Summer Undergraduate Research Experience

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Since the spring 2000 semester the Mathematics Department has sponsored a number of summer research experiences (SURE) for a selected number of undergraduates math majors. The Summer Undergraduate Research Experience is aimed at current undergraduate math students in their junior year or advanced sophomores. The project ends with an oral presentation in the beginning of the fall semester. Therefore, you must be on the NY campus to present your work and fulfill the requirements of this project.

Funds to support this activity are limited and student participants are chosen by a faculty committee based on grades, coursework, and fit between their research interests and those of the supervising faculty. Applications are considered more highly if students have found a faculty mentor, a specific research project planned out, and have taken Analysis and Algebra. 

The application for Summer 2024 is now closed.
The application deadline was Monday, March 18.
Application decisions will be announced by Monday, April 15.

 

CLICK HERE TO ACCESS THE SURE APPLICATION

 

Summer 2024

Name(s)	Topic	Research Mentor(s)
Zhen Bobby Bao	Application of clock tracer and isentropic analysis to Moist Rayleigh-Bénard Convection	Dr. Olivier Pauluis
Ruixin Robert Chen	Zero Temperature Dynamics on Ising Systems on Hypercubes	Drs. Nina Holden & Chuck Newman
Anthony Dender	Order-Embeddability of Topological Posets into Hyperspaces using Non-Canonical Embeddings	Dr. Efe A. Ok
Zhenyu Hong	Numerical Method for Solving the Shallow Ice Approximation	Drs. Georg Stadler & Gonzalo Gonzalez de Diego
Shurong David Huang	Stochastic Interpolants and Score-Based Diffusion Models: Analysis and Optimization of Diffusion Coefficients	Dr. Jonathan Weare
Kevin Pan	Topological Data Analysis for Financial Time Series data	Dr. Jonathan Goodman
Tan Su	Characteristic Class— Milnors Exotic sphere and Chern-Weil Theory	Dr. Slyvain Cappell
Haoran Horace Sun	Investigation and Comparison on the performance of associated methods of Score Based Transport Modelling in solving Fokker-Planck Equation on large scale systems	Dr.  Jonathan Weare
Weiming Devin Tang	Fine-grained Analysis for the Phase Transition of Moment Matching, with Application in Infinite-Armed Bandit Problem	Dr.Yanjun Han
Ruimou Ray Wang	Simple Homotopy Theory Motivated by Whitehead Torsion	Dr. Syvian Cappell
Youxuan Wei	Optimizing Machine Learning Methods for Solving Singularities in Fluid Dynamics Equations	Dr. Tristan Buckmaster
Jiawei Jimmy Xu	A Functional Flow Mapping with Stochastic Interpolant	Drs. Mingtao Xia & Eric Vanden-Eijnden
Wenqi Xu	Exploring Parameter Sensitivity and Dynamic Behavior in the Head-Direction Ring Network	Drs. Zhe Chen & Alex Mogilner

 

Summer 2023

Name(s)	Topic	Research Mentor(s)
Yuang Hu	Toward the error analysis of a Markovian reduction of spiking neural networks	Dr. Zhuocheng Xiao
Xianyang Eric Hu	Classical quantile regression and 1D vector quantile regression	Dr. Alfred Galichon
Yiheng Roger Jiang	Wasserstein Gradient Flows with applications to Variational Inference	Dr. Jonathan Niles-Weed
Xinran Kevin Li	Utility-based Portfolio Construction with Options using Stochastic Approximation	Dr. Jonathan Goodman
Yingnan Leo Liu	Complex Algebraic Geometry and Kähler Geometry	Dr. Fedor Bogomolov
Nanye Willis Ma	Generalization of Diffusion Models by Extending Markov Chain Diffusion Process to Infinite Time steps: Exploring Connections with Stochastic Differential Equations	Dr. Saining Xie
Yiqi Rao	Dynamic Analysis of Dispersive Kuramoto-Sivashinsky Equation	Dr. Jonathan Goodman
Ansh Saxena	Proving an analogous result for imaginary part of logarithm of the zeta function using the methods provided in "Maximum of the Riemann Zeta Function on a Short Interval of the Criticial Line" by L.P. Arguin, D. Belius, P. Bourgade, M. Radziwill, K. Soundararajan	Dr. Paul Bourgade
Liyang Leon Shen	Algebraic geometry and Diophantine geometry: a survey of equidistribution in the case of quasi-projective variety and its application to Bogomolov's conjecture	Dr. Fedor Bogomolov
Jianliang Ye	Schramm-Loewner Evolution	Dr. Nina Holden
Kexin Zhang	Simulation on Schramm-Loewner Evolution	Dr. Nina Holden
Andrew Zhang	Asymptotics in high dimensional binary classification	Dr. Quang Vuong

