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MATH-603: Subconvexity, Periods and Equidistribution

Summary

This course is a modern exposition of "Duke's Theorems" which describe the distribution of representations of large integers by a fixed ternary quadratic form. It will be the occasion to introduce the students to the adelic language, the theory of automorphic forms and their associated L-functions

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/subconvexity-periods-and-equidistribution-MATH-603

Moodle Page

http://go.epfl.ch/MATH-603

About this result

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Summary

Lectures

Instructor

Philippe Michel

Official source

https://edu.epfl.ch/coursebook/en/subconvexity-periods-and-equidistribution-MATH-603

Moodle Page

http://go.epfl.ch/MATH-603

About this result

Ontological neighbourhood

Mathematics

Algebra: Abstract algebra

Number theory: Topics in number theory

Lectures in this course (35)

Fermat's Theorem: Sums of Squares

Explores Fermat's Theorem, factorization of integers, properties of Z[i], and Hurwitz quaternions.

Proof of Lagrange Theorem

Covers the proof of Lagrange Theorem and explores quaternions, prime numbers, and equations.

Quadratic Forms and Symmetries

Explores quadratic forms, symmetries, representations, and orthogonal sums in mathematics.

Quadratic Spaces and Quaternion Algebra

Explores quadratic spaces, norms, and quaternion algebra over fields.

Integral Representations: Quadratic Lattices and Hasse Principle

Explores integral representations, quadratic lattices, and the Hasse Principle.

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