Connor Neely

Thesis Advisor: Dr. Dagan Karp (HMC - Department of Mathematics)

Second Reader: Dr. Dusty Ross (SFSU - Department of Mathematics)

Contact: cneely@hmc.edu

A Friendly Introduction to Gromov-Witten Theory

Enumerative geometry is an ancient field of mathematics rooted in solving simple counting puzzles, like "given three points in the plane, how many circles pass through all of them?" Questions like these are easy to state, but for centuries many of the simplest problems proved surprisingly difficult to solve. In recent decades, however, ideas from the seemingly far-flung world of theoretical physics have offered new ways of understanding a broad class of enumerative problems involving curves embedded in complex manifolds. This thesis offers an accessible introduction to this unique interaction between modern geometry and physics, now called Gromov-Witten theory, outlining the field's mathematical foundations and how they become manifest in supersymmetric string theory.