Math 545E - Applied Differential Geometry: Space and Time

Course Description: Pointillisme, Concepts of absolute space and absolute time, Newtonian classical mechanics and its relation to Euclidean geometry, Galilean relativity, Special relativity, Minkowski spacetime, Review of fiber bundles and tensors, Cartan calculus, Metric-affine geometry and its classification, Levi-Civita connections, Schouten decomposition, Cartan formalism, Introduction to variational calculus, Classical field theories, Noether theorem, Ricci scalar and Einstein-Hilbert action, Einstein tensor, General relativity, Projective and conformal structures with compatibility conditions between them, Weyl structures, EPS paper, Black holes, Cosmological solutions, Physical geometry beyond standard model, Algebroids, Pre-Leibniz algebroids, Metric-connection geometry on algebroids

Classes: Wed 14.30 - 17.30, FEB D106

Office Hours: Wed 13.30 - 14.30 (by appointment), FEB D422

Instructor: Dr. Keremcan Doğan (dogankerem[at].itu.edu.tr)

You can find the syllabus here.