Summer 2022

Name(s)	Topic	Research Mentor(s)
Ya Shi Zhang	Generalized Framework for Recursive Range Functions	Dr. Chee Yap
Kaiwen Tan	On the Well-posedness of Semi-linear Dispersive Equations	Dr. Ioakeim Ampatzoglou
Wenbo Bao	Monte Carlo Markov Chain Application in Bayesian Inferencete Carlo)	Dr. Michael Lindsey
Zihan Shao	Data-Driven Gravity Wave Parametrization in QBO-1D	Dr. Edwin Gerber
Zihan Zhang	Laboratory Iceberg Melts Down and Flips Over	Dr. Leif Ristroph
Gracie Zhou	Random Perturbations of Dynamical Systems	Dr. Yuri Bakhtin
Kitty Li	Simulating Sound on a Surface in 3D	Dr. Brennan Sprinkle
Chang Liu	Heawood Conjecture	Dr. Fedor Bogomolov
Kingsley Yeon	Deep Polynomial Approximation	Dr. Jonathan Goodman
Tong Zhao	Chaos and Dynamic Systems in Theta Model	Dr. Matteo Tanzi
Heng Wu	Diocotron Instability of Low-Density Non-Neutral Plasmas	Dr. Antoine Cerfon
Hongyi Zheng	Using Deep Neural Network Linear Embeddings to Represent Nonlinear Dynamics	Dr. Megan Morrison
Becky Bian	Adjusted Pair Trading Strategy with Geometric Brownian Motion to Altcoin Market	Dr. Leon Tatevossian
Ning Yu	Regularized time-crystal dynamics	Dr. Robert Kohn
Yan Liu	3-coloring problem	Dr. Fedor Bogomolov

Summer 2021

Name(s)	Topic	Research Mentor(s)
Tommenix Yu	A Non-Linear Contraction Theorem on Metric Posets	Dr. Efe Ok
Leyi Yan	The Exotic 7-Sphere	Dr. Sylvain Cappell
Linglai Chen	Adjoint DSMC (Direct Simulation Monte Carlo) Method for Spatially Inhomogeneous Boltzmann Equation	Dr. Yunan Yang
Wanzhou Lei	Numerical Methods for Wasserstein Natural Gradient Descent in Inverse Problems	Dr. Yunan Yang
Haiyang Wang	Special Linear Groups of Degree 2 over Finite Field: Group Algebras, Induced Projectors, Irreducible Projectors	Dr. Fedor Bogomolov
Jialiang Chen	Deep Reinforcement Learning for Portfolio Optimization	Dr. Kenneth Winston
Yang Zhang & Wenhan Yang	Convergence Analysis of Stochastic Gradient Descent on Overparameterized Neural Networks	Dr. Shuyang Ling
Zerui Ji	Mathematical Modeling of Confined Space Airborne Virus Transmission	Dr. Yury Ustinovskiy
Yucong Lei	Constructing surfaces with prescribed tangent planes	Dr. Robert Young
Frank Li	A Design of Autonomous Flapping Swimmers to Study Flow Interactions in Fish Schools	Dr. Leif Ristroph
Aolan Ding	Synchronization in Networks of Weakly Coupled Chaotic Rulkov Maps	Dr. Matteo Tanzi

