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Recent REU Projects

Summer 2022

Encoding Cohomology, Classifying Extensions, and Explicit Galois Gerbs
Author: Nir Elber
Mentors: Alexander Bertonloni Meli Patrick Daniels; Nicholas Rome
Funding: F053986-RTG: Number Theory and Representation Theory

Christoffel Transformations of Legendre Polynomials
Author: Andrew Fischer-Garbutt
Mentors: Ahmad Barhoumi
Funding: F056921-Random matrices, spin glass, and interactions

Differentially Private Algorithms for Graph Sequences
Author: Yiwei Fu
Mentor: Martin Strauss
Funding: RIP-Martin Strauss

Modular Principal Series Representation of GL2 Over Finite Rings
Authors: Gahl Shemy
Mentor: Charlotte Chan
Funding: F061315-Geometric methods in representation theory

Analyzing the Growth Dynamics of Bladder Cancer Using Ordinary Differential Equation Modeling
Authors: Joel Greenfield
Mentor: Daniel Bergman
Funding: F054152-Collaborative Research: Nonsmooth maps, co

Existence of Uncountably Many Singular Vectors in Rn for Higher Dimensional Generalizations of Dani Correspondence
Authors: Riley Guyett
Mentor: Nattalie Tamam
Funding: F057220-Rigidity Properties in Dynamics and Geometry

Federated Learning On Medical Applications
Authors: Sizhuang He
Mentor: Maria Han Veiga

Exmaples of Real Conic Bundles with Quartic Descriminant Curve
Authors: Mattie Ji
Mentor: Lena Ji
Funding: F060536Commutative Algebra: Extremal Singularitiex

The Linear Complimentarity Problem and its Applications in Physics Based Animation
Authors: Rohan Kodati
Mentor: Shravan Veerapaneni
Funding: F050847 - A Stud of Wave Patterns

The Logic of Choiceless Cardinality Comparison
Authors: Dhruv Kulshreshtha
Mentor: Matthew Harrison-Trainor
Funding: Chair Discretionary Funds - Math

Circular-Kernel-Based Curvature-Motion Algorithms
Authors: David Li
Mentor: Selim Esedoglu
Funding: F058006 - High Order Schemes for Gradient Flows

Aritmetic of Infinite Dedekind-finite Sets
Authors: Jing-Yi Liu
Mentor: Andreas Blass
Funding: Mathematics Department Special

Metric Diophantine Approximation on Non-Degenerate Manifolds
Author: Justin Liu
Mentor: Shreyasi Datta
Funding: F057220-Rigidity Properties in Dynamics and Geometry

Incorporating Domain Knowledge in Neural Networks
Authors: Zhongqi Ma
Mentors: Maria Han Veiga, Dao Nguyen
Funding: Mathematics Department Special

Computable Model Theory and Infinitary Logic
Authors: Miles Kretschmer
Mentor: Matthew Harrison-Trainor
Funding: F057220-Rigidity Properties in Dynamics and Geometry

Mechanics of Nonholonomic Hybrid Lagrangian Systems
Authors: Evan Ortiz
Mentor: Anthony Bloch
Funding: F061041-Dynamics, Integrability and Control of Mechanics

Deep Galerkin Method for Mean Field Control Problems

Authors: Jingruo Sun
Mentors: Asaf Cohen
Funding: Mathematics Department Special

Numerical Methods for the Heat Equation
Authors: Sofia Taylor
Mentor: Robert Krasny
Funding: F061623-Collaborative Research: Computational Tool

Overdamped Langevin Dynamics on Lie Groups

Authors: Xinchang Wang
Mentor: Qi Feng
Funding: U038823 - Research Incentive Program

Hardy-Littlewood Circle Method

Authors: Xun Wang
Mentor: Nicholas Rome
Funding: U038823 - Research Incentive Program

Predicting Gas Temperature in Protoplanetary
Authors: Jason Zheng
Mentors: Maria Han Veiga and Arthur Bosman
Funding: G014390 - James Van Loo Applied Mathematics and Physics Undergraduate Support Fund

Summer 2021

Computing the Constant in the Left-tail Asymptotic of Maximum Eigenvalue Distribution of Finite GUE
Author: Xiaoqi Peng
Mentors: Andrei Prokhorov & Fred Adams
Funding: G014390 - James Van Loo Applied Mathematics and Physics Undergraduate Support Fund

Bijections of Strictly Convex Sets & Closed Convexprojective Surfaces that Preserve Complet Geodesics
Author: Drimik Chowdhury
Mentors: Ralf Spatzier & Giuseppe Matrone
Funding: U038823 - Research Incentive Program

Convex Relations for a Generalization of Mumford-Shah
Author:Andrew Fischer-Garbutt
Mentor: Selim Esedoglu
Funding: F047060-Sub of F046971-Computational Tools & F058006-Sub of F058005-High Order Schemes

Using Mathematics and Computing to Understand How Bees UsePhysics to Keep Their Hives Cool

Authors: Jiashu Han
Research Advisor: Robert Krasny
Funding: U038823 - Research Incentive Program

Polychromatic Ramsey Properties of Ideals
Authors: Jonah Nan
Research Advisor: Zach Norwood
Funding: U048325 - Chair Discretionary Funds

Attempts to Approximate the Partition Function of Hamiltonian Cycles
Authors: James Walrad & Lily Wang
Research Advisor: Alexander Barvinok
Funding: F054167-Sub of F054157-FRG: Collaborative Research

QNM Expansion to Solutions of Maxwell's Equation in Open Domains
Authors: Kevin Ke
Research Advisor: Jorn Zimmerling
Funding: F050847-Sub of F050810

