Sabrina Enriquez

Major and Classification

Mathematics (Major) & Human Rights (Minor)

Faculty Mentor

Dr. Francis Bonahon


Dornsife: Mathematics

Research Gateway Project

“Investigating the Lengths of Simple Closed Curves on the Once-Punctured Torus”

Project Abstract

I am studying the behavior of the lengths of simple closed geodesics on the surface of a punctured torus endowed with hyperbolic metric. In particular, my goal is to identify the maximum and minimum values taken by the Mirzakhani function, over the space of all hyperbolic metrics on the punctured torus. The Mirzakhani function, introduced by Maryam Mirzakhani, controls the growth rate of lengths of simple closed curves on hyperbolic surfaces. Through a heuristic method, I have found that the minimum of the Mirzakhani function seems to be attained at the (unique) hyperbolic metric that has symmetry of order 3. The function is also unbounded.