Arithmetic reflection groups and crystallographic packings
December 14 to December 18, 2020
American Institute of Mathematics,
San Jose, California
and Alice Mark
This workshop will be devoted to the complete
classification of maximal hyperbolic arithmetic reflection groups. About 15
years ago, the number of such groups was shown to be finite, leaving open the
possibility of fully determining all of them, in a way that makes them
accessible for other applications, e.g., to the study of crystallographic sphere
packings. Recent advances, both theoretical and algorithmic, make it plausible
that with sufficient collaborative effort by experts in diverse areas from
geometry/topology, dynamics, arithmetic groups, and number theory, we will be able
to complete this program.
The main topics of the workshop are:
- Restricting the search space by, on one hand combinatorial and geometric
methods, and on the other, spectral gap (Ramanujan) methods
- Computation methods in arithmetic groups
- Vinberg-type and related algorithms
Material from the workshop
A list of participants.
The workshop schedule.
A report on the workshop activities.