Differential Closure of Ideals
Authors: Lillian McPherson, Monroe Stephenson, & Fuxiang Yang
Research Advisor: Jennifer Kenkel & Daniel Smolkin
Funding: F040585-Sub of F040563-CAREER & F050391-Sub of F050378-Participant Support-Commutative Algebra & F054167-Sub of F054157-FRG: Collaborative Research

Good-Deal Bounds in Asset Pricing
Authors: Mingxuan Ge
Research Advisor: Prakash Chakraborty
Funding: U038823 - Research Incentive Program

Modeling Vibrating Strings
Authors: Pengrun Huang & Ella Palacios
Research Advisor: Alejandro Uribe
Funding: U038823 - Research Incentive Program & F050847-Sub of F050810

Gender Prediction Using Email Data
Authors: Peihan Liu
Research Advisor: Martin Strauss
Funding: U029433 - RIP - Martin Strauss

Right tail of two-point distribution of the KPZ fixed point
Authors: Ron Nissim
Research Advisor: Jinho Baik
Funding: F056922-Sub of F056921-Random matrices

Using Infinite Games with Perfect Information to Characterize the Product Perfect Set Property
Authors: Terry Guan
Research Advisor: Iian Smythe
Funding: U031348 - Undergrad program funding

Wave Kinetic Equation and Kolmogorov-Zakharov Cascade Spectra
Authors: Yubing Cui & Joshua Messing
Research Advisors: Zaher Hani & Ricardo Grande Izquierdo
Funding: U038823 - Research Incentive Program & F054244-Sub of F054209-CAREER

Carnot Algebras with Small Graded Automorphism 
Authors: Ethan Cohen
Research Advisor: Thang Nguyen
Funding: F057224-Sub of F057220-Rigidity Properties

Efficient Sliding Locomotion of Three-Link Bodies with Inertia
Authors: Adam Earnest
Research Advisor: Silas Alben
Funding: F051415-Sub of F051324-Participant Support

Ratios for Spanning Tree Polynomials of Covering Graphs

Authors: Jeremy Flics and Brendan Nell
Research Advisors: Sunita Chepuri
Funding:F053989-Sub of F053988-Geometry of Cluster Algebras & F057224-Sub of F057220-Rigidity Properties

Faster Dynamic Algorithms and Sensitivity Oracles for Graph Connectivity Problems
Authors: Jingyi Gao
Research Advisors: Thatchaphol Saranurak and Michael Zieve
Funding: G014390 - James Van Loo Applied Mathematics and Physics Undergraduate Support Fund

Extensions of Representations of Division Algebras Over Non-Archimedean Local Fields 

Authors: Andrew Keisling and Dylan Pentland 
Research Advisors: Tasho Kaletha and Karol Koziol
Funding: F050174-Sub of F050164-Participant Support 

High-Wavenumber Steady Solutions of Two-Dimensional Rayleigh-Benard Convection Between Stress-Free Boundaries 
Authors: Alexander Takla
Research Advisors: Baole Wen
Funding: F040585 - 085629-Restricted Sub of F040563-CAREER

Singular Vectors in Fq((T-1))
Authors: Yewei Xu
Research Advisors: Shreyasi Datta 
Funding: U031348 - Undergrad program funding

Summer 2020

The Copy Lemma and Non-Shannon Information Inequalities 
Authors: Michael Tang
Research Advisor: Andreas Blass
Funding: F054167-Sub of F054157-FRG

Stochastic Volatility Modeling: From Rough Heston Model to Affine Volterra Equatio
Authors: Zixuan Wang & Yuanchun Ye
Research Advisor: Shuoqing Deng
Funding: U038823-Research Incentive Program & U053975-AMS-Simons Travel Award

Quiver Polynomials and Bumpless Pipe Dreams
Authors: Alexander Vidinas & Zixuan Xu
Research Advisor: Anna Weigandt
Funding: F042421-Sub of F042420-Combinatorics of Cluster Varieties & F050391-Sub of F050378-Participant Support  

Income Stability of Pooled Annuity
Authors: Ge Qu
Research Advisor: Thomas Bernhardt
Funding: U038823 - Research Incentive Program

Generating a Fractal Tree
Authors: Jingyi Gao
Research Advisor: Mitchell Newberry
Funding: G014390-James Van Loo Applied Mathematics and Physics Undergraduate Support Fund

Strongly Obtuse Rational Lattice Triangles
Authors: Anne Larsen
Research Advisors: Chaya Norton & Alex Wright
Funding: F054083-Sub of F054069-GL+(2,R) orbit closures 

Optimal Stopping of exotic American option by Deep Learning
Authors: Qinghao Lin
Research Advisor: Shuoqing Deng
Funding: U048325 - Chair Discretionary Funds-Math

Extensions of irreducible representations of quaternion algebras
Authors: Alex Wang
Research Advisor: Karol Koziol
Funding: F053987-Sub of F053986-RTG

Periodic points on the regular n-gon
Authors: Rafael Saavedra
Research Advisor: Chaya Norton & Alex Wright
Funding: F054083-Sub of F054069-GL+(2,R) orbit closures 

The Relativistic Vlasov-Maxwell System in Two Space Dimensions
Authors: Advika Rajapakse
Research Advisor: Neel Patel
Funding: F040585-Sub of F040563-CAREER

Medium Scale Curvature for Hyperbolic Groups
Authors: Andrew Keisling
Research Advisor: Thang Nguyen
Funding: F057224-Sub of F057220-Rigidity Properties

Ramsey Theory in Models of Set Theory Where the Axiom of Choice Fails
Author: Zekun Jia
Advisor: Zach Norwood
Funding: U038823 - Research Incentive Program

