TBD, Dima Fontaine & Louan Mol : Complex manifolds (Nakahara Ch. 8)
TBD, Nathan Godéchal : Fibre bundles and connections on fibre bundles (Nakahara Chs. 9 & 10)
Register for the next sessions here!
04.04.2025, 11:00, Augustin Basilavecchia : De Rham cohomology (Nakahara Ch. 6).
28.03.2025, 11:00, Thomas Smoes: Everything you always wanted to ask about manifolds but were too afraid to ask, pt.2 (Nakahara Ch. 5, Manifolds).
20.12.2024, 15:00, Thomas Smoes: Everything you always wanted to ask about manifolds but were too afraid to ask, pt.1 (Nakahara Ch. 5, Manifolds).
09.12.2024, 16:00, Louan Mol : From donuts to pies, a Christmas recipe (Nakahara Ch. 4, Homotopy groups).
Paths, loops, homotopic maps. Fundamental groups and examples, topological invariance, relation with the level-one homology group. Higher-homotopy groups, covering space and fermions.
02.12.2024, 16:00, Dima Fontaine : Homology made simplex (Nakahara Ch. 3, Homology groups).
Simplices, simplicial complexes, polyhedrons and triangulations. The boundary operator for oriented simplices, the chain group, its kernel and image: the cycle and boundary subgroups. Definition of the homology group of a simplicial complex, examples, interpretation and relation to the Euler characteristic.
23.10.2024, Maxime Weytens (Differential geometry, ULB): Basics of topology (equivalent to Nakahara Ch. 2).
Topological space: definition and examples. Continuous maps and homeomorphisms. Hausdorff spaces, connectedness and path-connectedness, compactness, Euler characteristic.