for this workshop

## Configuration spaces of graphs

at the

American Institute of Mathematics, San Jose, California

organized by

Gabriel C. Drummond-Cole and Ben Knudsen

This workshop, sponsored by AIM and the NSF, will be devoted to the topology of configuration spaces of graphs. First studied from the point of view of motion planning problems in robotics, these spaces have been the subject of increasing interest in recent years from perspectives as diverse as homotopy theory, commutative algebra, combinatorics, geometric group theory, and mathematical physics. We propose to channel these perspectives in a focused investigation into the (co)homology of these spaces.

This investigation will have three distinct but interrelated aspects, all informed by the same overarching question: how are invariants of a graph reflected in the (co)homology of its configuration spaces?

- Structure: development of algebraic formalisms; search for universal presentations; formality questions.
- Asymptotics: coefficients of growth polynomials and "stable" ranges; stability phenomena in the ordered case.
- Computation: the search for torsion; calculations for complete graphs and other examples; development of efficient computational tools.

This event will be run as an AIM-style workshop. 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.

For more information email *workshops@aimath.org*