Summer 2020

Name	Topic	Research Mentor
Amy Dai	Modeling and Simulation of Bacteria Population Dynamics using Markov Chain	Dr. Eric Vanden-Eijnden
Ron Nissim	Inverse Scattering and Riemann-Hilbert Problems	Dr. Percy Deift
Bob Junyi Zou	Optimal Transport Based Incomplete Data Clustering and Imputation	Dr. Esteban Tabak
Nhi Pham	Latent Factor Discovery in Markov Process through Optimal Transport	Dr. Esteban Tabak
Zan Ahmad	Mathematical Model for an Optimally Fenestrated Fontan Circulation	Dr. Charles Puelz & Charles Peskin
Zhijia Zhang	2D Stochastic Navier-Stokes Equations	Dr. Jalal Shatah
Yue Shi	Simulation on the Dynamics of the Trapped Ions with Laser Cooling	Dr. Antoine Cerfon
Yuanfan Wang	Analysis on the Stepped Pressure Equilibrium Model of Magnetically Confined Plasma in a Cylinder	Dr. Antoine Cerfon
Tianyi  Zhang	Existence of Localized Optical Vortex Solitons in Nonlinear Media	Dr. Luciano Medina
Yara Kyrychenko & Jason Rader	Methods and Applications of Numerical Matrix Inversion	Dr. Gerard BenArous
Junming Cui	Modeling the Development of Primary Visual Cortex	Dr. David McLaughlin
Xintong Zhu	Dynamics and Stability of Hula-Hoop Levitation	Dr. Leif Ristroph
Xinyu  Zhou	Étale Fundamental Groups and Curves in Positive Characteristic	Dr. Fedor Bogomolov
Zeyu Jing	Modeling of Auditory Perceptual Multi-Stability	Dr. John Rinzel
Yuepeng Wang	Learning Low-Dimensional Dynamical-System Models from Noisy High-Dimensional State Trajectories	Dr. Benjamin Peherstorfer
Zheng Wang	Optimal Experiment Design of a Spring-Kinetic ODE with DNN Estimators	Dr. Carlos Fernandez-Granda
Sihan Sienna Zhu	Robust cVaR Optimization with Artificial Bee Colony Algorithm	Dr. Kenneth Winston
Carol Long	Wasserstein_Barycenter_Applied_to_K-Means_Clustering.pdf	Dr. Yunan Yang
Yi  Lu	Marcov Representation of Voltage Gated Calcium Channels	Dr. David McLaughlin
Tanya Wang	Active Particles in Active Environments	Dr. Sophie Marbach
Rohit Pai	An analogue of Krasnoselskii’s theorem for Riesz spaces	Dr. Efe Ok

 

Summer 2019

Name	Topic	Research Mentor
Xinyu Li & Ziyu Lu	Stochastic Optimization Based Stochastic Optimal Control	Dr. Jonathan Goodman
Zhengyi Chen	Membrane Filtration with Complex BrancHing Pore Morphology and Elastic Sub-Branches	Dr. Pejman Senaei
Shiyue Liu	Diffusion Effects on Membrane Filtration Process	Dr. Pejman Senaei
Tiffany Li	Experimental Studies into Gliding and Soaring Flight	Dr. Leif Ristroph
Yuxiao Wen	Continuous Markov Chain Simulation on Turn-Based Games	Dr. Charles Peskin
Junyi Zou	Uncertainty Quantification of Edge Particle Flux in Magnetically Confined Plasma	Dr. Antoine Cerfon
Haitian Jin	Modeling of Simulation of Fetal Heart Circulation	Dr. Charles Peskin and Dr. DCharles Puelz
Joshua Tong	Shape Dynamics of Melting Ice at Temperatures Near Density Inversion	Dr. Leif Ristroph
Jack Messina	Whitehead Torsion of CW Complexes	Dr. Sylvain Cappell
Rahul Rajkumar	Branching Processes and a Model for Mitosis	Dr. S.R. Srinivasa Varadhan
Jiahao Ren	Solving General Lane Detection Through Special Clustering Via Nystrom Method and Hough Transform	Dr. Shuyang Ling
James Choi	Optimization of Feature Selection	Dr. Esteban Tabak

 

Summer 2018

Name	Topic	Research Mentor
Parthvi Bhutani	Markov Chains and Mixing Times	Dr. S.R. Srinivasa Varadhan
Jay Faris	Stochastically Modeling Vaccination on Scale-Free Evolving Networks	Dr. Lisa Hartung
Ruoming Gong	A Study of Quasicrystal with 12-folds and 18-folds Symmetry	Dr. Emilio Zappa
Yunqiu Guo	The Integrality of the K-Median Clustering Solutions When Input Data Has No Clustering Feature	Dr. Mutiara Sondjaja
Jaehoon Jung	Agent Trading-based Model of Stock Price	Dr. Jonathan Goodman
Yilun Song	Searching for Local Minima in a Random Landscape	Dr. Charles Newman and Dr. Daniel Stein
Jason Weitze	Variations of the Stochastic Block Model	Dr. Shuyang Ling
Jiayang Wang	Motion of High Energy Particly Beams in Cyclotrons	Dr. Antoine Cerfon
Jiaqi Xi	Optimal Transport in Spaces of Different Dimensions	Dr. Esteban Tabak
Jiadai Xia	The Impact of Financial Connectedness on Minimum Variance Portfolio	Joseph Cerniglia
Hongkang Yang	The Wasserstein Barycenter Problem as a Theoretical Framework for Categorical Clustering	Dr. Esteban Tabak

