Configuration spaces of graphs
February 3 to February 7, 2020
American Institute of Mathematics,
San Jose, California
Gabriel C. Drummond-Cole and Ben Knudsen
This workshop 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
- 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.
Material from the workshop
A list of participants.
The workshop schedule.
A report on the workshop activities.
A list of open problems.