Projects

Spring 2019

  • Gröbner bases and applications in characteristic p
    • Text: Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra, David A.Cox, Donal O’Shea, and John B. Little.
    • Mentee: Abrar Majidi Idrissi
    • Mentor: Huy Dang
  • Classification of the Simple Lie Algebras
    • Text: Introduction to Lie Algebras, Erdmann and Wildon
    • Mentee: Hisham M Assana
    • Mentor: Arun Kannan
  • The Geometry of Free Groups
    • Text: Geometric Group Theory: An Introduction, Clara Loeh
    • Mentee: Katherine Andrews
    • Mentor: Ian Runnels
  • Hamiltonian ODEs: Deterministic and probabilistic studies
    • Text: ODEs and Dynamical Systems, Gerald Teschl
    • Mentee: Yunlu Li
    • Mentor: Mouhamadou
  • The Yoneda Embedding and its Applications
    • Text: Categories for the Working Computer Scientist, Barr and Wells
    • Mentee: Joseph Snitzer
    • Mentor: Chris Chung
  • Real Analysis and Probability Theory
    • Text: Real Analysis, Folland
    • Mentee: Chris Pufko
    • Mentor: Ethan Zell
  • Representation Theory of Finite Groups
    • Text: Representations and Characters of Groups, James and Liebeck
    • Mentee: Jonah Newman
    • Mentor: Liron Speyer
  • Exploring Schottky Groups
    • Text: Indra’s Pearls: The Vision of Felix Klein, Mumford, Series, Wright
    • Mentee: Aaron Christian
    • Mentor: Jiajun Yan

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.