 

Summer 2017

Name	Topic	Research Mentor
Ling Lan and Zhengxu Li	Calibration of the Ross Recovery Theorem to Real-world Data, and Tests of its Practical Value	Dr. Robert Kohn
Zhijian Yang and Shiyu Zhang	A Confidence-based Bitcoin Pricing Model	Dr. Zsolt Pajor-Gyulai
Xinyi Cheng and Weiyi Lu	Analysis of Stochastic Gradient Descent	Dr. Gerard Ben Arous
Siqing Zhang	Two Results on Commuting Contractive Operators: Fixed Points and More	Dr. Efe Ok
Xinyuan Zhang	Trading European Volatility: VSTOXX Futures and ETNs	Dr. Marco Avellaneda
Giorgio Cocomello	Markov Chain and Markov Decision Processes	Dr. Srinivasa Varadhan
Jialin Mao	An Ensemble Version of the Preconditioned Crank Nicholson MCMC Sampler	Dr. Jonathan Goodman
Yunji Wu	How to find the correlation coefficient from only the S(t) values in a Heston Model	Dr. David Kelly
Pengcheng Han	Using Alternating Projection to Estimate Conditional Probability	Dr. Esteban Tabak
Nickolas Lewis	Ware-Driven Dispersion in Rotating Shallow Water	Dr. Shafer Smith
Nischal Mainali	Computer simulation of stringed instruments such as Guitar and Sitar	Dr. Charles Peskin
Yifeng Chen	A study on the performance and application of randomized matrix approximation	Dr. David Kelly
Samarth Tiwari	Limit Theorems for Metastable Markov Chains	Dr. Zsolt Pajor-Gyulai
Dan Simon	Network Reconstruction using Stochastic Block Models	Dr. Dennis Shasha
Anthony Isenberg	Vertically Averaged Velocity in Rayleigh-Benard Convection: A Numerical Approach	Dr. Michael S. Jolly, Indiana University

Summer 2016

Name	Topic	Research Mentor
Sanchit Chaturvedi	Numerical Solutions to ODE's Pertaining to Marcroscopic Stability of Plasma in a Cylinder with Magnetic Field	Dr. Antoine Cerfon
Benqi Chen	Discrete One-Dimensional System	Dr. Mark Wilkinson
Hong-Bin Chen and Zining Wang	Study of Percolation Theory, in Particular the Behavior of Invasion Percolation at the Critical Value Point in 3D	Dr. Chuck Newman
Monika Filipovska	Tropical Algebraic Geometry	Dr. Dmitry Zakharov
Xiaoyue Gong	A Unified Approach to Characterization of the Myerson Value and the Shapley Value Through Application of the Mobius Functions	Dr. Efe A. Ok
Dean Huang	An Investigation on Tesla's Valvular Conduit Design: Creation of a One-Way Valve with No Moving Parts	Dr. Leif Ristroph
Varun Kambhampati	On the Limitations of Mean Squared Error with Regards to the Analysis of Optimal Multi-Source Parameter Estimation	Dr. Dimitris Giannakis
Ildebrando Magnani	Stochastic Modelling in Macroeconomics	Boyan Jovanovic
Yi Mi	An Improved Monte Carlo Algorithm to Compute the Volume of a Shape in High Dimension	Dr. Miranda Holmes-Cerfon
Stephanie Sauma	Computer Simulation of the Violin	Dr. Charles Peskin
Andrei-Florian Stoica	Mathematical Modeling of the Glioma	Dr. Charles Peskin
Xizi Zhu	Particle Filtering in Finance and Problem of Degeneracy in Non-linear Context	Dr. David Kelly

