96760 - Geometric and Topological Tools for Applications

Academic Year 2023/2024

  • Teaching Mode: Traditional lectures
  • Campus: Bologna
  • Corso: Second cycle degree programme (LM) in Mathematics (cod. 5827)

Learning outcomes

At the end of the course the student acquires the knowledge of geometric and topological tools that could be used to construct mathematical models. The student knows some examples that could be involved in applications.

Course contents

The course will introduce geometric, topological and combinatorial techniques. They will be exemplified through the theory of hyperplane arrangements. Applications to other fields of mathematics will be provided.

More specifically, the course will contain an introduction to real and complex hyperplane arrangements and we will discuss the de Rham cohomology algebra, CW complexes and homotopy groups. The corresponding examples for hyperplane arrangements will be the Orlik-Solomon algebra, the Salvetti complex and some classifying spaces.

Readings/Bibliography

Teaching methods

Lectures and exercise sessions. Exercises will be handed out during the lectures, in addition to the ones available in the suggested textbooks.

During office hours, students will be coached in a personalized way.

Assessment methods

Oral exam on the program carried out

Teaching tools

Appropriately sized blackboard and suitable chalks

Office hours

See the website of Roberto Pagaria