Coding Theory & Grassmannian Varieties
Author: Pengrun Huang
Advisor: Eric Canton
Funding: U053975 - AMS-Simons Travel Award

A Low Dimensional Model for Mouse Circadian Rythms
Author: Carrie Fulton
Advisor: Victoria Booth
Funding: F054171-Sub of F054152-Collaborative Research

Hilbert Functions of Square-Free Monomial Ideals
Author: Marianne Debrito & Meixuan Sun
Advisor: Janet Page & Timothy Ryan
Funding: F050391-Restricted Sub of F050378-Participant Support & U038823 - Research Incentive Program

Thurston’s fibered faces for non-orientable 3-manifolds and an application to minimal stretch factors
Author: Caleb Partin
Advisor: Becca Winarski
Funding: F054332-Sub of F054307-Logarithmic gauged linear sigma models

Summer 2019

More on the Magnus Representation of the Torelli Group
Authors: Mira Wattal
Research Advisor: Becca Winarski

The Faces of Toric Arrangements
Authors: Junshan Chen & Amanda Yao
Research Advisor: Christin Bibby


Symbolic Powers of Defining Ideals of Veronese Rings
Authors: Fangu Chen & Alan Tang
Research Advisors: Eric Canton, Eloisa Grifo, & Jack Jeffries


Children's Drawings and the Riemann-Hilbert Problem
Author: Drimik Roy Chowdhury
Research Advisor: Caleb Ashley


Fast Phase Retrieval from Masked Fourier Measurements
Author: Cyril Cordor
Research Advisors: Aditya Viswanathan, Yulia Hristova, Alejandro Uribe-Ahumada


Local Cohomoology of L (1,1,...,1) Module
Author: Zhou Fang
Research Advisor: Andrew Snowden


A Classification of Certain Symmetric Ideals
Author: Vignesh Jagathese
Research Advisor: Andrew Snowden


Low Energy Band-Limited Surfaces
Author: Stephen Jasina
Research Advisor: Ian Tobasco


The Hofer-Zehnder Capacity of Symplectic Toric Manifolds
Author: Yichen Liu
Research Advisor: Alejandro Uribe


Efficient Sliding Locomotion of a Two-Link Scallop
Author: Connor Puritz
Research Advisor: Silas Alben


One-Dimensional Domains of Large Type
Author: Amanda Schwartz
Research Advisor: Mel Hochster


Heronian Friezes
Author: Linus Setiabrata
Research Advisor: Sergey Fomin


Global Decay for Medium Intiial Data in the Inhomogeneous Muskat Problem
Author: Nikhil Shankar
Research Advisor: Neel Patel


Form-Function Divergence in Induced Trisomy-7
Author: Roy Siegelmann
Research Advisor: Indika Rajapakse


Weak Formulation of Discrete Time Principal Agent Problem
Author: Xinjie Sun & Zhenxi Wu
Research Advisor: Nicolas Hernandez & Alexandros Saplaouras


Visualizing Fluid Flows Using Line Integral Convolution Method
Author: Shuyang Wang
Research Advisors: Shravan Veerapaneni & Ruowen Liu


The Uniformization Theorem
Author: Zachary Halberstam
Research Advisor: Caleb Ashley

Duplicitous Permutations and Bumpless Pipe Dreams
Author: Rainie Heck
Research Advisor: Anna Weigandt

Summer 2018

Some Ramsey-theoretic statements without the Axiom of Choice
Authors: Joshua Brot and Mengyang Cao
Advisor: David Fernández-Breton

Gauged Linear Sigma Model Spaces
Author: Felipe Castellano-Macias
Advisor: Felix Janda

Identifiability of linear compartmental models of infectious disease transmission
Author: Jeremy D'Silva
Advisor: Marisa Eisenberg

Energetics of Elastic Curves
Authors: Jaeyoon Kim and Charles Devlin
Advisor: Ian Tobasco

A decision-theory based model of HPV vaccination and infection dynamics
Author: Alison Elgass
Advisor: Marisa Eisenberg

Min-Max Method and Gromov's Waist Inequality
Authors: Shiliang Gao and Juntai Zhou
Advisor: Daniel Burns

A Population-Based Model of the Effects of Spinal Cord Stimulation on Pain Processing
Author: Ariella Goldberg
Advisor: Sofia Piltz

Minimal Triangulations of Sphere Products
Author: Jonathon Jacobs
Advisor: Hailun Zheng

Mobius-invariant Lorentz geometry of the space of circles on S2
Author: Ben Johnsrude
Advisor: David Barrett

Symplectic Geometry Through Polytopes
Authors: Colby Kelln
Advisor: Daniel Burns

Syzgies of the Serge Embedding via Simplicial Complexes
Authors: Luke Kiernan and Ryan Capouellez
Advisor: Andrew Snowden

Balanced Triangulations of Sphere Products with Minimal Vertices
Author: Alexander Wang
Advisor: Hailun Zheng

The Scaling Function Connection Problem in the Two-Dimensional Ising Model
Author: William Warner
Advisor: Thomas Bothner

Galois Representations Valued in Reductive Groups and Their Centralizers
Authors: Nikolay Grantcharov and Wyatt Reeves
Advisor: Tasho Kaletha

Summer 2017

Symmetric and Asymmetric Centroid Bodies of the Regular
Author: Ryan Britton 
Advisor: Beatrice-Helen Vritsiou

Reduced Words of (p,q)-Clans
Author: Brian Burks
Advisor: Brendan Pawlowski

Constructing a Simple Hybrid Model of Perineural Invasion
Author: Jeremy D'Silva 
Advisor: Marisa Eisenberg

