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MATH-521: Advanced analytic number theory

Summary

This year we will present some further applications of the theory of modular forms (compared to MATH-511). These may include the following:

Equidistribution of points on spheres
Construction of Ramanujan Graph
Invariant means on the spheres
Complex multiplication for elliptic curves

Lectures

Instructor

Philippe Michel

Ph. Michel's main research interest lie in the field of analytic number theory and range over a variety of techniques and methods which include: arithmetic geometry, exponential sums, sieve methods, automorphic forms and allied representations, L-functions and more recently ergodic theory. Ph. Michel is a former student of ENS Cachan and obtained his PhD in Universté Paris XI in 1995 under the guidance of E. Fouvry. From 1995 to 1998 he was maître de conférence at Universté Paris XI and full professor at Université Montpellier II until 2008 then when he joined EPFL. Ph. Michel was awarded the Peccot-Vimont prize, has been member of the Institut Universitaire de France and wa invited speaker at the 2006 International Congress of Mathematician.

Official source

https://edu.epfl.ch/coursebook/en/advanced-analytic-number-theory-MATH-521

Moodle Page

http://go.epfl.ch/MATH-521

About this result

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Summary

This year we will present some further applications of the theory of modular forms (compared to MATH-511). These may include the following:

Equidistribution of points on spheres
Construction of Ramanujan Graph
Invariant means on the spheres
Complex multiplication for elliptic curves

Lectures

Instructor

Philippe Michel

Official source

https://edu.epfl.ch/coursebook/en/advanced-analytic-number-theory-MATH-521

Moodle Page

http://go.epfl.ch/MATH-521

About this result

Ontological neighbourhood

Mathematics

Number theory: Topics in number theory

Lectures in this course (2)

Prime Gaps and Multiplicative Sieve Inequalities Log in to Mediaspace to watch this video

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

Linear Maps and the Duality Principle in Mathematics Log in to Mediaspace to watch this video

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

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