AND DISCUSS THE SOLUTION OF PROBLEMS. MOREOVER HE/SHE WILL BE ABLE TO PROVE IN A RIGOROUS WAY THE MOST IMPORTANT RESULTS IN LIE THEORY BY USING A CORRECT MATHEMATICAL LANGUAGE.
THIS COURSE AIMS TO REFINE THE ANALYTIC ABILITIES OF THE STUDENT, HIS/HER MASTERING IN APPROACHING NEW AND ADVANCED TOPICS RELATING THEM TO THE KNOWN ALGEBRAIC STRUCTURES.
Prerequisites

THE STUDENT NEEDS SOME FAMILIARITY WITH CONCEPTS OF LINEAR ALGEBRA AND DIFFERENTIAL GEOMETRY SUCH AS MANIFOLDS, VECTOR FIELDS AND CARTAN CALCUCUS.
Contents
1. LIE GROUPS AND EXAMPLES
2. LIE ALGEBRAS AND EXAMPLES
3. RELATION BETWEEN LIE GROUPS AND ALGEBRAS
4. LIE GROUP ACTIONS
5. LIE GROUP COHOMOLOGY
Teaching Methods

THE COURSE WILL CONSISTS OF LECTURES. ALSO THERE WILL BE HOMEWORK CONSISTING OF PROBLEMS TO BE SOLVED IN ORDER TO INVOLVE THE STUDENTS IN THE LEARNING PROCESS.
Verification of learning
THE EXAM WILL BE ORAL AND AIMS TO CHECK THE GLOBAL KNOWLEDGE OF THE TOPIC AND THE CORRECT USE OF THE MATH LANGUAGE. IF THE STUDENT HAS SOLVED THE ASSIGNED HOMEWORKS, THE EXAM CAN CONSIST IN A SEMINAR (60 MINUTES) ABOUT AN ADVANCED TOPIC, NOT DISCUSSED DURING THE LECTURES.
Texts
LECTURE NOTES

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