A seminar with Jorge Basilio, City University of New York, Sarah Lawrence College.
What does it mean for one space, which others might call a universe, to be "close to" another space? To answer this question, we will introduce the far-reaching mathematical ideas of convergence and manifold. Convergence aims to make precise the notion of "gets close to" and this applies to many things: numbers, functions, and even spaces. Meanwhile, manifolds are vast generalizations of physical space which includes higher-dimensional spheres, tori, and, of course, our universe. Finally, Basilio will introduce a new technique he developed for creating spaces called "sewing." Roughly speaking, sewn spaces are built using increasingly many tiny tunnels (or stargates) within the original space bending in such a way that is consistent with solutions to Einstein's Equations (of General Relativity) and, therefore, could potentially correspond to a physical configuration of a universe. Audience participation is encouraged and you'll have an opportunity to actively create a model of sewn spaces, gaining insight into the chosen name for these spaces. The majority of this talk should be accessible to anyone with an open mind, though a study of calculus would be helpful for some of the examples.