- Docente: Roberto Pagaria
- Credits: 6
- SSD: MAT/03
- Language: English
- Moduli: Roberto Pagaria (Modulo 1) Roberto Pagaria (Modulo 2)
- Teaching Mode: Traditional lectures (Modulo 1) Traditional lectures (Modulo 2)
- Campus: Bologna
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Corso:
Second cycle degree programme (LM) in
Mathematics (cod. 5827)
Also valid for 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
Introduction to quivers, quiver representations, and path algebra associated with.
Reflection functors, Gabriel theorem, classification of quivers into finite type/Euclidean/wild.
Quiver varieties, GIT quotients, Kac theorems and finite fields.
Application to flag varieties, to Hilbert scheme, and to persistent homology (topological data analysis).
Readings/Bibliography
Derksen, Harm; Weyman, Jerzy An introduction to quiver representations.
Graduate Studies in Mathematics, 184. American Mathematical Society, Providence, RI, 2017.
Kirillov, Alexander, Jr. Quiver representations and quiver varieties.
Graduate Studies in Mathematics, 174. American Mathematical Society, Providence, RI, 2016.
Oudot, Steve Y. Persistence theory: from quiver representations to data analysis. Mathematical Surveys and Monographs, 209. American Mathematical Society, Providence, RI, 2015.
Teaching methods
Lecture and exercise sessions in blended mode. Summer school only in person in Bologna from May 22nd to 26th. For further information see eventi.unibo.it/bip-quiver
Assessment methods
Exercises to be done by the end of the course and short oral discussion of them.
Teaching tools
Blackboard, slides, Teams app.
Links to further information
https://eventi.unibo.it/bip-quiver
Office hours
See the website of Roberto Pagaria