for this workshop
Polyhedral geometry and partition theory
American Institute of Mathematics, San Jose, California
Federico Ardila, Benjamin Braun, Peter Paule, and Carla D. Savage
This workshop, sponsored by AIM and the NSF, will be devoted to the study of problems at the interface of polyhedral geometry and partition theory. Recent results have demonstrated that polyhedral geometry is a powerful tool connecting problems in lattice point enumeration, permutation statistics, and partition theory. Further intriguing relationships make it clear that there are deeper connections, both theoretical and computational, to be uncovered.
The main topics for our workshop include:
- the geometric and algebraic structure of lecture hall partitions; their
relationship to permutation and Coxeter groups, (rational) Catalan
combinatorics, and hyperplane arrangements.
- the geometry, combinatorics, and computation of vector partition functions;
the interpretation and application of recent structural results; the discovery
of new formulas.
- unimodality/real rootedness questions in Ehrhart theory, partition theory, and Coxeter groups.
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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