Below, you will find past DRP projects listed by academic year. Links to the final presentations are provided where available. Prospective students are encouraged to browse recent projects for inspiration.
For projects prior to Spring 2022, see the old archive. The Rutgers DRP has been running since Summer 2005.
🌞 denotes Student Presentation Award.
🌝 denotes Honorable Mention.
A Brief Introduction to Differential Geometry
Mentee Ahmadh Hassan
Mentor António Gouveia
Abstract
An overview of the basic notion of manifolds to the geometric tools—Riemannian metrics, geodesics, and curvature tensors—that let us measure shape and curvature.
Algebraic Number Theory and the Sum of Squares
Mentee Sophia Pan
Mentor Nicholas Backes
Abstract
This presentation discusses the ring of Gaussian integers as an introduction to Algebraic Number Theory. We explore some of its properties and provide a proof of Fermat’s theorem on sums of two squares.
An Introduction to Elasticity Theory
Mentee Mahadevan Seetharaman
Mentor Samuel Wallace
Abstract
Elasticity Theory is the branch of continuum mechanics dealing with the deformation of elastic bodies. It applies many branches of mathematics, including functional analysis, PDE theory, differential geometry, and more. In this talk, we will give the basic definitions of concepts in elasticity and see how they arise from physical considerations. We will also look at a problem in elasticity to illustrate these concepts.
An Introduction to the p-adic Numbers and Hensel’s Lemma
Mentee Hamshika Rajkumar
Mentor Omar Aceval Garcia
Abstract
What if 5 were closer to 130 than to 6? By redefining what it means for numbers to be “close”, the p-adic numbers create a number system with surprising and counterintuitive properties. In this talk, I will introduce the p-adic norm and explain how it gives rise to the p-adic numbers. We will build some intuition for their topology in relation to Q and prove Hensel’s Lemma.
Mentee Jessie Wang
Mentor Bojue Wang
Abstract
Using Burnside’s Lemma to count distinct ways to color the four vertices of a square using two colors. Combining group theory to introduce the formula and illustrate the counting process step by step. Then induce the general way to solve those symmetry-based coloring problems.
Brownian Bridges in Stochastic Calculus
Mentee Artem Ivaniuk
Mentor Minhao Bai
Abstract
A presentation covering the foundations of Stochastic Calculus learned during the semester, culminating in the discussion of Brownian Bridges—Gaussian Processes or Brownian motions that are conditioned on some future value of the process, starting from an initial value.
Calculating Effective Volume for a Gaunt–Fisher Configuration
Mentee Derek Chan
Mentor Qidong He
Abstract
This topic explores how to rigorously define and calculate the effective volume associated with a given Gaunt–Fisher configuration—a defect in a close packing ground state.
Categories and the Yoneda Lemma
Mentee Winston Li
Mentor Bojue Wang
Abstract
The Yoneda Lemma is an important result in category theory. I will introduce some definitions and examples of categories. Then, I will go over the lemma, its proof, and a short application.
Mentee Alon Danai
Mentor Alexander Day
Abstract
Category theory is a nice way of abstracting various concepts in math, and it gives us a general language to describe many things. We will go over basic category theory as well as discuss limits and adjoints with examples.
Mentee Nuray Kutlu
Mentor Dennis Hou
Abstract
This presentation will introduce and provide some nice examples of Cayley graphs.
Mentee Yilan Liu
Mentor Joy Hamlin
Abstract
In this presentation, I will introduce the basic concepts of Topology and the key terms related to one theorem related to the compactness of Topology. The theorem is “The image of a compact space under a continuous map is compact.”
Complex Differentiation, Integration, and Cauchy’s Theorem
Mentee Alankar Sovani
Mentor Ryan Mc Gowan
Abstract
The theory of functions of a complex variable has been a substantial area of study for some of the greatest mathematicians since the 1700’s up to the modern day. In this talk, we will see how the concepts of differentiation and integration change when working with complex numbers, leading us to the ever-important Cauchy’s Integral Theorem.
Conformal Maps and the Riemann Mapping Theorem
Mentee Jason Liu
Mentor Ryan Mc Gowan
Abstract
In this presentation, I give an introduction to conformal maps, some examples, and present the Riemann Mapping Theorem (RMT), which gives the existence of conformal maps under very general conditions. If time permits, I also discuss the Schwarz–Christoffel theorem, which gives explicit maps from the upper half plane onto polygons, as well as the Uniformization theorem, a generalization of the RMT.
