- Docente: Roberto Pagaria
- Credits: 6
- SSD: MAT/03
- Language: English
- Teaching Mode: Traditional lectures
- Campus: Bologna
- Corso: Second cycle degree programme (LM) in Mathematics (cod. 5827)
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from Feb 20, 2024 to May 31, 2024
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
- Orlik, Terao, Arrangements of Hyperplanes, 1992
- Hatcher, Algebraic Topology https://pi.math.cornell.edu/~hatcher/AT/AT.pdf
- Kozlov, Combinatorial Algebraic Topology, Springer, 2008
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