The Topology of Random Spaces

Mentor: Sander Kupers, Kyler Siegel

Topology studies the shape of spaces. Many interesting spaces are built by gluing together smaller pieces in a particular way. We’ll be looking at what happens when you fix the pieces, but vary the gluing. Of particular interest are the values of certain invariants coming from algebraic topology, which we’ll learn how to compute. Our goal is to eventually look at spaces with relevance in theoretical physics, for example moduli spaces of curves and dynamical triangulations.