Continuum Mechanics: Formulating the Harmonic Oscillator
Mentee Aditya Raman
Mentor Erik Bahnson
Abstract
Going over spectral theorem and introducing notions and properties of infinite dimensional Hilbert spaces. Then understanding spectral theorem and then applying it to the position operator. Then demonstrating self adjointness and demonstrating the position operators failure of self adjointness alongside the Riesz Representation Theorem and introducing notions of operator domains to obtain self-adjoint extensions. Finally, using all of the above to formulate the harmonic oscillator.
De Finetti’s Theorem: Exchangeability and Its Consequences
Mentee Luke Wernyj
Mentor Forrest Thurman
Abstract
This talk introduces the idea of exchangeability and presents De Finetti’s Theorem, which characterizes infinite sequences of exchangeable random variables as mixtures of i.i.d. variables. We will see how this result bridges symmetry to probability theory and forms a foundation for Bayesian inference.
Dive into the Cantor Space: A Visualization Using Trees
Mentee Jason Billings
Mentor Danae Rupp
Abstract
In this presentation we will be building an intuitive picture and model of how the Cantor space is built. Along the way, we’ll see how trees offer a natural way to describe the topology of the space, connect finite approximations to infinite objects, and visualize key properties like compactness.
Exploring Applications of Linear Optimization for the Maximum Flow Problem
Mentee Vikram Kirhsnaswamy
Mentor Anupam Nayak
Abstract
This presentation will explore linear optimization, its applications, and its uses in solving the maximum flow problem. Additionally, this presentation will go over the Ford–Fulkerson approach to solving the maximum flow problem.
Exploring Thresholds for Properties of Random Graphs
Mentee Jeffrey Xu
Mentor Milan Haiman
Abstract
In this presentation, we will introduce the concept of random graphs and threshold functions, before looking at some specific graph properties, such as connectivity or the existence of specific subgraphs.
Mentee Akhil Vasagiri
Mentor Ben-Zion Weltsch
Abstract
Consider the set of all infinite sequences of natural numbers. Intuitively, it seems there should be no “empty space”; between any two sequences there should always be a third that lies in between. However, when we impose a certain ordering and utilize uncountable numbers, unexpected gaps begin to appear. In this presentation, we will explore these gaps and their relation to the Continuum Hypothesis.
Mentee Nick Belov
Mentor Natasha Ter-Saakov
Abstract
I’ll start with a brief overview of algebra in the ring of formal power series. Then I’ll get into exponential families with cards, decks and hands and eventually build up to the exponential formula!
Group Extensions and Ext
Mentee Nadya Belova
Mentor Timothy Bates
Abstract
We will motivate and introduce basic notions in homological algebra by discussing their relationship to the problem of group extensions, and ultimately to the problem of classifying finite groups.
Kähler Geometry
Mentee Maxwell Goldberg
Mentor Riley Guyett
Abstract
I will be introducing the basics of Riemannian geometry and using that to introduce Kähler geometry.
Non-Sliding Hard-Core Lattice Particle Models—Proving Crystallization
Mentee Harry Haedrich
Mentor Qidong He
Abstract
I will introduce some basic concepts from the paper “High-Fugacity Expansion and Crystallization in Non-sliding Hard-Core Lattice Particle Models Without a Tiling Constraint” in an informal matter, go over the main result of the paper and what it says about particle systems that satisfy its assumptions.
High Girth and Chromatic Number
Mentee Frederick Chang
Mentor Caleb Fong
Abstract
The girth of a graph is the length of its shortest cycle, and its chromatic number is the smallest number of colors required to properly color its vertices. For every positive integer k, l, is there a graph with girth greater than l and chromatic number greater than k? It turns out there is!
Insurance Company Simulation Using ML
Mentee Tanesha More
Mentor Minhao Bai
Abstract
I am working on applying what I learned in my machine learning course and my actuarial courses to try and simulate how a basic insurance company must estimate losses incurred from a person, then trying to price the insurance premium that the person will need to pay.
Mentee Shreya Ghosh
Mentor Adam Earnst
Abstract
In this talk I will discuss basic topics of measure theory, the connection between measure theory and ergodicity, and the Ergodic Theorem.
