Projects

Fall 2018

  • Support vector machines and kernel methods
    • Text: Foundations of Machine Learning by Mohri, Rostamizadeh, and Talwalkar
    • Mentee: Dylan Hunt
    • Mentor: George Seelinger
  • All groups can be realized as a fundamental group
    • Text: Algebraic Topology, Hatcher
    • Mentee: Kyle Hoffmann
    • Mentor: John Harnois
  • Topological proof of the Nielsen-Schreier Theorem (a subgroup of a free group is free)
    • Text: Algebraic Topology, Hatcher
    • Mentee: Mia Shaker
    • Mentor: Chris Lloyd
  • Difference between algebraic bases and Schauder bases
    • Text: Real Analysis: Modern Techniques and Their Applications, Folland
    • Mentee: Yifei Yang
    • Mentor: Joseph Eisner
  • Wirtinger presentations of fundamental groups of knot complements
    • Text: Algebraic Topology, Hatcher
    • Mentee: Zach Baugher
    • Mentor: Rostislav Akhmechet
  • Theorem: Let G be a finitely generated group with two different finite generating sets S and S’. Then G with the word metric induced by S is quasi-isometric to G with the word metric induced by S’
    • Text: Office Hours with a Geometric Group Theorist, Clay and Margalit
    • Mentee: Sam Dulin
    • Mentor: Ian Runnels
  • Constructing hyperbolic structures on closed surfaces (of genus g)
    • Text: Low-dimensional geometry: from euclidean surfaces to hyperbolic knots, Bonahon
    • Mentee: Andrew Zazzera
    • Mentor: Jiajun Yan
  • Brownian Motion and its Applications
    • Text: Brownian Motion by Peter Morters and Yuval Peres
    • Mentee: Xinru Cheng
    • Mentor: Ethan Zell

Summer 2018

  • An Introduction to Computability Theory and ‘Universal Programs’
    • Text: Computability: An introduction to recursive function theory, N.J. Cutland
    • Mentee: Parker Lazear
    • Mentor: John Harnois
  • A Counterintuitive Subset of the Baer Space
    • Text: Notes On Set Theory, Yiannis N. Moschovakis
    • Mentee: Henry Carscadden
    • Mentor: John Harnois

A great place to see more DRP projects is at other DRP program pages.