for this workshop
Discrete geometry and automorphic forms
American Institute of Mathematics, San Jose, California
Henry Cohn and Maryna Viazovska
This workshop, sponsored by AIM and the NSF, 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?
The workshop will differ from typical conferences in some regards. Participants will be invited to suggest open problems and questions before the workshop begins, and these will be posted on the workshop website. These include specific problems on which there is hope of making some progress during the workshop, as well as more ambitious problems which may influence the future activity of the field. Lectures at the workshop will be focused on familiarizing the participants with the background material leading up to specific problems, and the schedule will include discussion and parallel working sessions.
The deadline to apply for support to participate in this workshop has passed.
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