Sphere Packings, Lattices and Codes Spring 2021
- Lecturer
- Danylo Radchenko
- Coordinator
- Cynthia Bortolotto
- Time and place
- Wednesdays 12:00-14:00 in zoom (Meeting ID: 971 3514 3351)
Content
In this seminar we will 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.
Some of the topics include: the 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.
Here is a list of topics together with detailed references.
Talks
| Speaker/Topic |
Date |
Notes |
|
Introduction and distribution of topics
|
February 24 |
|
|
Danylo: Overview and motivation
|
March 3 |
Slides
|
|
Léo: The sphere packing problem
|
March 10 |
Notes
|
|
Monika: Error-correcting codes
|
March 17 |
Notes
|
|
Josiah: Shannon capacity of graphs
|
March 24 |
Slides
|
|
Nils: Steiner systems and finite projective planes
|
March 31 |
Notes
|
|
Emanuel: The binary Golay code and the Leech lattice
|
April 14 |
Slides
|
|
Manuel: Spherical designs and spherical codes
|
April 21 |
Notes
|
|
Benjamin: The kissing number problem
|
April 28 |
Notes
|
|
Raphaël: Linear programming bounds for sphere packings I
|
May 5 |
Notes
|
|
Chantal: Modular forms for the group \( \operatorname{PSL}_2(\mathbb{Z}) \).
|
May 12 |
Notes
|
|
Nikomedes: Theta functions of lattices
|
May 19 |
Notes
|
|
Max: Linear programming bounds for sphere packings II
|
May 26 |
Notes
|
|
Baptiste: The sphere packing problem in 8 dimensions
|
June 2 |
Notes
|
Literature
- Sphere Packings, Lattices and Groups by J.H. Conway and N.J. Sloane (3rd edition, Springer-Verlag New York, 2017)
- Lattices and Codes: A Course Partially Based on Lectures by Friedrich Hirzebruch by W. Ebeling (3rd edition, Springer Spektrum, Wiesbaden, 2013)
- Elliptic modular forms and their applications by D. Zagier in "The 1-2-3 of Modular Forms" (Universitext, Springer, Berlin, 2008)
- Sphere Packings by C. Zong (Universitext, Springer-Verlag New York, 1999)