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.

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.

1° Year

ModulesCreditsTAFSSD
One course chosen from the following
One course chosen from the following
One course chosen from the following

2° Year  activated in the A.Y. 2013/2014

ModulesCreditsTAFSSD
Prova finale
32
E
-
ModulesCreditsTAFSSD
One course chosen from the following
One course chosen from the following
One course chosen from the following
activated in the A.Y. 2013/2014
ModulesCreditsTAFSSD
Prova finale
32
E
-
Modules Credits TAF SSD
Between the years: 1°- 2°
One course chosen from the following
6
C
MAT/05
Between the years: 1°- 2°
Other activities
4
F
-
Between the years: 1°- 2°

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.




S Placements in companies, public or private institutions and professional associations

Teaching code

4S001100

Credits

12

Language

Italian

Scientific Disciplinary Sector (SSD)

MAT/03 - GEOMETRY

The teaching is organized as follows:

Modulo 1

Credits

6

Period

I semestre

Academic staff

Mauro Spera

Modulo 2

Credits

6

Period

II semestre

Academic staff

Gaetano Zampieri

Learning outcomes

Module: 1
Learning objectives:


The course provides an introduction to differentiable manifolds
and Riemannian geometry; it will possess a quite concrete character and will be based
on examples emerging from other areas of mathematics as well.

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Program

Module: 1
Syllabus:
Multilinear algebra.
Differentiable manifolds.
Lie groups.
Tensor calculus. Lie group actions on manifolds and their orbit spaces.
Riemannian manifolds.
Levi-Civita connection.
Curvature tensors (Riemann, sectional, Ricci, scalar).
Geodesics and their variational aspects.
Exponential map.
Riemannian geometry of Lie groups.


Module: 2

First Part:

0) Integration on manifolds and Stokes Theorem

1) Riemannian Geometry: connections, parallel transport, curvature
tensors, Levi-Civita connection, geodesics and applications (Chap. 1 and 2
of Chavel's Book "Riemannian Geometry, a modern Introduction" (2nd
Edition, Cambridge University Ppress, 2006).

2) Morse theory: Morse lemma and applications ( J. Milnor "Morse Theory" ,
Annals of Mathematics Studies, Princeton University Press).


3) De Rham cohomology and applications (Chap.1 of Bott, Tu "Differential
Forms in Algebraic Topology" , Graduate Texts in Mathematics, 82).




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Examination Methods

Exam methods (1st module): written test, immediately followed by an oral exam. The final grade will be assigned after completion of the second module.

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

Teaching materials e documents