Geometry & Topology Seminar: "Shapes of Balls in Step 2 Nilpotent Groups"
Hannah Alpert, Ohio State
Abstract: Each oriented loop in the plane encloses a signed area. Given an oriented loop in 3-space, we can project it to the three coordinate hyperplanes and record the three signed areas. In the reverse direction, given the three signed areas, what is the L^1-shortest loop in 3-space that gives those areas? Questions like this one are the continuous analogue of questions about balls under word length in generalizations of the Heisenberg group. The questions turn out to be disappointingly complicated. Joint work with Moon Duchin.
Host: Xiang Tang