Sphere Packings, Lattices and Codes Spring 2021
 Lecturer
 Danylo Radchenko
 Coordinator
 Cynthia Bortolotto
 Time and place
 Wednesdays 12:0014:00 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 errorcorrecting codes, combinatorial and spherical designs, and modular forms.
Some of the topics include: the sphere packing problem; the kissing number problem; errorcorrecting 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: Errorcorrecting 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, SpringerVerlag 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 123 of Modular Forms" (Universitext, Springer, Berlin, 2008)
 Sphere Packings by C. Zong (Universitext, SpringerVerlag New York, 1999)