# Course Details

#### Name:

**Advanced Geometry 2 / Geometria Superiore 2**

### Basic information

##### Credits:

*Master Degree in Mathematics:* 6 Ects (b)

##### Degree(s):

Compulsory 2^{nd} year Master Degree in Mathematics curriculum Generale

##### Language:

English

### 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).

### Teaching Methods

**Language**: English

Lectures

### Assessment Methods and Criteria

Oral exam

### Course page updates

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

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