Applied Topology and Differential Geometry


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Applied Topology and Differential Geometry

Code: 239982
ECTS: 4.0
Lecturers in charge: doc. dr. sc. Matija Bašić
prof. dr. sc. Željka Milin Šipuš
Take exam: Studomat

1. komponenta

Lecture typeTotal
Lectures 30
* Load is given in academic hour (1 academic hour = 45 minutes)
COURSE OBJECTIVES: To equip students to use basic concepts and techniques from (algebraic) topology and differential geometry in applications to biology and biomedicine.

1. Metric spaces. Concept of metric and topology. Topological and differential manifolds. Tangent vectors. Bundles.
2.Simplicial complexes. Definition of simplicial complexes and examples in biomedicine and data analysis. Triangulations and simplicial approximation. Simplicial maps.
3.Topological data analysis. Betti numbers. Introduction to persistent homology.
4. Applications of topology in molecular biology and biomedicine. Topology of viral evolution. Topology of cancer. Visualization and clustering algorithms.
5. Discrete differential geometry. Discretization of curves and surfaces. Special classes and parametrizations.
6. Curvatures of discrete planar curves. Characterizations of curvature in the smooth setting. Principle of preservation of properties.
7. Curvatures of discrete surfaces. Conjugate nets. Orthogonal nets. Surfaces parametrized with curvature or asymptotic lines. Discrete surfaces with constant negative Gaussian curvature.
8. Geometric modelling with discrete differential geometry. Application of discrete curves and surfaces and analysis of their properties.
1. semester
Elective courses 1, 2 - Regular study - Biomedical Mathematics

2. semester Not active
Elective courses 1, 2 - Regular study - Biomedical Mathematics

3. semester
Elective course 3 - Regular study - Biomedical Mathematics
Consultations schedule: