Course

MATH-417: Number theory II.c - Selected topics

Summary

This year's topic is "Addictive combinatorics." We will introduce various methods from additive combinatorics, establish sum-product type theorems over finite fields and derive various applications (bounds for exponential sums, construction of expander graphs).

Lectures

Instructors

Official source

https://edu.epfl.ch/coursebook/en/number-theory-ii-c-selected-topics-MATH-417

Moodle Page

http://go.epfl.ch/MATH-417

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Summary

Lectures

Instructors

Official source

https://edu.epfl.ch/coursebook/en/number-theory-ii-c-selected-topics-MATH-417

Moodle Page

http://go.epfl.ch/MATH-417

About this result

Lectures in this course (11)

Exponential Maps: Properties and Applications in Lie Groups

Covers the properties of the exponential map in Lie groups and their algebras, including smoothness and the relationship between subgroups and algebras.

Linear Lie Groups: Definitions and Theorems

Discusses linear Lie groups, their definitions, properties, and the relationship between integral curves and vector fields.

Linear Maps and the Duality Principle in Mathematics

Covers the duality principle in linear algebra and its implications in mathematics.

Prime Gaps and Multiplicative Sieve Inequalities

Covers the Bombieri-Vinogradov theorem and its implications for prime gaps and multiplicative sieve inequalities.

Inverse Limits and Topologies

Explores inverse limits, profinite completions, and Hausdorff topologies in group theory and topology.

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