Pricing a Perpetual American Put Option
Mentee Arnav Kondagunta
Mentor Daniela Elizondo
Abstract
This presentation will cover the binomial model for asset pricing in discrete time. We will introduce martingales and stopping times, then derive the price of a perpetual American put option.
Mentee Akash Dubey
Mentor Hong Chen
Abstract
This presentation explores the q-Binomial Theorem, highlighting its combinatorial and algebraic meanings. We introduce q-analogues, define q-binomial coefficients, and explain their role in weighted counting and generating functions.
Mentee Taha Rana
Mentor Yiyang Liu
Abstract
A discussion of regular surfaces in R³ and the three major criteria of regular surfaces.
Mentee Anusha Iyer
Mentor Brittany Gelb
Abstract
How can we use the “shapes” found in datasets to draw conclusions about them? This project explores the fundamental concepts behind topological data analysis while applying persistent homology techniques using Ripser to demonstrate these concepts visually.
The Mycielski Construction
Mentee Arya Swaminathan
Mentor Milan Haiman
Abstract
The Mycielski construction provides a method to construct a graph with a certain clique number and an infinitely high chromatic number.
Mentee Michael Fiore
Mentor Ben-Zion Weltsch
Abstract
This presentation aims to understand the Wold Decomposition Theorem by building up the required prerequisite knowledge and understanding the implications of the theorem and how it is influential in modeling.
Understanding the Wold Decomposition Theorem
Mentee Pranav Tikkawar
Mentor Forrest Thurman
Abstract
This presentation aims to understand the Wold Decomposition Theorem by building up the required prerequisite knowledge and understanding the implications of the theorem and how it is influential in modeling.
A Brief Overview of Point-Set Topology
Mentee Ahmadh Hassan
Mentor Joy Hamlin
Abstract
I will be doing a general presentation on some theorems in point set topology and examples of how it works.
A Look into Lie Theory: Exploring Lie Theory Through Matrix Groups
Mentee Maxwell Goldberg
Mentor Riley Guyett
Abstract
Lie groups are a very important structure in mathematics. By studying groups which are also smooth manifolds, we are able to study symmetries of a wide array of systems. In this talk, we will learn about some fundamental Lie groups, such as SO(n), as well as the connection between them and Lie algebras.
“Climability” of Aronszajn Trees: Cofinal Branches in Trees of Height ω and ω1
Mentee Harry Haedrich
Mentor Ben-Zion Weltsch
Abstract
When do trees have branches? For trees of countable height and finite levels, it can be easily shown that there must be some branch (a cofinal branch) which reaches all the way to the top—in plain words, you can “climb” them, one node at a time. However, when we move past the countable into the uncountable, things get tricky. Can Jack climb the ℵ1-Aronszajn beanstalk?
Combinatorial Game Theory: Toads and Frogs
Mentee Nuray Kutlu
Mentor Dennis Hou
Abstract
This presentation will introduce Combinatorial Game Theory notation, definitions, and game reduction techniques along with some Toads and Frogs results.
Elliptic Curves and Fermat's Last Theorem
Mentee Alon Danai
Mentor Preston Tranbarger
Abstract
We will sketch an outline of how Fermat’s Last Theorem was proven using the theory of elliptic curves and modular forms.
Energy Methods for the Wave Equation
Mentee Ish Shah
Mentor Anupam Nayak
Abstract
The wave equation is one of the most fundamental examples of a linear partial differential equation (PDE), solvable through elementary means. However, solving the PDE is not necessary for studying some qualitative properties of solutions. In this talk, we will explore physics-inspired energy methods that allow for the study of some qualitative properties, such as the uniqueness of solutions.
Mentee Jessie Wang
Mentor Bojue Wang
Abstract
The Gershgorin Disk Theorem helps locate the eigenvalues of a square matrix by showing they lie within specific disks in the complex plane. This presentation will explain the theorem, its proof, and its applications, with examples to make it clear.
Incompleteness and Undecidability
Mentee Michael Fiore
Mentor Ben-Zion Weltsch
Abstract
An introduction to undecidable problems and unprovable statements.
