Abstract: Quantizing the gravitational field has taught us that physical laws are themselves quantized: the fundamental parameters in Nature are integers. In string theory these integers record the topology of six additional spatial dimensions. A task for mathematicians and physicists is to determine what values these numbers can take, and how experimental observables can be expressed in terms of them. Through an interplay of string theory and computational algebraic geometry, we have computed the fundamental integers in a vast class of geometries. We will explain how we have used this knowledge to construct cosmological solutions of string theory in which the dark energy density has an allowably small magnitude. We will also highlight other mathematical questions at the frontier of string theory.

Immediately after the colloquium we will hold an informal, open discussion on mathematical problems arising from theoretical physics. This discussion will serve as a first organizational meeting to gauge interest in developing connections and collaborations between the two departments. All are welcome.