Research
Groups, Geometry, and Dynamical Systems
Broadly my research focuses on analyzing discrete sets arising from geometry. My inspiration often comes from the study of translation surfaces. This Numberphile video is a great introduction to the types of problems I enjoy working on. I'm currently working with people in the field of nonlinear algebra to apply translation surfaces as a way of constructing algebraic curves with certain properties. This article gives an overview of nonlinear algebra. Finally, I have a budding interest in the interactions between dynamics and machine learning. If you don't know what machine learning is, see for example this nice AMS Notices article.
Crossing the transcendental divide: from Schotty groups to algebraic curves
S. Fairchild, Á.D. Ríos Ortiz
Arxiv, submitted
Mean value theorems for the S-arithmetic primitive Siegel transforms
S. Fairchild and J. Han
Arxiv, submitted
Pairs in discrete lattice orbits with applications to Veech surfaces
C. Burrin, S. Fairchild with an appendix by J. Chaika
ArXiv, accepted to the Journal of the European Mathematics Society
Average degree of the essential variety
P. Breiding, S. Fairchild, P. Santarsiero, E. Shehu
Counting pairs of saddle connections
J.S. Athreya, S. Fairchild, H. Masur
Crossing the transcendental divide: from translation surfaces to algebraic curves
T. Ö. Çelik, S. Fairchild, Y. Mandelshtam
Families of well approximable measures
Higher Moments for the Siegel--Veech transform over quotients by Hecke triangle groups
S. Fairchild
The abelian sandpile model on fractal graphs
S.Fairchild, I. Haim, R.G. Setra, R. Strichartz, T. Westura
From the Cornell 2014 REU Arxiv
Rigid Tilings of quadrants by L-shaped n-ominoes and notched rectangles