Introduction to Symmetric Polynomials
Mentee Kevin Guether
Mentor Hong Chen
Abstract
A polynomial is said to be symmetric if permuting the variables results in the original polynomial. Three examples of these would be the elementary symmetric polynomials, the complete symmetric polynomials, and power sums. Each of these come with their own generating function. We will be examining the relation between these three types of polynomials and their generating functions.
Lagrangian Mechanics, Manifolds, and Noether's Theorem
Mentee Keshav Badri
Mentor Yiyang Liu
Abstract
Newton’s laws provide us with a fundamental set of rules to analyze these systems but have a fundamental limitation when considering problems of higher complexity. Instead, physicists tend to prefer the Lagrangian method for solving these problems. The Lagrangian method has further advantage in being able to describe “motions” in Quantum Field Theory and Electromagnetism. This talk will discuss the Lagrangian method and a mathematical derivation for Lagrangian mechanics using manifolds and its relevant spaces. We will then use this manifold definition to prove an intuitive formula and definition for Noether’s Theorem, which describes the relation between symmetries and conserved quantities in a given system. We will then connect these mathematical concepts with physical systems to motivate our intuition behind this important result of Lagrangian mechanics.
🌞Obtaining Perfect Matchings of Bipartite Graphs Through Augmentation
Mentee Valentina Pappano
Mentor Natasha Ter-Saakov
Abstract
This talk will introduce the concepts of bipartite graphs, Hall's Theorem, and matching. We will describe how to utilize augmented paths to extend a partial matching on a bipartite graph to find a perfect matching.
Orientation and Poincaré Duality: Relating Algebraic Invariants of Orientable Manifolds
Mentee James Belov
Mentor Timothy Bates
Abstract
We will discuss homology and cohomology of topological spaces, and a helpful theorem relating them in a wide and interesting class of spaces.
🌝Rational Points on Cubic Curves
Mentee Shreya Ghosh
Mentor Adam Earnst
Abstract
This presentation explores the properties of rational points on cubic curves using Group Laws. It highlights Mordell’s Theorem, which states that the group of rational points on an elliptic curve is finitely generated.
Sperner's Theorem and Its Applications
Mentee Akshat Singh
Mentor Milan Haiman
Abstract
How Sperner’s theorem can be applied to problems such as the Littlewood–Offord problem.
The Unreasonable Effectiveness of the Calculus of Variations
Mentee Mahadevan Seetharaman
Mentor Samuel Wallace
Abstract
The calculus of variations is a general framework for finding the critical points of functionals (functions depending on functions, rather than finitely many real variables). Problems that can be tackled by variational techniques arise in many areas of mathematics and physics, and the subject is an active area of research. We will derive the Euler–Lagrange equation, a basic result that can be used to solve many variational problems, then talk about some examples with interesting solutions, including the brachistochrone problem and the isoperimetric problem.
The Weierstrass Factorization Theorem
Mentee Jason Liu
Mentor Ryan Mc Gowan
Abstract
In this presentation we examine the Weierstrass factorization theorem, which can be seen as a generalization of the Fundamental Theorem of Algebra, its proof, and, if time permits, some applications.
Mentee Liza Ter-Saakov
Mentor Nicholas Backes
Abstract
What sort of properties are true for groups with topologies on them? In this talk, we will introduce topological groups and discuss some interesting theorems that shed light on their structure and significance, which then leads us to locally compact groups and the Haar measure on them.
Understanding Singular Value Decomposition
Mentee Aiman Koli
Mentor Nilava Metya
Abstract
My presentation will go over Singular Value Decomposition and its applications in Machine Learning that include Dimensionality Reduction, Recommendation Systems, and reconstructions. I will also address how I have implemented this computationally in a real-life project and show the limitations of the implementation. The next part will go over root finding techniques and will build to problems in convex optimization such as quadratic approximations and least squares.
Mentee Sophia Pan
Mentor Sam Spiro
Abstract
An introduction to combinatorial game theory, the study of sequential games with perfect information. This presentation focuses on 2-player games and introduces Nim, nimbers, impartial games, value of games, and concludes with the Sprague–Grundy Theorem.
An Overview on Park and Pham’s Proof of the Kahn–Kalai Conjecture
Mentee Rui Zhang
Mentor Charles Kenney
Abstract
I will provide a brief review of Jinyoung Park’s proof of the Kahn–Kalai Conjecture, which demonstrates the close relationship between expectation thresholds and actual thresholds in random structures.
