Discrete geometry and automorphic forms

September 24 to September 28, 2018

at the

American Institute of Mathematics, San Jose, California

organized by

Henry Cohn and Maryna Viazovska

Original Announcement

This workshop will be devoted to exploring the consequences of Viazovska's recent solution of the sphere packing problem in eight dimensions, in which she developed new connections with automorphic forms.

The main topics of the workshop will include the following questions, as well as others suggested by recent developments:

  1. What is the significance of these special functions within the field of automorphic forms? Can they be placed in a broader context? Do they have number-theoretic applications beyond determining the Hermite constant?
  2. How can these techniques be applied more broadly in discrete geometry? Are there other exceptional structures that can be analyzed similarly? What about connections with mathematical physics?
  3. Linear programming bounds can be interpreted in physics terms as constraints on the pair correlation function of a particle system. Can Viazovska's techniques be extended to higher-order correlation functions?

Material from the workshop

A list of participants.

The workshop schedule.

A report on the workshop activities.

A list of open problems.

View this workshops videos