Refreshments at 3:15 pm, Davis 2nd floor
Mathematics and physics have grown up as influential siblings, pushing each other to be the best that they could be. Pondering the motions of the heavens led Newton to develop the Calculus; Riemann’s approach to geometry provided the correct mathematical framework for Einstein’s Theory of General Relativity.
In this talk we will describe how a principle of symmetry appearing in string theory, known as mirror symmetry, has found application in algebra and combinatorics. We will briefly discuss how mirror symmetry was used by theoretical physicists in the 1980s to settle problems of geometry dating back to the 1800s, a result that stunned the mathematical community. We will then explain how polynomials appearing in mathematical models of string theory can be used to count combinatorial objects called standard Young tableaux. Finally, we will describe how a process of mutation on polynomials that appears in these models leads to algebraic structures related to the pentagon of pentagons below.
This talk will assume minimal mathematical background and will be accessible to a broad audience.