The (4,3) Property in Families of Fat Sets in the Plane
Author: Shiliang Gao 
Advisor: Shira Zerbib Gelaki

Obstructing Embeddings of Finite R-Partite Right-Angled Artin Groups into Mapping Class Groups
Author: Ben Gould 
Advisor: Wouter Van Limbeek

Permanents of Positive Semi-Definite Hermitian Matrices
Author: Wu Han and Roi Orzach
Advisor: Alexander Barvinok

Random Walks on the Fundamental Group of the OncePunctured Torus
Author:  Adam Holeman and Jennifer Jones-Baro
Advisor: Caleb Ashley and Harrison Bray

Numerical Solution of Nonlinear Poisson Boltzmann Equation
Author: Jingzhen Hu 
Advisor: Robert Krasny

A Topological Characterization of the Knotted and Linked Products Arising from Site-Specific Recombination on T(2, n)#C(2, r) DNA Substrates
Author: Jordan Katz 
Advisor: Diana Hubbard

Hindman's Theorem in Abelian Groups
Author: Sung Hyup Lee 
Advisor: David Fernandez-Breton

Complexity in Predator Prey Dynamics:Population Increase via Reciprocal Predation
Author: Xuenan Li
Advisor: Charles Doering and David Goluskin

Invariant Differential Operators Associated with the Pick's Matrices
Author: Wanxing Liu
Advisor: Daniel Burns

Ellipsoid Collision as a Linear Complementarity Problem
Author: Izak Oltman and Jaewon Hur
Advisor: Eduardo Corona

Thurston Norm of 2 Generator, 1 Relator Groups
Author: Natalia M. Pacheco-Tallaj
Advisor: Kevin Schreve and Nicholas Vlamis

Long-Time Simulations of Vortex Sheet Dynamics
Author: Daniel Solano
Advisor: Silas Alben and Ling Xu

Coherent Con guration on Infi nite Set
Author: Jincheng Wang
Advisor: Andreas Blass

Distributions for TASEP models
Author: Han Wu
Advisor: Jinho Baik

Calyxes and Corollas
Author: E. Dean Young
Advisor: Harm Derksen

Summer 2016

The Complex Roots and Approximation of Permanents
Authors: Han Wu & Max Kontorovich
Advisor: Alexander Barvinok

Cyclic Sieving of Matchings
Authors: Grant Bowling & Qingzhong Liang
Advisor:  Thomas Lam

Understanding Sleep-Wake Dynamics with Two Process Model and BDB Model
Author: Diya Sashidhar
Advisor: Victoria Booth

Isometries And Equivalences Between Point Configurations, Extended To ε-diffeomorphism
Author: Neophytos Charalambides
Mentors: David Speyer

Almost-Isometries for Point Cloud and Image Registration
Author: Cyrus Anderson
Mentors: Steven Damelin & David Speyer

Labeling Isometric and Almost Isometric n-Point Configurations in RD
Author: Michael Lu
Mentors: David Speyer

Green's function method, pKa calculation, and Poisson-
Boltzmann Equation

Author: Jingzhen Hu
Mentor: Robert Krazny

Computing examples of Hurwitz correspondences in cyclic and non-cyclic portraits.
Author: Julio Soldevilla
Mentor: David Speyer

On the Metastatic Mechanisms of Ovarian Cancer
Author: Ali Farhat
Mentor: Trachette Jackson

A Polynomial Time Deterministic Algorithm for Identity Testing Read-Once Polynomials
Author: Daniel Minahan
Mentor: Ilya Volkovich & Jeffrey Lagarias

First Koszul Homology over a Local Artinian Ring
Author: Nina Pande
Mentor: Mel Hochster

Weak Choice Principles and Forcing Axioms
Author: Elizabeth Lauri
Mentor: David Fernandez Breton

On the Pseudospctrum of One-Dimensional Schrödinger Operators with Complex Potential
Author: Xiyu Zhai
Mentor: Alejandro Uribe

Parameter Optimization and Data Fitting for the Flip-Flop Model of Sleep-Wake Regulation
Author: Michael Buiteweg
Mentor: Victoria Booth

The Hadwiger Conjecture for Unconditional Convex Bodies
Author: Daniel Barg
Mentors: Beatrice Vritsiou & Boaz Slomka

Billiard Dynamics on Surfaces of Revolution
Author: Isaac Garfinkle
Mentor: Daniel Visscher

Degree Bounds in the Nonmodular Case Invariant Theory
Author: Moise Mouyebe
Mentor: Harm Derksen

Curve Complexes of Non-Orientable Surfaces
Author: Alex Pieloch
Mentor: Richard Canary

Entropy of Triangular Lattices
Author: Shangnan Zhou
Mentors: Xiaoming Mao & Stephen DeBacker

Partial Recovery on Random Regular Graphs
Authors: Dylan Airey & Steven Damelin
Mentors: Steven Damelin & David Speyer

The Fundamental Theorem of Affine Geometry on Tori
Authors: Jacob Shulkin & Wouter Van Limbeek
Mentor: Wouter Van Limbeek

Algorithms for the Evolution of Surfaces
Author: Matthew Stone
Mentor: Selim Esedoglu

A Polarization Operation for Psuedomonomial Ideals
Author: Jeffrey Sun
Mentors: Sema Gunturkun & Jack Jeffries

Understanding ɛ-Distorded Diffeomorphisms
Author: Sean Kelly & Steven Damelin
Mentors: Steven Damelin & David Speyer

