96760 - Geometric and Topological Tools for Applications

Course Unit Page

Academic Year 2022/2023

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).


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


Office hours

See the website of Roberto Pagaria

See the website of