### Hidden Convexity, Rotation Matrices, and Algebraic Topology

- Series
- Algebra Student Seminar
- Time
- Thursday, January 18, 2024 - 11:00 for 1 hour (actually 50 minutes)
- Location
- Clough 262
- Speaker
- Kevin Shu – Georgia Tech – kshu8@gatech.edu

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.