Daniel Alvey

Assistant Professor, Mathematics

Dan Alvey recieved his Ph.D. from Wesleyan University in 2021. He studies metric number theory and dynamical systems as well as mathematical questions regarding chess. His Ph.D. dissertation was on the extremal approximation of affine subspaces of Euclidean space by rationals. He is a veteran of the United States Army, having served for five years as an armor officer, including a tour in Afghanistan. He left service as a Captain.

Education

  • PhD, Wesleyan University
  • BS, The United States Military Academy

Courses Taught

  • MATH 285 Calculus III
  • MATH 372 Linear Algebra I
  • Research

    My primary research interests are in the areas of metric number theory and homogeneous dynamics. Metric number theory is concerned with describing the size of sets of numbers which satisfy certain number theoretic properties. Often, these properties concern how well the numbers can be approximated either by rational numbers, or some other dense subset of the real numbers. These questions have a surprising but beautiful connection with homogeneous dynamics. The result being that studying the ergodic properties of transformations on homogeneous spaces and shrinking target problems in those settings can answer questions about the size of sets which satisfy approximation restrictions.

     

    I additionally have been exploring answering questions about chess through a mathematical lens. For example, questions about how the knights move on the chess board, and if a knight can be contained in some way, can be answered by examining properties of the resulting knight's graph, and subgraphs thereof.