- 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

- 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.