Sphere Packings, Lattices and Codes Spring 2021

Danylo Radchenko
Cynthia Bortolotto
Time and place
Wednesdays 12:00-14:00 in zoom (Meeting ID: 971 3514 3351)


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.


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