Studying at the University of Verona
Here you can find information on the organisational aspects of the Programme, lecture timetables, learning activities and useful contact details for your time at the University, from enrolment to graduation.
Study Plan
This information is intended exclusively for students already enrolled in this course.If you are a new student interested in enrolling, you can find information about the course of study on the course page:
Laurea magistrale in Mathematics - Enrollment from 2025/2026The Study Plan includes all modules, teaching and learning activities that each student will need to undertake during their time at the University.
Please select your Study Plan based on your enrollment year.
1° Year
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1 module between the following1 module between the following3 modules among the followingLegend | Type of training activity (TTA)
TAF (Type of Educational Activity) All courses and activities are classified into different types of educational activities, indicated by a letter.
Homological algebra (seminar course) (2021/2022)
Teaching code
4S001439
Teacher
Coordinator
Credits
6
Language
English
Scientific Disciplinary Sector (SSD)
MAT/02 - ALGEBRA
Period
Secondo semestre dal Mar 7, 2022 al Jun 10, 2022.
Learning outcomes
This reading course is devoted to some topics in homological algebra and representation theory. Prerequisites: Representation Theory.
Program
The first part will consist in an introductory lecture series "Quivers and representations" by Raquel Coelho Simoes
from Lancaster University in the period March 15-25, see
https://www.di.univr.it/?ent=seminario&id=5596
With this background, we will then focus on some algebraic and homological methods that are applied in topological data analysis. Given a set of data, which is viewed as a set of points in euclidean space, the idea is to detect the topological features which are relevant and thus persist when varying the scale of observation. This leads to the notion of persistent homology, which is investigated with methods from homological algebra and representation theory of quivers.
We will study some aspects of this algebraic approach to persistence by reading the following material:
• Chapters 1.1. and 1.2 in
Oudot, S.Y., Persistence theory: from quiver representations to data analysis. Mathematical Surveys and Monographs, 209. American Mathematical Society, Providence, RI, (2015).
• B. Blanchette, T. Brüstle, E.J. Hanson: Homological approximations in persistence theory, preprint 2021, https://arxiv.org/abs/2112.07632
Students interested in a short introduction to persistence homology may watch https://www.youtube.com/watch?v=DJSaTaEQWDA
Please note: the prerequisite Representation Theory is helpful, but not strictly necessary for attending this course.
Examination Methods
Students actively participate in the course and deliver a seminar talk.