Summer 2015

Name	Topic	Research Mentor
Sebastian Ament	Application of Generalized Gaussian Quadratures in Computational Statistics	Dr. Michael O'Niel
Tejas Devanur	Higher Order Terms in the Ergodic Theorem	Dr. Peter Nandori
Likhit Ganedi	Shape Evolution of Soap Films Under Aerodynamic Forces	Dr. Leif Ristroph
Junichi Koganemaru	Distributions with Applications to Partial Differential Equations	Dr. Pierre Germain
Hao Hua Li	A Diode for Flowing Fluids	Dr. Leif Ristroph
Ruinan Lu	Graph Theory Analysis of the Network of Genes in the Chromosome	Dr. Trushant Majmudar
Vadim Semenov	A Study of General Topology with Applications to Differentiable Manifolds	Professor Sylvain Cappell
Yiyang Shen	A Study of Stable Distribution and its Applications in Financial Data	Dr. Michael O'Niel
Huangyi Shi	Estimating the Invariant Probability Measure of Stochastic Differential Equations	Professor Yao Li
Raghav Singhal	A Study of Dynamical Processes on Complex Networks	Professor Lai-Sang Young
Ruitu Xu	Random Walks, Brownian Meanders and the Heat Equation	Dr. Peter Nandori
Hongtao Xue	Simulation and Comparison of Glycolysis in Normal and Cancer Cells	Professor Charles Peskin
Qiushi Zhang	An Investigation on Stochastic Volatility in Black-Scholes Model -- with Analytical and Numerical Approaches	Dr. Mark Wilkinson & Dr. Lisa Larsson
Tianze Zhou	Computer Simulation of the Clarinet	Professor Charles Peskin

Summer 2014

Name	Topic	Research Mentor
Mian Umair Ahsan	Algebraic Topology and Cohomology	Professor Sylvain Cappell
Alex Becker	Do Fluid Flows Matter	Dr. Leif Ristroph
Olivia Chu	Analysis of the "Euglenoid" Motion - locomotion by Shape Deformations	Dr. Trushant Majmudar
Taher Dahleh	Bosuk-Ulam Type Theorems and Their Applications to Combinatorics	Professor Sylvain Cappell
Yingjie Fei	A Numerical Investigation of the Time Evolution of Entropic Functionals for a Chaotic Dynamical System	Professor Richard Kleeman
Jonathan Friedman	Behavior of the Geometric Picard Ranks of Abelian Surfaces Over Q	Professor Yuri Tschinkel
David Goldberger	Exhaustive Lattice-Sampling for RNA Folding Prediction	Professor Tamar Schlick
Sam Jeralds	Distribution of Torsion Subgroups of Elliptic Curves Over the Rationals	Professor Yuri Tschinkel
Harshita Kajaria	Detecting Deterministic Nonlinear Dynamics in Financial Data	Dr. Trushant Majmudar
Junichi Koganemaru	Polar Rational Polygons and Vanishing Roots of Unity	Dr. Sophie Marques
Feier Li	Fast Algorithm for Kernel Density Estimation	Dr. Sivaram Ambikasaran
Thomas Mitchel	Evolving an Ideal Flapping Wing for Underwater Locomotion	Dr. Leif Ristroph
Ryan Moreno-Vasquez	Hydrogen Delocalization and Vibrational States of Ni(dmg) by a Discrete Variable Method	Dr. Margaret Mandziuk
Shaofei Sang	Stochastic Self-Folding of Cube from a Two Dimensional Net	Dr. Miranda Holmes-Cerfon
Zeyu Shen	Donsker's Theorem and its Extension to Local Time	Dr. Peter Nandori
Tobias Shin	Instability for Higher-Order Sigma-Delta Quantization Under the Greedy Quantization Rule	Dr. Sinan Gunturk
Janet Yi	Game Theoretic Approach to Trading Strategies -- Analyzing the Treasury Bond Futures Market	Professor Arun Sundararajan
Zhen Sun	Fast Algorithm on Radial Basis Function Interpolation	Dr. Sivaram Ambikasaran

