#
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:

- 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?
- 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?
- 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

Papers arising from the workshop:

Packable hyperbolic surfaces with symmetries

by Maria Dostert, Alexander Kolpakov

Kissing number in non-Euclidean spaces

by Maria Dostert, Alexander Kolpakov

Kissing number in spherical space

by Maria Dostert, Alexander Kolpakov

Kissing number in hyperbolic space

by Maria Dostert, Alexander Kolpakov

Optimal measures for p-frame energies on spheres

by Dmitriy Bilyk, Alexey Glazyrin, Ryan Matzke, Josiah Park, Oleksandr Vlasiuk

Energy on spheres and discreteness of minimizing measures

by Dmitriy Bilyk, Alexey Glazyrin, Ryan Matzke, Josiah Park, Oleksandr Vlasiuk