This lecture covers the topology of Riemann surfaces, focusing on orientation, orientability, and smooth maps between open subsets. It discusses the significance of orientation and the conditions for a manifold to be orientable.
Maryna Viazovska did her bachelor studies at the Kyiv National Taras ShevchenkoUniversity and completed her MSc at the Technical University Kaiserslautern.She obtained her PhD in 2013 in Bonn.She was a postdoctoral researcher at the Institut des Hautes Etudes Scientifiquesand at the Humboldt University of Berlin, and in 2017 was a Minerva DistinguishedVisitor at Princeton University. She joined EPFL in 2017 as Tenure-Track AssistantProfessor and was promoted Full Professor in 2018.
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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
Covers the concepts of local homeomorphisms and coverings in manifolds, emphasizing the conditions under which a map is considered a local homeomorphism or a covering.