Birkhoff ’s Curve Shortening Process
Mentee Eric Shim
Mentor Dongyeong Ko
Abstract
An introduction to geodesics, the Birkhoff curve shortening process, and some applications for chords of manifolds with boundaries.
Brownian Motion and the Dirichlet Problem
Mentee Andrew Xie
Mentor Anupam Nayak
Abstract
Theory of stochastic processes with selected applications to potential theory and the Dirichlet problem such as representation of solutions and properties of harmonic functions.
Coproducts in Algebraic Categories
Mentee Kyan Valencik
Mentor Alexander Day
Abstract
An overview of coproducts in various categories (Set, Group, Vect, etc.). Based on the readings of Algebra: Chapter 0 by Aluffi.
Demystifying Sheaves: A Basic Introduction to Sheaves
Mentee Maxwell Goldberg
Mentor Riley Guyett
Abstract
For my talk, I will be explaining what sheaves are and attempting to develop intuition for understanding them and what they do.
Differential Forms: Theory and Applications
Mentee Mahadevan Seetharaman
Mentor Ishaan Shah
Abstract
We will explain what manifolds are and construct differential forms on manifolds. We will briefly discuss applications.
∞-Categories with a View Toward Simplicial Homotopy Theory
Mentee Qichang Huangfu
Mentor Jishen Du
Abstract
Introduction to ∞-categories and simplicial homotopy theory.
Introduction to Stochastic Calculus and Its Applications in Finance
Mentee Pranav Tikkawar
Mentor Forrest Thurman
Abstract
An introduction to stochastic calculus and its applications in finance.
Mentee Nick Belov
Mentor Maxwell Aires
Abstract
A solution to the following problem: How do you partition the nodes of cactus into pairs so that you maximize the sum of the shortest distances between the nodes in the pairs?
Quantum Groups and Knot Invariants
Mentee Trisha Kothavale
Mentor Dennis Hou
Abstract
An introduction of the theory of quantum groups and how representations of quantum groups can be used to derive the Jones polynomial for a framed link.
Smooth Manifolds & Symplectic Manifolds
Mentee Nilay Tripathi
Mentor Forrest Thurman
Abstract
We start by giving a brief overview of topological manifolds, smooth structures on manifolds, and differential forms. We then discuss the basic concepts and definitions regarding symplectic manifolds and some brief applications in Hamiltonian mechanics.
Mentee James Belov
Mentor Timothy Bates
Abstract
An overview of one of the most efficient methods for computing fundamental groups.
A Brief Introduction to Differential Topology
Mentee Iris You
Mentor Bernardo Do Prado Rivas
Abstract
This presentation offers an introduction to the foundations of differential topology. Beginning with smooth maps, we illustrate how one obtains smooth manifolds and discuss their properties. Then tangent spaces are introduced as tools for studying the infinitesimal behavior of manifolds. Finally, we introduce tensors as a way to encode geometric relationships on curved spaces.
Mentee Ramesh Balaji
Mentor Rashmika Goswami
Abstract
This presentation provides an overview of what error-correcting codes are, what differentiates low-density parity-check (LDPC) codes from other kinds of error-correcting codes, and an overview of different decoding algorithms for LDPC codes.
An Overview of the Prime Number Theorem
Mentee Ish Shah
Mentor Nicholas Backes
Abstract
In this presentation, the prime number theorem will be stated. Key ingredients used in the proof, such as the Riemann zeta function, will be discussed. Finally, the presentation culminates in an overview of the proof of the prime number theorem.
Mentee Hanbo Xie
Mentor Forrest Thurman
Abstract
Basic introduction to strongly regular graphs and their connection with association schemes.
🌞Braid Groups and the Burau Representation
Mentee Ava Ostrem
Mentor Dennis Hou
Abstract
This presentation will cover the definition of braid groups and their basic properties. Then we will discuss linear groups and the linearity of the braid groups.
Mentee Trisha Kothavale
Mentor Bojue Wang
Abstract
An overview of the multilinear construction of the Clifford algebra and some of its basic properties, and some examples.
