Fiches de cours

The Fourier transform in algorithms and optimization

MATH-696

Lecturer(s) :

Eisenbrand Friedrich

Language:

English

Remarque

Next time: From 1.10.2018 to 9.11.2018

Summary

This course deals with applications of Fourier analysis in algorithms and optimization. We will discuss the following themes: finite setting, Fourier transform, convolution, KLL theorem. classical Fourier transform with proof of the strongest transference bounds for lattice free convex bodies.

Content

This course is on applications of Fourier analysis in algorithms and optimization. We start with the finite setting, the Fourier transform, and applications like Linearity Testing and Roth¿s theorem. Then we discuss convolution and the KLL theorem. We continue with the classical Fourier transform and prove the, up to now, strongest transference bounds for lattice free convex bodies. The course ends with the discussion of very new contributions, like the Hoberg-Rothvoss theorem on the discrepancy of random set systems.

Note

This course will be in the form of a seminar. Each participant is expected to give a talk, and to propose exercises. Furthermore, each participant is expected to solve and present the exercises that are presented by the speakers.

Learning Prerequisites

Required courses

Basic knowledge in linear algebra and optimization

In the programs

  • Mathematics (edoc), 2018-2019
    • Semester
    • Exam form
      Oral
    • Credits
      2
    • Subject examined
      The Fourier transform in algorithms and optimization
    • Number of places
      10
    • Lecture
      12 Hour(s)
    • Practical work
      12 Hour(s)

Reference week

Lecture
Exercise, TP
Project, other

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  • Lecture in French
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