- Lecturer: Vidit Nanda
General Prerequisites:
Some familiarity with the main concepts from algebraic topology, homological algebra, and category theory will be helpful.
Course Term: Hilary
Course Lecture Information: 16 lectures
Course Weight: 1
Course Level: M
Course Overview:
Ideas and tools from algebraic topology have become more and more important in computational and applied areas of mathematics. This course will provide at the masters level an introduction to the main concepts of (co)homology theory, with a view towards efficient practical computations.
Learning Outcomes:
Students should gain a working knowledge of homology and cohomology of simplicial complexes and cellular sheaves, and improve their geometric intuition. Furthermore, they should gain awareness for the algorithmic aspects of computing (co)homology.
Course Synopsis:
Here is the course syllabus: simplicial complexes, geometric realisations, and simplicial maps; homotopy equivalence, carriers, nerves and fibres; homology and its computation; exact sequences and the snake lemma; cohomology, cup and cap products, poincare duality; persistent homology; cellular sheaves; discrete Morse theory.