With 76 pairings, this was another banner semester for the DRP. We are, as always, grateful for the effort of the mentors and department staff who make all this possible. We couldn’t do it without them.

Now for one of my favorite parts of the program: sharing the completed projects! The pairs who submitted a final paper or do a presentation at our end-of-semester conference are featured below. We hope you find their work entertaining and educational — and that it might serve as a resource if you’re considering starting a DRP project yourself.

Mentee	Mentor	Project
Ariana Abel	Akash Narayanan	Connectedness vs Path Connectedness
Nicholas Ballesteros	Alexander Burka	Stone Duality for Boolean Algebras and Cylindric Algebras
Edward Beckon	Leonard Tomczak	Dirichlet’s Theorem on Arithmetic Progressions
Ryan Chan	Zoe McDonald	The Itô Integral
Juan Claver	Yahya Bashandy	Local Kronecker-Weber
Antonio Cortijo	Liza Jacoby	Descriptive Set Theory
Amelia Craciun	Marco David	Enumerative Geometry
Omkar Guha	Jake Hofgard	Combinatorial Upper Bounds for Self-Avoiding Walks on the Integer Lattice
Michelle Holland	Alexander Burka	Lindström’s Theorem
Yang Hu	CJ Dowd	$p$-Adic Hodge Theory
Diana Hu	Ruslans Aleksejevs	Arnold’s Topological Proof of Abel’s Impossibility Theorem
Michael Lan	Katalin Berlow	Nielsen–Schreier theorem
Dylan Lu	John Nolan	Bézout’s Theorem in Algebraic Geometry
Runze Lu	Lewis Pan	Markov Chain Monte Carlo
Shijie Lyu	Ely Sandine	Navier-Stokes Equations for 2-Dimensional Incompressible Slightly Viscous Flow Along Curved Wall
Benedikt Vilji Magnússon	Lizzie Pratt	A Geometric Introduction to Representation Theory
Nathan Mann	Smita Rajan	Algebraic Geometry
Dron Mongia	Thomas Browning	Real Analysis with Filters
Connor Murray	Jerry Yang	De Rham Cohomology
Andrew Nguyen	Nilay Patel	Why Are All Meteorologists Eventually Wrong?
Vignesh Nydhruva	Akash Narayanan	Algebraic Number Theory
Partha Krishna	Swapnil Garg	Verma Modules and the Harish-Chandra Isomorphism
Yifei Qi	Joao Basso	On Matrix Analysis Methods in Quantum Entropy
Xiang Shi	Vinh-Kha Le	The Application of Machine Learning and Deep Reinforcement Learning on Quantum Optimization
Ailsa Sun	Etienne Phillips	Yoneda’s Lemma
Yuxin Tan	Sai Sanjeev Balakrishnan	Primes of the form $x^2+ny^2$
Sofia Torelli	Izzy Detherage	Cheeger’s Inequality
Ayisha Umar	August Noë	A Nonstandard Proof of the Bolzano-Weierstrass Theorem
Ethan Eugene Wynner	Will Fisher	Some Notions in Étale Cohomology
Stephanie Yao	Alex Feiner	Elliptic Curves and Finding Torsion Points
Brian Zhou and Woong Choi	Reed Jacobs	Fundamental Groups