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MATH-410: Riemann surfaces

Summary

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 domains under discontinuous group actions, as algebraic curves.

Lectures

Instructor

Maryna Viazovska

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.

Official source

https://edu.epfl.ch/coursebook/en/riemann-surfaces-MATH-410

Moodle Page

http://go.epfl.ch/MATH-410

About this result

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Summary

Lectures

Instructor

Maryna Viazovska

Official source

https://edu.epfl.ch/coursebook/en/riemann-surfaces-MATH-410

Moodle Page

http://go.epfl.ch/MATH-410

About this result

Lectures in this course (14)

Riemann Surfaces: Complex Manifolds

Covers Riemann surfaces as complex manifolds of dimension 1, including transition maps and holomorphic functions.

Holomorphic Functions: Taylor Series Expansion

Covers the basic properties of holomorphic maps and Taylor series expansions in complex analysis.

Differential Forms on Manifolds

Introduces differential forms on manifolds, covering tangent bundles and intersection pairings.

Differential Forms Integration

Covers the integration of differential forms on smooth manifolds, including the concepts of closed and exact forms.

Harmonic Forms: Main Theorem

Explores harmonic forms on Riemann surfaces and the uniqueness of solutions to harmonic equations.

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