MATH-322: Differential geometry II - smooth manifolds
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Résumé
Smooth manifolds constitute a certain class of topological spaces which locally look like some Euclidean space R^n and on which one can do calculus. We introduce the key concepts of this subject, such as vector fields, differential forms, etc.
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This course is an introduction to the theory of Riemann surfaces. Riemann surfaces naturally appear is mathematics in many different ways: as a result of analytic continuation, as quotients of complex
We develop, analyze and implement numerical algorithms to solve optimization problems of the form min f(x) where x is a point on a smooth manifold. To this end, we first study differential and Riemann
This course will serve as a first introduction to the geometry of Riemannian manifolds, which form an indispensible tool in the modern fields of differential geometry, analysis and theoretical physics