Summer 2013

Name	Topic	Research Mentor
Anastasios Bountouvas	The Properties and Power of Benford's Law	Antti Knowles
Portia Chan	The impact of topography on the atmospheric circulation	Professor Edwin Gerber
Jianyu Chen	Application of Graph Theory to the Chemical and Electrical Networks of the Human Sleep-Wake Promoting System	Dr. Lisa Rogers
Han Hao	Models in Time Series: Review and Application of ARMA Models	Dr. Katherine Newhall
Tyler Herrmann	Defects and Galois groups of quartic polynomials	Professor Yuri Tschinkel
Gulnaz Jenish	Limiting Properties of Ising Model	Dr. Hana Kogan
Tessa Kelly	Model of Thermoregulation	Professor Charles Peskin
Saad Khan	Stochastic Modeling of Circadian Rythms	Professor Charles Peskin
Sunjeong Bonna Kim	Fluid Dynamics and Swimming of Microorganisms	Dr. Trushant Majmudar
Zhiran Li	Utility Maximization through Investment in Human Capital and Family Consumption	Dr. Lisa Rogers
Monty Liu	Stress Analysis Of An Ellipse Cut Along The Segment Connecting Its Foci Subject To Arbitrary Concentrated Boundary Forces	Dr. Trushant Majmudar
Jing Lu	Constructing a Potential Counterexample to Shafarerich Conjecture	Lukas Koehler
Colette Porter	clerotinia sclerotiorum Spore Spread Over Plant Arrays	Professor Charles Peskin
Stefan Stark	A Bayesian Approach to Free Energy Calculations	Dr. Mark Tuckerman
Steve White	A quantitative analysis of US charitable giving, 2004-2008	Dr. Thomas LaGatta
Ruida Xie	The Regime-Switching Vasicek Model	Dr. Hana Kogan
Serena Yuan	Topology Applied to Data Mining	Dr. Thomas LaGatta
Boyang Zhao	Spectrum Analysis of Violin and Piano Strings and the Assessment of Their Timbers	Antti Knowles
Daniel Zhou	Growth Processes Regulating the Double Helical Structure of the Human Cochlea	Dr. Lisa Rogers
Calvin Zhu	The Advantages of Minimizing Travel Time and Congestion by Optimizing Traffice Flow	Dr. Katherine Newhall

Summer 2012

Name	Topic	Research Mentor
John Carges	Group Structure of Elliptic Curves over Finite Fields	Professor Yuri Tschinkel
Zhuoxi Chen	Kingman's Subadditive Ergodic Theorem	Dr. Thomas LaGatta
Weilun Du	Connecting 3-D Heart Valve Model with Cardiac Circulation Model	Professor Boyce Griffith
Mildred Dwyer	Analysis of Metadata Correlations in the Mathematics Genealogy Graph	Dr. Thomas LaGatta
Keyue Gao	Real time version of splitting a pizza	Dr. Wesley Pegden
Pawel Gut	Full-Plane Appollonian Circle Packings With Respect to Residue Points	Professor Yuri Tschinkel
Saad Khan	Stochastic simulation of the mammalian circadian clock	Professor Charles Peskin
Yungjoo Lee, Timothy Mok, Haochuan Wang	Existence or non-existence of small amplitude flows in different fluid regions	Dr. Samuel Walsh
Xiaowei Wang	Stochastic Model for Describing S&P 500 Stock Progressions	Professor Marco Avellaneda
Zijun Wang	Introduction to Dirichlet Characters And The Proof of Prime Progression Theorem	Professor Yuri Tschinkel
Brandon Williams	Comparison of Stochastic and Deterministic Behavior in Predator-Prey Models	Professor Charles Peskin
Xiaojun Wu	Modeling of sleep-wake cycle	Dr. Lisa Rogers
Xu Yan	Truss Shape Optimization	Dr. Benedikt Wirth
Jing Ye	Predictability in Zero-Temperature Dynamics	Professors Charles Newman and Daniel Stein
Xuan Yu	Efficient Stochastic Investment Modeling: Review and Simulation of the Wilkie Model	Dr. Katherine Newhall

Summer 2011

Name	Topic	Research Mentor
Jack Amadeo	Computational Model for Particle Diffusion	Professor Aleksandar Donev
Jacob Carruth	The Kolmogorov-Smirnov Statistic in Goodness of Fit Testing	Dr. Rachel Ward
Jiayang Gao	The Efficiencies of the Root-Mean-Square and Power Divergence Statistics for Testing Goodness-of-Fit	Professor Mark Tygert
Jason Gruener	Simple Stochastic Gene Networks: The Random Basis of Random Cell Fate	Professor Daniel Tranchina
Michael Khanarian	Numerical Study of Schramm Loewner Evolutions in the Disordered Ising Model	Professor Charles Newman and Dr. Michael Damron
Sun Hyoung Sonya Kim	Embedding a Riemannian Surface in R^3	Dr. Thomas LaGatta
John Koo	Zero-Temperature Ferromagnetic Ising Models, Specifically the Chaotic Time Dependence of Infinitely Large Lattices	Professor Charles Newman and Professor Daniel Stein
Brian Law	On the Outcome of Elementary Graph Operations on the Hat Game	Dr. Wesley Pegden
Douglas McLaren	Survival of Mistaken Traders in Financial Markets	Professor Robert Kohn
Peter Wang	Dominating Sets	Will Perkins
Patrick Wilson	Developing and Understanding A Model of Cloud Formation in the Tropics	Professor Olivier Pauluis