Complex Analysis: The Beautiful Implications of Being Holomorphic
Mentee Maxwell Goldberg
Mentor Riley Guyett
Abstract
Complex analysis isn't always an area of math focused on in a Rutgers undergraduate curriculum. However, it has many amazing results and consequences that don't appear in real analysis. In my presentation, I will give a highlight reel of complex analysis to showcase its beauty and convince you to learn it as well.
Dirichlet Characters, L-functions, and Applications
Mentee Liza Ter-Saakov
Mentor Charles Kenney
Abstract
I will give an introduction to characters and Dirichlet characters, then L-functions and applications. Prerequisites are basic group theory.
Mentee Rui Zhang
Mentor Ben-Zion Weltsch
Abstract
Filters are powerful mathematical structures with diverse applications in set theory, topology, and beyond. This presentation explores the fundamental concepts and properties of filters in the context of set theory.
Financial Mathematics and Personal Financial Decisions
Mentee Elvina Abzalimova
Mentor Minhao Bai
Abstract
The application of mathematical methods to financial problems, in particular personal finance. A look into mortgage and retirement calculations.
Optimized Portfolio Allocation
Mentee Artem Ivaniuk
Mentor Minhao Bai
Abstract
An overview of the Brownian Motion assumption in the stock market, its applications through the Geometric Brownian Motion (GBM) Model, which yield Markowitz’s Modern Portfolio Theory (MPT), and most recent research on optimizing the MPT through risk-averse 1/n into each n Brownian motions strategy.
Poset Dimensions and Scrambling Sets
Mentee Eric Yang
Mentor Milan Haiman
Abstract
The order dimension of partially ordered sets on the Boolean lattice is closely related to the notion of minimal scrambling sets, which describe the minimum number of permutations of n elements needed to place any one element above any k others. Exact values are not known for small values of k compared to n, but a variety of combinatorial and probabilistic techniques have narrowed the bounds on this value.
Results in Analysis and General Topology
Mentee Mahadevan Seetharaman
Mentor Ishaan Shah
Abstract
Point-set topology and mathematical analysis form a significant subset of the foundation for more advanced mathematics and have interesting applications in their own right. In the first half of this talk, we will discuss and prove some results about topological spaces and continuous functions. In the latter half of this talk, we will discuss three theorems from analysis: the Contraction Mapping Principle, the Inverse Function Theorem, and the Implicit Function Theorem. We will prove these theorems and talk about some applications.
Schemes from the Viewpoint of “Functor of Points”
Mentee Qichang Huangfu
Mentor Theodore Gonzales
Abstract
Considering the functor of points of a scheme can make it easier to study some problems in algebraic geometry such as the theory of algebraic groups. I will mainly discuss a theorem about a condition for a functor to be representable by a scheme.
The Addressing Problem for Loop Switching
Mentee Nuray Kutlu
Mentor Natasha Ter-Saakov
Abstract
This presentation talks about the math behind creating short and efficient addresses for data blocks in networks that transmit data between loops.
Mentee Zachary Roth
Mentor Ben-Zion Weltsch
Abstract
A history of choice and its controversy and some independence results.
🌝The Undecidability of Hilbert's Tenth Problem: Applications of Recursion Theory
Mentee Sean LeClair
Mentor Fanxin Wu
Abstract
Is there an algorithm that can decide if a Diophantine equation has an integer solution? No!
Untangling Knot Theory: Seifert Surfaces and Knot Genus
Mentee Jeffrey Tang
Mentor Timothy Bates
Abstract
A quick overview on knots, knot diagrams, classification of knots, and the notion of knot equivalence. The main focus will be on Seifert surfaces and Seifert's algorithm as a method for knot classification. Additionally, describing the genus of a knot using a Seifert surface and its properties and applications.
Algebraic Geometry: An Introduction with Hilbert's Nullstellensatz
Mentee Maxwell Goldberg
Mentor Riley Guyett
🌞An Overview of Hermite Polynomials
Mentee Nilay Tripathi
Mentor Forrest Thurman
Mentee Liza Ter-Saakov
Mentor Charles Kenney
Groups and Representations in Quantum Mechanics: Representations of Finite-Dimensional Groups
Mentee Mahadevan Seetharaman
Mentor Ishaan Shah
Mentee Daniel Elwell
Mentor Ben-Zion Weltsch
Representation Theory and Symmetric Functions
Mentee Emily Howlett
Mentor Hong Chen
Mentee Nuray Kutlu
Mentor Pablo Blanco
🌝ZFC and the Continuum Hypothesis
Mentee Ava Ostrem
Mentor Dennis Hou
Banach Fixed-Point Theorem and Application
Mentee Hana Huber
Mentor Karuna Sangam
Fourier Transform with Its Application
Mentee Xinchen Hua
Mentor Weihao Zheng
Gröbner Bases: A Sledgehammer for Solving Systems of Polynomials
Mentee Maxwell Goldberg
Mentor Bojue Wang
Introduction to Computational Homology
Mentee Varshini Gopalakrishnan
Mentor Brittany Gelb
Minesweeper Complexity: Is Minesweeper NP-complete?
