Jonas Sjöstrand: The lit-only sigma game

Abstract: The lit-only sigma game is played on an undirected graph, each vertex
of which has a lamp that is either on or off. A move consists of choosing any lit vertex and toggle the state of all adjacent vertices. Usually, the goal is to reach a position with as few lit vertices as possible or to reach a specific position. The associated reachability problem (which positions can be reached from a given
position?) can be expressed in terms of orbits of a vector space under dual symplectic transvections, and a beautiful quadratic form enters
the scene! I will introduce you to the intriguing mathematics of this problem and its solution, which lie in the intersection between graph theory and linear algebra.