Summer 2010

Name	Topic	Research Mentor
Lauren Bandklayer	On the stability for chaotic sigma-delta quantization	Dr. Rachel Ward
Clement Chan	Numerical Methods for tracer sigma-delta quantization	Professor Edwin Gerber
Zachary DeStefano	On the Torsion Subgroup of an Elliptic Curve	Dr. Sonal Jain
Corey Everlove	Alexander Polynomials of Knots and Links	Professor Sylvain Cappell
Jacob Hickey	Belyi functions with a limit on ramification	Professor Fedor Bogomolov
Chaney Lin	Deriving and interpreting Gopakumar-Vafa invariants	Dingyu Yang
Samantha Lozada	Glucose Regulation in Diabetes	Professor Charles Peskin
Michael Sharpnack	Stochastic Modeling of Prion Diseases	Professor Charles Peskin
Michael Weiss	Computing Grobner Bases in Python with Buchberger's Algorithm	Dr. David Harvey

Summer 2009

Name	Topic
Aukosh Jagannath	Further extensions of adiabatic invariant theory for charged particle motion
Shunxin Jiang	Random Walks with Correlated Steps
Stephanie Lewkiewicz	Winner-Take-All Neural Networks and Visual Search Tasks
Rachel Marano	Mathematical Modeling and Biological Systems: What are the effects of smoking on fetal and maternal circulation?
Trang Nguyen	Auction Theory: Risk-Return Analysis for Risk-Averse Seller.
Kelly Sielert	The Impact of Resolution on General Circulation Models
Dominick Villano	The effects of action potential backpropagation on precision coincidence detection in MSO neurons
Scott Yang	A Numerical Approach to Two and Three Dimensional Invasion Percolation

Summer 2008

Name	Topic
Daniel Parry	Bounds on Biased and Unbiased Random walks
Dhruva Chandramohan	Effects of Recurrent Excitation on Models for Perceptual Bistability
Iva Vukicevic	Error Bounds and Estimates for a Discrete Sine-Gordon Model
Ken Zhao	Barotropic Instability of Interacting Planetary Waves
Nitin Goyal	The Esophagus and Esophageal Diseases: A Mathematical Approach
Vinay Mahadeo	Constructing an Optional Filter for Nuclear Medicine Image Data

Summer 2007

Name	Topic
Charles Hankin	A One-Dimensional Dither Mask and Its Discrete Fourier Transform
Jessica Lin	A Theory of Induced Dynamics for Infinite-Dimensional Dynamical Systems
Richard Nelson & Priyam Patel	The World in a Tank: Simulating the Circulation of the Atmosphere and Oceans in a Laboratory Setting
Michael Ontiveros	Recursive Constructions of Sequences Not Containing Arithmetic Progressions
Sinziana Picu	PISM and Ice Dynamics

Summer 2006

Name	Topic
Jasmine Narody & Terri Scott	The mechanics of slithering: experiment and theory
Awad Ahmed	Analysis of environmental parameters in the Arctic terrain: depth, distance to coast, offshore wind
Henry Jacobs	Marangoni convection and temperature
Michael Harmon	Collision of paired vortices in two dimensions

Summer 2005

Name	Topic
Anna Mazover	Introduction of tensile strength to sea-ice modeling
Diana Tung	Lebesgue integration and measure
Erica Kim	Drop impact on various surfaces
Gabriel Shaykin	Modeling of Arctic sea ice
Gregory Fein	Representing groups through finite geometries
Tatyana Kobylyatskaya	Twisted Alexander polynomials of frame spun knots
John Adamski	Shooting pool in a non-Euclidean universe
Jonathan Keyes	Investigation in the field of adiabatic invariant theory
Kathleen Mareck	Elastic loop in a flowing soap film
Ryan Witko	"Easy as Pi"
Michael Kramer	A statistical approach to time course gene microarray analysis
Nathaniel Huebscher	Flow visualization of vortex structures produced by a flapping wing
Mehul Mehta	Statistical models and MCMC estimation

