Topic: stability

Natural behavior reveals the way that gaze serves the needs of the current task, and the complex cognitive control mechanisms that are involved. It has become increasingly clear that even the simplest actions involve complex decision processes that depend on an interaction of visual information, knowledge of the current environment, and the intrinsic costs and benefits of actions choices. I will explore these ideas in the context of walking in natural terrain, where we are able to recover the 3D structure of the visual environment. We show that subjects choose flexible paths that depend on the

Alexander Lubotzky examines whether infinite groups can be approximated by asymptotic homomorphisms into finite symmetric or unitary groups. He describes finitely presented groups that admit no unitary approximation in the Frobenius norm and several other norms. The argument links vanishing of higher cohomology to stability, then uses Garland’s method and high-dimensional expanders arising from Bruhat–Tits buildings. Certain non-residually finite central extensions of lattices in p-adic Lie groups are stable, preventing such approximations. These extensions come from a p-adic analogue of a res