Mentee Raj Limbasia
Mentor Robert Dougherty-Bliss
Representation Theory with Representations of S3 as an Example
Mentee Qichang Huangfu
Mentor Tae Young Lee
Shannon's Noisy Channel Coding Theorem over a Binary Symmetric Channel
Mentee Ramesh Balaji
Mentor Adarsh Srinivasan
Sylow Subgroups and Wilson's Theorem
Mentee Sakshi Koul
Mentor Dennis Hou
The Basics of Fourier Analysis
Mentee Tijil Kiran
Mentor Nicholas Backes
Mentee Alexander Valentino
Mentor Rashmika Goswami
An Overview of Kaplansky's Set Theory and Metric Spaces
Mentee Hasan Kunukcu
Mentor Fanxin Wu
Complex Analysis: An Introduction
Mentee Anish Suresh
Mentor Devin Bristow
Elliptic Curves and Cryptographic Applications: The Discrete Log Problem and Diffie-Hellman
Mentee Brian Zhang
Mentor Forrest Thurman
High Frequency Trading in a Limit Order Book
Mentee Akhil Sharma
Mentor Minhao Bai
Introduction to the Theory of Computation
Mentee Jean Paul Sadia
Mentor Devin Bristow
Pendulums and ODEs
Mentee Varshini Gopalakrishnan
Mentor Soham Chanda
Streaming Model and Misra–Gries Algorithm
Mentee Rohit Rao
Mentor Aditi Dudeja
Mentee Emily Howlett
Mentor Hong Chen
Mentee Jonathan Rasnitsyn
Mentor Caleb Fong
Mentee Yebai Zhao
Mentor Bojue Wang
A Probabilistic Perspective on the Open Question of When to Stop
Mentee Akhil Sharma
Mentor Minhao Bai
An Extremely Quick Look at the Sensitivity Conjecture
Mentee Ravi D'Elia
Mentor Sam Spiro
Complexity Theory
Mentee Daniel Baumgartner
Mentor Caleb Fong
Elliptic Curves over ℂ
Mentee Francisco del Campo
Mentor Nicholas Backes
Introduction to Knot Theory
Mentee Varshini Gopalakrishnan
Mentor Karuna Sangam
Lagrange's Theorem
Mentee Yakov Burton
Mentor Bojue Wang
Numeric Algorithms and RSA Encryption
Mentee Devin Holmes
Mentor Quentin Dubroff
The Lebesgue Integral
Mentee Vincent Caputo
Mentor Brittany Gelb
Complexity Theory
Mentee Gloria Liu
Mentor Maxwell Aires
Equivariant Maps and the Equivariant Rank Theorem
Mentee Daniel Bernstein
Mentor Lawrence Frolov
Mentee Ethan Kwok
Mentor Mitchell Bast
Mentee Mark Vaysiberg
Mentor Bojue Wang
Lie Groups, Homogeneous Spaces, and Model Geometries
Mentee Emily Howlett
Mentor Dennis Hou
Polynomial Factorization over Finite Fields, a Computational Approach
Mentee Alex Valentino
Mentor Louis Gaudet
Riemannian Geometry
Mentee Cormac Grindall
Mentor Dongyeong Ko
The Cauchy Integral Formula, Liouville's Theorem, and the Fundamental Theorem of Algebra
Mentee Yakov Burton
Mentor Sriram Raghunath
Mentee Akhil Sharma
Mentor Minhao Bai
Differential Topology: A Brief Journey
Mentee Maxwell Goldberg
Mentor Soham Chanda
Stochastic Processes and Time Series
Mentee Akhil Sharma
Mentor Minhao Bai