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401-3520-21L 4 Credits BSC , MSC D-MATH

Sphere Packings, Lattices and Codes

Lecturers & Examiners: Dr. Danylo Radchenko
Number of participants limited to 12.
VVZ CR n/a

Last Updated: 2026-02-05 15:54:09

Abstract

Seminar on Sphere Packings, Lattices and Codes

Objective

To learn about the sphere packing problem and its connection to various other topics such as error-correcting codes, combinatorial and spherical designs, and modular forms.

Content

Some of the tentative topics include: sphere packing problem; the kissing number problem; error-correcting codes; Shannon capacity; finite projective planes; binary Golay code; spherical designs; theta functions of lattices; linear programming bounds for spherical codes and sphere packings.

Resources

Literature

J.H. Conway, N.J. Sloane, Sphere Packings, Lattices and Groups, 3rd edition, Springer-Verlag New York, 2017. W. Ebeling, Lattices and Codes: A Course Partially Based on Lectures by Friedrich Hirzebruch, third edition, Springer Spektrum, Wiesbaden, 2013. D. Zagier, Elliptic modular forms and their applications, in "The 1-2-3 of Modular Forms" (K. Ranestad, ed.), Universitext, Springer, Berlin, 2008. C. Zong, Sphere Packings, Universitext, Springer-Verlag New York, 1999.

Learning Materials (Links)

General Information

Language
English
Levels
BSC , MSC

Examination

Type
ungraded semester performance

Registration & Places

Limited places (Special selection)
Signup Start
04.01.2021
Signup End
19.02.2021
Priority: Registration for the course unit is only possible for the primary target group

Course Components

Type Title Time & Place Hours
seminar Sphere Packings, Lattices and Codes
  • Wed 12:15-14:00 (HG G 26.1)
2 h weekly

Offered In

  • Mathematics Bachelor
    • Seminars (This semester, many seminars have a waiting list with special selection procedure. If no other criteria apply, a definitive registration will be granted first of all to students who haven't got another seminar registration. Here is the best procedure for dealing with two waiting lists: first choose your preferred seminar and a few minutes later choose an alternative seminar. IMPORTANT: Do not waitlist yourself for more than two seminars!)
  • Mathematics Master
    • Seminars and Semester Papers
      • Seminars (This semester, many seminars have a waiting list with special selection procedure. If no other criteria apply, a definitive registration will be granted first of all to students who haven't got another seminar registration. Here is the best procedure for dealing with two waiting lists: first choose your preferred seminar and a few minutes later choose an alternative seminar. IMPORTANT: Do not waitlist yourself for more than two seminars!)