Travis Willse: The remarkable geometry of generic 2-plane distributions on 5-manifolds

Current Topics Seminar

Speaker	Travis Willse
Title	The remarkable geometry of generic 2-plane distributions on 5-manifolds
Date	March 3 4:00pm PDL C-36

The possible configurations of two given surfaces tangent to one another can be parametrized by a $5$-dimensional manifold $M$; the physical no-slip, no-spin conditions restrict the ways these surfaces can roll along each other, defining a $2$-plane field (distribution) $D$ on $M$. The resulting geometry of generic 2-plane distributions on $5$-manifolds, which dates at least to Cartan's investigation of them in 1910, enjoys numerous and surprising connections to diverse ideas in other areas, including the algebra of split octonions, PDEs of the form $z' = F(x, y, y', y'', z)$, conformal geometry, nearly K\"{a}hler geometry, and the exceptional Lie group $G_2$. In this talk I will survey the geometry of these distributions and sketch some of these connections; familiarity with manifolds will be helpful but not necessary for understanding this talk.