We had the very auspicious number of 88 total pairings this semester. Those who completed a final presentation or project are featured below. As always, we’d like to thank our mentors and the department staff.

This was also Ronan O’Gorman’s last semester organizing the DRP, and Alan Goldfarb’s first. Ronan, thank you for all that you’ve done; Alan, welcome to the team!

Mentee	Mentor	Project
Ben Aldaghi	Mitsuki Hanada	Symmetric Functions and the Symmetric Group
Nicholas Ballesteros	Ronan O’Gorman	An Introduction to Affine Schemes
Smokey Child	Spencer Taylor	An Introduction to Algebraic Topology and Differentiable Manifolds
Juan Claver	Yahya Bashandy	Topological $K$-Theory
Ren Colley	Ryan Martinez	Continuous Nonlinear Dynamical Systems
Theo Danial	Etienne Phillips	Monads
Tala De La Cruz	Sai Sanjeev Balakrishnan	Galois Theory Through Cyclotomic Symmetry
Arjun Garg	Etienne Phillips	An Introduction to Quasi-Categories
Omkar Guha	Jake Hofgard	SLE and Universality
Rayan Gummiid	Vilas Winstein	Proof by Brownian Motion
Jesse Hart	Benjamin Daniels	Smooth Manifolds and Lie Groups
Diana Hu	Ruslans Aleksejevs	Turán’s Theorem and Extremal Graph Theory
Carson Humphreys	Yvette Ren	Sacks’ Splitting Theorem through the Finite Injury Priority Method
Spencer Kim	Siming He	Optimal Transport
Elizabeth Lau	Danat Duisenbekov	Mixing Times and Applications
Alexander Lee and Zayan Boghani	Jenna Plute	The Spectral Theorems
Wangyuan (Peter) Li	Amy Dai	Numerical Methods for Stochastic Differential Equations
Austin Lin	Swapnil Garg	Profunctors and Double Categories
Yuhao Liu	Jacob Erlikhman	Grassmannian, Hilbert, and Quot Schemes as Moduli Spaces
Owen McGinty	Sai Sanjeev Balakrishnan	Abelian Extensions of Exponent $n$
Andrew Nguyen	Nilay Patel	Period Three Implies Chaos (on $\mathbb{R}$)
Vignesh Nydhruva	Akash Narayanan	Sheaf Cohomology & Mittag-Leffler
Lucas Park	Harper Wells	Continuum Hypothesis and Forcing in Set Theory
Lia Park	Eric Jankowski	Representation in Dihedral Groups
Milena Safaryan	Isabel Detherage	Spectral Independence
Laney Saye	Ning Tang	Geometrically Constraining Vacuum Spacetime
Justin Shaw	Ethan Ebbighausen	Fractal Geometry
Daniel Song	Etienne Phillips	Enriched Category Theory
Jorge Speck	Leonard Tomczak	Elliptic curves over $\mathbb{C}$, Lattices, and Sum of Squares Theorems
Sofia Torelli	Isabel Detherage	Mixing Times of Markov Chains
Andrew Wang	Benjamin Daniels	De Rham Cohomology of Smooth Manifolds
Jiaxiang Xu	Haoen Li	A Numerical Study of Random Trace Estimators for the Inverse Laplacian
Stephanie Yao	Alex Feiner	Tensoring Exact Sequence
Katherine Yuan	Leonard Tomczak	Sphere Packing and Lattice-Based Cryptography
Tina Zejda	Michael Kielstra	Möbius Automorphisms of the Unit Disk
Zhouling Zhang	Marco David	From Classical Curve Counting to Gromov-Witten Invariants