Summer 2015

Volume Preserving Threshold Dynamics for Grain Networks
Author: Jing An
Advised by: Prof. Selim Esedoglu

The Problem of Constructing Efficient Universal Sets of Quantum Gates
Authors: Qingzhong Liang and Jessica Thompson
Advised by: Dr. Steven Damelin and Prof. Martin Strauss

A Finiteness Property of Torus Invariants
Authors: Stella Gastineau and Samuel Tenka
Advisor: Prof. Andrew Snowden

Stability of Junctions in Grain Networks
Authors: Scott Ginebaugh
Advisor: Prof. Selim Esedoglu

New Examples of Dimension Zero Categories and a Computer Program for Calculations in Representation Theory
Author: Andrew Gitlin
Advisors: John Wiltshire-Gordon and Prof. David Speyer

Study of A Particular Combinatorial Game
Authors: Zifan Li and Yuan Chen
Advisor: Prof. Andrew Snowden

A Mathematical Model of a Rod Photoreceptor Population
Author: Louis Joslyn
Advisor: Prof. Adam Stinchcombe

Degree Bounds on the Ring of Invariants
Author: Moise Mouyebe
Advisor: Harm Derksen

Numerical Ring Invariants and the Alternating Sums of Graded Betti Numbers
Author: Michael Phelan
Advisor: Prof. Sarah Kitchen

Perturbation analysis on HJB equations
Author: Guanting Chen
Advisor: Prof. Virginia Young

A One Loop Test of AdS/CFT on AdS4 x S7=Zk
Author: Wenli Zhao
Advisors: Prof. James Liu and Prof. David Speyer

An Analytic Approach to the Problem of Matroid Representibility
Authors: D. Capodilupo, S. Freedman, M. Hua, and J. Sun
Advisor: Dr. Steven Damelin and Prof J. Lagarias

Investigating Torus Orbit Closures in the Hilbert Scheme of Points in the Plane
Author: Kristofer Siy
Advisor: Prof. Jenna Rajchgot

Space Complexity of Infinite Turing Machines
Author: Dylan Stephano-Shachter
Advisor: Prof. Andreas Blass

Passive Elasticity in a Model of Snake Locomotion
Author: Angelia Wang
Advisors: Prof. Xiaolin Wang and Prof. Silas Alben

Lower Bound Cluster Algebras: Presentations, Cohen-Macaulayness and Normality
Author: Bradley Zykoski
Advisors: Prof. Greg Muller and Prof. Jenna Rajchgot

Properties of a Chain-Like Linkage
Author: Shangnan Zhou
Advisors: Prof. Xiaoming Mao and Prof. Stephen DeBacker

Multiscale Modeling of the Sleep/Wake Systems
Author: Elena Malloy
Advised by: Prof. Victoria Booth

The Conditional Distribution of the Eigenvalues of the Ginibre Ensemble
Authors: Hwanwoo Kim & Eugene Siegel
Mentors: Alon Nishry & Diego Ayala


Summer 2014

Tropical Constructions and Lifts
Author: Hunter Ash
Advised by: Prof. Tyler Foster

Modeling Type One Diabetes with a Linear Response Function Based Model
Authors: Matthew Bauerle and Xinyan Han
Advised by: Prof. Yaniv Plan and Prof. Roman Vershynin

Biases in statistical inference: measles as a case study
Author: Alexander Becker
Advisor: Prof. Aaron King

Invariant Distributions on l-spaces
Author: Ben Brady
Advisor: Prof. Stephen DeBacker

A Permutation Model with Finite Partitions of the Set of Atoms as Supports
Author: Benjamin Bruce
Advisor: Prof. Andreas Blass

Substitution Polynomials and the Decomposition of Rational Functions
Author: Eric Levin
Advisor: Prof. Danny Neftin

Relatively Prime and Squarefree Integers
Author: Nora Farouk
Advisor: Prof. Patrick Boland

Exploring the Geometric Model of Riffle Shuffling
Authors: Jieun Lee, Janine Lewandoski, and Kevin Reifor
Advisor: Prof. Mark Conger

Elliptic Curves and Their Torsion
Author: Siyan “Daniel” Li
Advisor: Prof. Ian Shipman

Effect of Transaction Tax on Optimal Portfolio Liquidation and Predatory Trading
Author: Enkhjargal Lkhagvajav
Advisor: Prof. Sergey Nadtochiy

On Robust Arm-Acquiring Bandit Problems
Author: Shiqing Yu
Advisor: Prof. Xiang Yu

Sleep-wake cycles and jet lag
Author: Channa Schramm
Advisor: Prof. Victoria Booth

Hyperbolic geometry and moonshine groups
Author: Bazyli Szymanski
Advisor: Prof. Pat Boland

The Number of Generators of the First Koszul Homology of an Artianian Ring
Author: Alex Zhongyi Zhang
Advisor: Prof. Mel Hochster

Fund Manager's Portfolio Choice
Author: Zhiqing Zhang
Advisor: Prof. Gu Wang

Summer 2013

Monte Carlo Valuation of High Dimensional American Options
Author: Michael Angileri
Advised by: Dr. Arash Fahim

A Fast Algorithm to the RadiativeTransport Equation and Implementation of
Theory Into an Applet
Author: Mihai V. Avram
Advised by: Manabu Machida

Monomial Valuations, Cusp Singularities, and Continued Fractions
Author: David Bruce and Molly Logue

Extended Vamos Matroids and the Half-Plane Property
Author: Sam Burton and Yewon Youm

Numerical Methods for the One Way Water Wave Equation
Author: Sean Carney
Advised by: Smadar Karni

Data Assimilation using Optimal Control and Kalman Filtering
Author: Wei Chen and Evelyn Lunasin

