Georgia Institute of Technology College of Sciences

This talk will describe connections between algebraic geometry, convex geometry and algebraic topology. We will be discussing linear projections of the special orthogonal  group and when they are convex (in the sense that every pair of points in the image of the projection are connected by a line segment contained in the projection). In particular, I'll give a proof of the fact that the image of SO(n) under any linear map to R^2 is convex using some elementary homotopy theory. These kinds of question are not only geometrically interesting but are also useful in solving some optimization problems involved in space travel.