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
Abstract and geometrical implicial complexes.
Singular homology and simplicial homology.
Cohomology
Duality Theorems
Persistent homology and data analysis
Elements of differential topology
Differential forms and de Rham cohomology
Vidit Nanda: Computational Algebraic Topology - Lecture notes
James R. Munkres : Topology Prentice Hall.
Raoul Bott, Loring W. Tu,Differential forms in algebraic topology.Springer, (1986).
Marco Abate, Francesca Tovena,Geometria Differenziale.Springer, (2011).
Programme
Categories.Abstract and geometrical implicial complexes.
Singular homology and simplicial homology.
Cohomology
Duality Theorems
Persistent homology and data analysis
Elements of differential topology
Differential forms and de Rham cohomology
Core Documentation
Allen Hatcher: Algebraic topology Cambridge University press.Vidit Nanda: Computational Algebraic Topology - Lecture notes
James R. Munkres : Topology Prentice Hall.
Raoul Bott, Loring W. Tu,Differential forms in algebraic topology.Springer, (1986).
Marco Abate, Francesca Tovena,Geometria Differenziale.Springer, (2011).
Type of evaluation
Written exam and discussion of proposed exercises during the lectures. teacher profile teaching materials
Abstract and geometrical implicial complexes.
Singular homology and simplicial homology.
Cohomology
Duality Theorems
Persistent homology and data analysis
Elements of differential topology
Differential forms and de Rham cohomology
Vidit Nanda: Computational Algebraic Topology - Lecture notes
James R. Munkres : Topology Prentice Hall.
Raoul Bott, Loring W. Tu,Differential forms in algebraic topology.Springer, (1986).
Marco Abate, Francesca Tovena,Geometria Differenziale.Springer, (2011).
Mutuazione: 20410465 GE450 - TOPOLOGIA ALGEBRICA in Matematica LM-40 MASCARENHAS MELO ANA MARGARIDA
Programme
Categories.Abstract and geometrical implicial complexes.
Singular homology and simplicial homology.
Cohomology
Duality Theorems
Persistent homology and data analysis
Elements of differential topology
Differential forms and de Rham cohomology
Core Documentation
Allen Hatcher: Algebraic topology Cambridge University press.Vidit Nanda: Computational Algebraic Topology - Lecture notes
James R. Munkres : Topology Prentice Hall.
Raoul Bott, Loring W. Tu,Differential forms in algebraic topology.Springer, (1986).
Marco Abate, Francesca Tovena,Geometria Differenziale.Springer, (2011).
Type of evaluation
Written exam and discussion of proposed exercises during the lectures.