Course Details for A.Y. 2018/2019

The information on this page refer to the academic year 2018/2019. Therefore, several links are not available and data may be incomplete. To read the current information on the course, if it is still available, go to the university course catalogue . To read information relating other academic years, use the list at the bottom of this page.

A. Year:

2018/2019

Name:

Geometria Superiore 2 / Advanced Geometry 2

Type:

Module

Main course:

Geometria Superiore / Advanced Geometry

Basic information

Code:

DT0119

Sector:

MAT/03

Credits:

: Master Degree in Mathematics 6 CFU (b)

Term:

2^nd semester

Degree(s):

Master Degree in Mathematics 2^nd anno curriculum Generale Compulsory

Language:

English

Teacher(s):

Lucio Bedulli

Course Objectives

-The goal is to acquire a good knowledge of basic concepts about topological manifolds, CW-complexes and simplicial complexes (Fedeli). - The student should learn the basic notions of the theory of Riemann surfaces necessary to establish some theorem and to solve problems about this subject (Nelli)

Course Content

Smooth manifolds with boundary and Stokes' theorem
de Rham Theorem
Hodge theory
Vector bundles
Introduction to Riemannian Geometry

Learning Outcomes (Dublin Descriptors)

On successful completion of this course, the student should

The student should learn the basic notions of Riemann surfaces theory.

The student should have a basic knowledge on topological manifolds and complexes.

The student should be able to solve small problems about the theory Riemann surfaces, using notions and theorems of the course.

The student should be able to use the acquired tools.

The student should understand how to apply the acquired notions of Riemann Surfaces theory to the proposed problems.

The student should be able to understand and solve problems.

The student should be able to explain the statements and the proofs of the theorems about Riemann surfaces.

The student should be able to present in a clear and rigorous way the acquired knowledge.

The student should have acquired the ability of reading and understanding more advanced result about Riemann surfaces.

The student should develop those learning skills necessary to deal with the subsequent studies.

Prerequisites and Learning Activities

An introductory course on algebraic topology (fundamental group and singular homology) Basics on smooth manifolds (in particular differential forms and de Rham cohomology).

Assessment Methods and Criteria

Oral exam

Course page updates

This course page is available (with possible updates) also for the following academic years:

To read the current information on this course, if it is still available, go to the university course catalogue .

Course information last updated on: 30 novembre 2016, 12:59