To explain ideas and methods of algebraic topology, among which co-homology, homology and persistent homology. To understand the application of these theories to data analysis (Topological Data Analysis)
Curriculum
teacher profile teaching materials
Cathegories.
Anstract and geometric simplicial complexes.
Singular and simplicial homology.
Cohomology.
Duality theorems.
Data analysis.
Vidit Nanda: Computational Algebraic Topology - Lecture notes
Lucia Caporaso : Lezioni di topologia
Mutuazione: 20410465 GE450 - TOPOLOGIA ALGEBRICA in Matematica LM-40 CAPORASO LUCIA
Programme
Fundamental grupo and covering spaces.Cathegories.
Anstract and geometric simplicial complexes.
Singular and simplicial homology.
Cohomology.
Duality theorems.
Data analysis.
Core Documentation
Allen Hatcher: Algebraic topology Cambridge University press.Vidit Nanda: Computational Algebraic Topology - Lecture notes
Lucia Caporaso : Lezioni di topologia
Type of delivery of the course
In class lectures available online.Type of evaluation
Oral exam or seminar. teacher profile teaching materials
Cathegories.
Anstract and geometric simplicial complexes.
Singular and simplicial homology.
Cohomology.
Duality theorems.
Data analysis.
Vidit Nanda: Computational Algebraic Topology - Lecture notes
Lucia Caporaso : Lezioni di topologia
Mutuazione: 20410465 GE450 - TOPOLOGIA ALGEBRICA in Matematica LM-40 CAPORASO LUCIA
Programme
Fundamental grupo and covering spaces.Cathegories.
Anstract and geometric simplicial complexes.
Singular and simplicial homology.
Cohomology.
Duality theorems.
Data analysis.
Core Documentation
Allen Hatcher: Algebraic topology Cambridge University press.Vidit Nanda: Computational Algebraic Topology - Lecture notes
Lucia Caporaso : Lezioni di topologia
Type of delivery of the course
In class lectures available online.Type of evaluation
Oral exam or seminar.