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MATH-511: Number theory II.b - Modular forms

Summary

In this course we will introduce core concepts of the theory of modular forms and consider several applications of this theory to combinatorics, harmonic analysis, and geometric optimization.

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/number-theory-ii-b-modular-forms-MATH-511

Moodle Page

http://go.epfl.ch/MATH-511

About this result

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Summary

In this course we will introduce core concepts of the theory of modular forms and consider several applications of this theory to combinatorics, harmonic analysis, and geometric optimization.

Lectures

Instructor

Maryna Viazovska

Official source

https://edu.epfl.ch/coursebook/en/number-theory-ii-b-modular-forms-MATH-511

Moodle Page

http://go.epfl.ch/MATH-511

About this result

Ontological neighbourhood

Mathematics

Number theory: Topics in number theory

Lectures in this course (17)

Canonical Divisors and Modular Forms

Covers canonical divisors on Riemann surfaces and properties of modular forms.

Meromorphic Differentials and Modular Forms

Explores meromorphic differentials on Riemann surfaces and modular forms on congruence subgroups.

Modular Lambda Function: Properties and Applications

Explores the modular lambda function, its properties, and applications in modular forms.

Principal Congruence Subgroup of Level 2

Explores the principal congruence subgroup of level 2 and its group structure.

Modular Curves: Genus and Mapping Theorems

Explores holomorphic maps, ramification points, and the genus of a modular curve.

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