Monday, February 13, 2023 - 3:30pm
George Mason University
When two submanifolds meet non-transversely their intersection may fail to be a manifold. However, such bad intersections can be dealt with as smooth objects in the setting of derived geometry. Derived manifolds are objects constructed by iteratively taking fibered products, starting with smooth manifolds. We will show how such a theory can be derived from basic principles and explain its connection to derived algebraic geometry. Time permitting, we will discuss applications to quantum field theory.