Investigating Hyperbolic Geometry
Author: Sean Douglas and Caleb Springer

An Alternative Model for Card Shuffling
Author: Christopher Drouillard

Central Simple Sugeralgebras and the Spin Group
Author: Benjamin Gammage

Binary Matrix Completion and its Application to Restaurant Recommendation System
Author: Chenrui Gao
Advisors: Prof. Yaniv Plan, Prof. Roman Vershynin

Fundamental Domain and Hyperbolic Geometry
Author: Yubo Guo

Staircase ribbons in Sn
Author: Colin Holmes

Seeking Mechanisms Behind the Formation of Synchronized Behavior in
Cellularly Diverse Neural Networks
Author: Scott Knudstrup
Advisors: Victoria Booth

Multicategory and Monoidal Category
Author: Luhang Lai

Weakly Circle-Preserving Maps in Inversive Geometry
Author: Joel C. Gibbons and Yusheng Luo

Optimizing Snake Locomotion
Author: Matthew Osborne
Advisor: Professor Silas Alben

Time Series of Implied Density
Author: Wonho Rhee
Advisor: Prof. Sergey Nadtochiy

Polynomial Identities on Eigenforms
Author: Joseph Richey and Noah Shutty

Mathematical Model and Analysis of Cellular Diffusion
Author: Dylan Corey Sena

Modeling Retinal Neurons
Author: Jonathan Timkovich

A Bound on Length Isospectral Families and Applications
Author: Weston Ungemach

Discrete Groups of Isometries and Fundamental Domains
Author: Yutong Wang
Advisor: Patrick Boland, Lizhen Ji

On Multivariate Path-Dependent Pricing
Author: Zhiyuan Wang
Advisor: Xiang Yu

Computations in the Lie Algebra of F4 and a Parameterization of Nilpotent Orbits
Author: Karl Winsor
Advisor: Stephen DeBacker

Summer 2012

Chaotic Planetary Dynamics in Post Main-Sequence Stellar Systems
Kassandra Anderson
Advisors: Fred Adams & Anthony Bloch

Random Matrices with Prescribed Row and Column Sums
Dangxing Chen
Advisor: Alexander Barvinok

Towards a Szego Limit Theorem for Berezin-Toeplitz Operators with Singular Symbols
Tyler Friedman
Advisor: Alejandro Uribe

Calculations on a Lattice L Spanned by a Set of Conformal Vectors
Todd Gaugler
Advisor: Robert Griess

Commutators in the Metaplectic Group
Daniel Hast
Advisor: Dmitriy Boyarchenko

Non-consecutive Congruences of Dedekind-finite Sets
Author: John Holler and Matthew Tanzer
Advised by: Andreas Blass

Examining the Sample Complexity of the Maximum Likelihood Estimator in
Phylogenetic Tree Reconstruction
Sangwon Hyun
Advisor: Jose Alcala Burgos

Fundamental Domains of Discrete Groups Acting on Euclidean Space
John Kilgore
Advisor: Lizhen Ji

Quiver Representations
Molly Logue
Advisor: Harm Derksen

L1 Norm of the Valle-Poussin Kernel
Harsh Mehta
Advisor: Hugh Montgomery

Forbenius Manifold of K3 LG-model
Non-symplectic Automorphisms of Prime Order on K3-Surfaces
Rachel Suggs
Advisor: Yongbin Ruan

The Kreiss Stability Condition for Initial Boundary Value Problems
Michaela Wood
Advisor: Divakar Viswanath

Summer 2011

Summer 2011

Dispersive Quantization
Sudarshan Balakrishnan
Advisors: Professor Benson Muite

Numerical Integration of Black Hole Solutions to the Einstein/Yang-Mills Equations
Rebekah Bartlett
Advisor: Professor Joel Smoller

A Multivariate Median in Banach Spaces and Applications to Robust PCA
David Bruce
Advisor: Professor Roman Vershynin

F-Pure Thresholds
Sifat Rahman & Joseph Billian
Advisor: Professor Bhargav Bhatt

Explorations in Genetic Oscillators
Christopher Chung
Advisor: Professor Richard Yamada

Face Vectors of Sphere Products
Kit Clement
Advisor: Patrick Boland

Modeling Human Sleep Patterns
Rebecca Gleit
Advisor: Professor Victoria Booth

Analysis of Mutual Predation in an Age-Structure System
Nathan Golovich
Advisor: Professor Charles Doering

Exploring KGH Bounds in t = 4
John Holler and Nick Wasylyshyn
Advisor: Professor Brett Hemenway

Zeta Functions, the Tate Conjecture, and Catanese Surfaces
Paul Lewis
Advisor: Professor Christopher Lyons

The Evolution of One Dimensional Crystal Surfaces in Two Configurations
Mark Liu
Advisor: Professor Hala Al Hajj Shehadeh

Calculation Process for a Star with Magnetic Field
Xiaotong Suo McClure
Advisor: Professor Joel Smoller

An Analysis of Position Probability Distributions of Trilateration
and Triangulation for Extremely Deep Space Navigation
David McMillon
Advisor: Professor Mark Conger

Geodesics of Periodic Metrics on R2
Daniel Smolkin
Advisor: Professor Ralf Spatzier

Convergence and Error Bounds of the Trotter-Kato
Scheme for the HJB equation in a two-factor model
Howard Xu
Advisor: Professor Erhan Bayraktar0

Establishing Conditions for REM Cycling in Different Networks
Aparna Ananthasubramaniam
Advisors: Professors Cecilia Diniz Behn and Victoria Booth

