Studying at the University of Verona

Here you can find information on the organisational aspects of the Programme, lecture timetables, learning activities and useful contact details for your time at the University, from enrolment to graduation.

Study Plan

The Study Plan includes all modules, teaching and learning activities that each student will need to undertake during their time at the University.
Please select your Study Plan based on your enrollment year.

CURRICULUM TIPO:

1° Year 

ModulesCreditsTAFSSD
12
B
MAT/05
6
B
MAT/07
6
B
MAT/03
6
B
MAT/05
6
B
MAT/06

2° Year   activated in the A.Y. 2022/2023

ModulesCreditsTAFSSD
6
B
MAT/05
Final exam
32
E
-
activated in the A.Y. 2022/2023
ModulesCreditsTAFSSD
6
B
MAT/05
Final exam
32
E
-
Modules Credits TAF SSD
Between the years: 1°- 2°
1 module between the following
6
B
MAT/02
6
B
MAT/02
Between the years: 1°- 2°
1 module between the following
6
B
MAT/08
6
B
MAT/08
Between the years: 1°- 2°
3 modules among the following
6
C
MAT/03
6
C
MAT/02 ,MAT/03
6
C
MAT/08
6
C
MAT/08
6
C
MAT/02
6
C
MAT/06
6
C
INF/01
6
C
MAT/05
6
C
MAT/09
6
C
MAT/08
6
C
MAT/08
6
C
MAT/07
6
C
INF/01 ,MAT/06
Between the years: 1°- 2°
12
D
-
Between the years: 1°- 2°
Further activities
4
F
-

Legend | Type of training activity (TTA)

TAF (Type of Educational Activity) All courses and activities are classified into different types of educational activities, indicated by a letter.

A Basic activities
B Characterizing activities
C Related or complementary activities
D Activities to be chosen by the student
E Final examination
F Other training activities
S Placements in companies, public or private institutions and professional associations

Differential geometry  (2021/2022)

Teaching code

4S003196

Teacher

Nicola Sansonetto

Coordinator

Nicola Sansonetto

Credits

6

Language

English en

Scientific Disciplinary Sector (SSD)

MAT/03 - GEOMETRY

Period

Primo semestre dal Oct 4, 2021 al Jan 28, 2022.

Lessons timetable MoodleMoodle Seminars 0

Learning outcomes

The course aims to provide students with the basic concepts on Differential Geometry of manifolds. At the end of the course the student will know the main terminology and definitions about manifolds and Riemannian manifolds, and some of the main results. He/she will be able to produce rigorous arguments and proofs on these topics and he/she will be able to read articles and texts of Differential Geometry.

Program

DIFFERENTIABLE MANIFOLDS
Manifolds, submanifolds, mappings. The Tangent Bundle and vector bundles. Vector fields and flows. Lie derivative and Frobenius' Theorem.

TENSORS CALCULUS
Tensor product of vector spaces, and tensor algebra. Tensor bundles and tensor fields. Lie derivative of a tensor field.

DIFFERENTIAL FORMS
Exterior algebra, determinants, volumes and star Hodge operator. Differential forms, the exterior derivative, interior product and Lie derivative. Introduction to de Rham theory.

RIEMANNIAN GEOMETRY
Covariant derivative , torsion and curvature. The metric tensor, the Riemannian connection and curvature of a Riemannian manifold.

Bibliography

Vai alla bibliografia
Visualizza la bibliografia con Leganto, strumento che il Sistema Bibliotecario mette a disposizione per recuperare i testi in programma d'esame in modo semplice e innovativo.

Examination Methods

During the exam, students must show that:
- they know and understand the fundamental concepts and techniques of differential geometry
- they have analytical, abstraction and computational abilities
- they support their argumentation with mathematical rigor.

The exam is composed of a written test and an oral examination.
The written test contains both exercises and theoretical questions.
The oral part is optional, but it becomes mandatory to obtain an assessment greater than 27/30.

Students with disabilities or specific learning disorders (SLD), who intend to request the adaptation of the exam, must follow the instructions given HERE