Configuration spaces of graphs

February 3 to February 7, 2020

at the

American Institute of Mathematics, San Jose, California

organized by

Gabriel C. Drummond-Cole and Ben Knudsen

Original Announcement

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 configuration spaces?

  1. Structure: development of algebraic formalisms; search for universal presentations; formality questions.
  2. Asymptotics: coefficients of growth polynomials and "stable" ranges; stability phenomena in the ordered case.
  3. 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.

Workshop Videos