A quantitative study of the triangulated molecular surfaces perturbations caused by small displacements of the atomic centers
Mo Bai
Advisor: Professor Weihua Geng

Dark Halo Orbits and Tidal Stripping With the Spirographic Approximation
Rebekah Bartlett
Advisor: Professor Anthony Bloch

Tumor Angiogenesis
James Brunner
Advisor: Professor Trachette Jackson

Mathematically modeling the light responses of ganglion-cell photoreceptors
Samuel Faught
Advisor: Professor Daniel Forger

Investigations of Coupled Oscillators
Kara Fulton
Advisor: Professor Richard Yamada

Computation of Equilibrium Measures and Other Quantities of Interest for Random Matricies
Asad Lodhia
Advisor: Professor Jinho Baik

Pattern Avoidence on Arch Connected Graphs
Benjamin Kornacki
Advisor: Professor Pavlo Pylyavskyy

Sums of Isometric Pairs of Lattices
Paul Lewis
Advisor: Professor Robert Griess

Impulse Control of MultiDimensional Jump Diffusions with Infinite Variation
Christopher Link
Advisor: Professor Erhan Bayraktar

Checking For Isomorphism in Circulant Graphs
Augustus Odena
Advisor: Professor Michael Zieve

REU Paper 2010
Claudia Raithel
Advisor: Professor Anthony Bloch

Characterization of the full degree 2 del Pezzo Surface over the field of nine elements
Daniel Smolkin and Erin Kelly
Advisor: Professor Amanda Knecht

On the 2D Orientation Preserving Crystallographic Groups
Kyle Sinclair and Pearce Washabaugh
Advisor: Professors Christopher Mooney and Ralf Spatzier

An Algebraic Approach to Conformal Eld Theory
Yang Xiu
Advisor: Professor Igor Kriz

Summer 2009

Affine Alternating Sign Matrices
Michael Bennett
Advisor: Professor Pavlo Pylyavskyy

A Universal Degree Bound for Rings of Invariants of n Point Configurations Modulo Torus Actions
Jonathan Brito
Advisor: Professor Benjamin Howard

A Mathematical Model of Tumor Growth and Angiogenesis
Akshay Desai
Advisor: Professor Trace Jackson

A Model of Suprachiasmatic Nucleus Firing Rate in the Rodent
Michelle Fleshner
Advisor: Cecilia Diniz Behn

Long Time Behavior of a Modified Becker-D¨oring System: Initial Conditions Without Compact Support
Lee Gunderson
Advisor: Professor Peter Smereka

Singularities of Logarithmic Potentials at Analytic Corners
Boaz Haberman
Advisor: Professor Divakar Viswanath

Algorithms for Threat Detection: An Inverse Boundary Value Problem
Casandra Hall
Advisor: Professor Selim Esedoglu

Analyzing Tori in Split Groups over Quasifinite Fields via Bruhat-Tits theory
Wade Hindes
Advisor: Professor Stephen DeBacker

Developing Stochastic and Deterministic Models of Quorum Sensing
Tyler Johnson
Advisor: Richard Yamada

The Recursive Computatibility of Hyperelliptic Hodge Integrals with at Least One 1 Class
Andrew Kiluk
Advisor: Professor Renzo Cavalieri

The Effects of Varying Connectivity Strength on the Frequency of Inhibitory Neurons in Several Network Types
Khalid Kunji
Advisor: Professor Victoria Booth

Reconstruction and prediction of chaotic signals
Xuan Liang
Advisor: Professor Divakar Viswanath

Improving the Upper Bound on Dirichilet L-Functions Induced by a
Character Modulo a High Power of a Prime
Christopher Link
Advisor: Professor Djordje Milicevic

Heegaard Splittings and Bounds for Closed Hyperbolic 3-Manifolds
Brian Mann
Advisors: Professors Richard Canary and William Breslin

Linear Factors and the Pollard Rho Method
Brian Nixon
Advisor: Professor Harm Derksen

The 100% Off Auction:
Daniel Russo
Advisor: Professor Tilman Borgers

Using periodic orbits to predict trajectories on the Lorenz attractor
Kirill Serkh
Advisor: Professor Divakar Viswanath

Approximating Dendrimer Bonding Site Locations
Stephen VandenBrink
Advisor: Professor Jack Waddell

The Thermodynamics of Solid Tumor Growth: A Continuum Mechanics Approach
Sarah Verner
Advisor: Professor Krishna Garikipati

The Caldero degenerations of the Grassmannian of 3-planes in 6-space and the positive tropical G(3,6)
Seth Wolbert
Advisor: Professor Benjamin Howard

Summer 2008

The Kernel of a Derivation on the Field of Rational Functions and the Zariski Closure of Local Integral Curves
Wade Hindes
Advisor: Professor Harm Derksen

Mathematical Models for Quorum Sensing in Vibrio harveyi and Pseudomonas aeruginosa
Kaytlin Brinker
Advisor: Professor Jack Waddell

Model of an Orexin Neuron
Katie Williams
Advisor: Cecilia Diniz Behn

Tropical Intersections and Shadow Points
Alex Larson
Advisor: Renzo Cavilieri

Coexistence of Multiple Parasitoids on a Common Host in a Globally Connected Metapopulation
Benjamin Berman
Advisor: Aaron King

Total Promotion
Kevin Dilks
Advisor: Kyle Peterson

Properties of Steady State Solutions for Critical Two-Layer Shallow Water Flows
Alfredo Wetzel
Advisor: Smadar Karni

Synchronization of Signaling Systems
Hasan Cheema
Advisor: Daniel Forger

An Equivalent Condition for the Reducibility of Tropical Curves
Brian Mann
Advisors: Hannah Markwig and Renzo Cavalieri

Generalising Cut and Join and Recursions of Hurwitz Numbers
Andrew Kiluk
Advisor: Renzo Cavalieri

Equidistribution of Descent-Like Statistics for the Hyperoctahedral Group
Laurie Lai
Advisor: Kyle Peterson

Summer 2007

Sub-game Perfect Equilibria of the Simultaneous Ascending Auction
Brian Baisa
Advisor: Professor Tilman Börgers

Steinberg Complexes and Affine Descents
Kevin Dilks
Advisor: Professors Kyle Petersen and John Stembridge

Action Potential Behavior in Hodgkin-Huxley and FitzHugh-Nagumo Models and Networks of O and I-cells
Stephen Gao
Advisor: Professor Victoria Booth

Optimization of Hydroelectric Pumped Storage: An Extension of Optimal Switching
Anthony Kuehne
Advisor: Professor Michael Ludkovski

Level Sets of the Takagi Function and Hausdorff Dimension
Zachary Maddock
Advisor: Professor Jeffrey Lagarias

Working with Maple
Anna M. Musial, Sam L. Rosenbaum
Advisor: Professor Arthur Wasserman

Two New Exceptional Quivers of Finite Mutation Type
Theodore Owen
Advisor: Professor Harm Derksen

Hyperelliptic Hodge Integrals
Peter Troyan
Advisor: Professor Renzo Cavalieri

Changes in Betti numbers of Hessenberg varieties on restricted tableaux
Derek Van Farowe
Advisor: Professor Julianna Tymoczko

Properties of Steady State Solutions for Shallow Water Flows
Alfredo Wetzel
Advisor: Professors Smadar Karni and Jorge Balbas

Ternary Basic Digit Sets
Christopher J. Young
Advisor: Professor Jeffrey Lagarias

Summer 2006 - 2003

Summer 2006

Ex-Post Equilibria in Games of Incomplete Information
Timothy McQuade
Advisor: Professor Tilman Borgers

The Gap Size Distribution of Parked Cars and the Coulomb Gas Model
Anthony Fader
Advisor: Professor Jinho Baik

Properties of the Takagi Function
Zachary Maddock
Advisor: Professor Jeffrey Lagarias

Virtual Cathode Simulation in 1D using a Grid-Free Poisson Solver
Ying Ki Yim
Advisor: Professor Lyudmyla Barannyk

Probabilistic Interpretations of Variables in Transient M/G/1 Random Walks
Drew Bollinger and David Wheeler
Advisor: Professor B.A. Taylor

Summer 2005

A Generalization of Conway Number Games to Multiple Players
Christopher Cunningham
Advisor: Professor Igor Kriz

Efficient And Accurate Unstructured Mesh Generation
Matthew Elsey
Advisor: Professor James Rossmanith

A Transformation Of A Standard Random Walk
Jason Goldstick
Advisor: Professor Joseph Conlon

Using Lattice Packings to Create Extended Codebooks
Daniel Sikora
Advisor: Professor Anna Gilbert

Directed Last-Passage Site Percolation with Bernoulli Site Distribution
Robert Hines
Advisor: Professor Jinho Baik

Dynamics of Interacting Point Charges and Vortices within a Constant Magnetic Field
Stephen Marin
Advisor: Professor Andrew Christlieb and Robert Krasny

Summer 2004

Momentum Matching for the Pendulum on Cart Problem
Esha Krishnaswamy
Advisor: Professor David Schneider

Linear Perturbations of a Class of Berezin-Toeplitz Operators
Adam Bendorf
Advisor: Professor Alejandro Uribe

New Results in Extremal Number Theory
Randolph Pistor
Advisor: Professor Kannan Soundararajan

Homeomorphism Groups of the Sierpinski Carpet and Sierpinski Gasket
Joel Louwsma
Advisor: Professor Bruce Kleiner

Computing Traveling-Wave Front Solutions in a Diffusive Predator-Prey Model
Brian Kim
Advisor: Professor Gregory Lyng

Inversions Within Restricted Fillings of Young Tableaux
Sarah Iveson
Advisor: Professor Julianna Tymoczko

Stabilization of Inverted Pendulum Systems
David Aristoff
Advisor: Professor Tony Bloch

An Overview of Green's Functions on Metrized Graphs
Douglas Li
Advisor: Professor Mattias Jonsson

Some R-tree Results
Jeremy Cook
Advisor: Professor Elmas Irmak

On a conjecture concerning non-intersecting congruence classes
Robert Hines
Advisor: Professor Kannan Soundararajan

The Problem of Type
Charles Crissman
Advisor: Professor Mario Bonk

The Likelihood of Cyclic Results in Pairwise Elections
Greg Malivuk
Advisor: Professor Divakar Viswanath

Summer 2003

Inverted Double Planar Pendulum on a Cart: Feedback Stabilization Using the Method of Controlled Lagrangians
David G. Aristoff
Advisor: Professor Anthony Bloch

A Mathematical Model of Receptor-Mediated Apoptosis: Fas Trimerization and FADD Recruitment
Ronald Lai
Advisor: Professor Trachette Jackson

The Temperly-Lieb Functions on Totally Non-Negative Matrices
Brendon Rhoades
Advisor: Professor Mark Skandera

Schur Positivity Conjectures about Temperly Lieb functions on Jacobi Trudi Matrices
Sean Gerrish
Advisor: Professor Mark Skandera

Dynamical Systems and Circle Maps
Ronit Slyper
Advisor: Professor Nikola Petrov

Bertrand J. Guillou
Advisor: Professor Andreas Blass