Summer 2004

Name	Topic
Thomas Ferriss	Steady-state models of glacial growth
Mike Greenberg	Applications of algebra to finite geometries
Shari Eli	Applications of the revenue equivalence problem
Marco Stillo	Integrate-and-fire neurons
Roy Han	The supervised learning problem
Tatyana Kobylyatskaya	Knotted tori in R^4
David Valdman	Surface involutions and gear mechanics
Uri Laserson	Discovering functional RNAs via RNA motifs
Andy Gewitz	Ergodic dynamical systems
Ryan Witko	Are Tracy and Widom in your local telephone directory?
Karishma Parikh	Experimental suspension dynamics of slender rigid rods

Summer 2003

Name	Topic
Sabera Asar	Quantification of the change in RNA secondary structure that occurs upon mutation
Jonathan Bober	On the Distribution of the Multiplicative Inverse in Finite Fields of Prime Order
Kamalijit Chowdhary	An Experiment in Rolling and Sliding Friction
Karma Cinnante	Simulation of Left Coronary Arterial Blood Flow
Adam Cone	Towards Modeling Neural Networks with Physiologically Different Populations: Constructing a Monte-Carlo Model
Sam Fryd	Characteristics of Ideal Magnetohydrodynamic Systems in Closed Volume
Ben Glaser	Applications of the SVD, CSD and GSVD Matrix Decompositions
Fareed Hawwa	The Science Behind Programming Traffic Lights in New York City
Patricia Tong	Extensions of Incomplete Contracts

Summer 2002

Name	Topic
Meredith Bergman	Mathematical modeling of HIV in population/body
Rachel Blumberg	Dynamics of viral infection in body and effects on population
Kamalijit Chowdhary	Fractal river basins, modeled by minimization of dissipation energy
Darin Comeau	Fractal geometry of Julia Sets & dynamical systems in the complex plane
Adam Cone	Mathematical modeling of the human visual cortex
Josué Díaz	Model volatility of derivatives and other securities
Teobaldo Fernandez	Spike-train patterns in the Primary Visual Cortex
David Lorentz	Computational modeling of the NMDA neuroreceptors in a network of neurons
Timothy Novikoff	Investigate the behavior of an "Integrate & Fire" model neuron receiving periodic pulsatile input
Hilary Sarneski-Hayes	Econometric study of equity index options
Vivek Hungund	Use fluid dynamics to determine movements of a mechanical snake in river
Joel Schlosberg	Study the topology of knots and links in 3-manifolds
Leonid Shteyman	Work on effective description of Galois group of polynomials
Brad Weir	Study algorithms in real algebraic geometry

 

Summer 2001/Fall 2001/Spring 2002

Alex Ancheta (VIGRE-supported) was a student in the new course, Mathematical Neuroscience, which Professors David McLaughlin and Michael Shelley offered in Spring 2001 -- a course designed to introduce undergraduate and graduate students to research topics in mathematical neuroscience. Dr. Louis Tao (a postdoc at the Courant Institute and the Center for Neural Science) assisted in the development and presentation of the course. The students also joined the visual neuroscience working group, attending the working seminar "Neural Tuesday." Alex began an undergraduate research project in summer 2001, which continued during the academic year and will continue into summer 2002. During the academic year, his research work will be applied toward an undergraduate honors thesis. The research project studies coarse-grained mean field approaches to global modeling of the primary visual cortex. The work began with a literature search to unveil coupling architectures between the cortical layers of V1, from anatomical laboratory observations. Alex then constructed the architecture of an idealized network and began the construction of a numerical model under the large-scale scientific computational guidance of Professor David Cai.

Rachel Blumberg studied mathematical modeling of epidemics and the evolution of gene frequencies under the pressure of natural selection with Professor Daniel Tranchina. Rachel studied both discrete-time and continuous time models with an emphasis on the formulation of equations and on their numerical solution. Rachel learned about first-order and second-order accurate methods for solving systems coupled nonlinear differential equations and how to implement these methods in Matlab. Other topics touched on include phase plane analysis, analytic solution of trajectories, and Monte Carlo simulations for small population sizes.

Darin Comeau (VIGRE-supported) worked with Professor Lai-Sang Young and William Cowieson (VIGRE Postdoc) in the summer of 2001. As a preparation he read Devaney's book "An Introduction to Chaotic Dynamical Systems" and successfully completed two projects. In the first, he worked out by himself, following hints from a book, a proof of Sarkovskii's Theorem. (Sarkovskii's Theorem is a well known theorem - with an elementary proof - concerning periodic behavior for one-dimensional maps.) The proof was written up formally in a report. Comeau's second project was to carry out a numerical study of the H\'enon maps. Using Matlab, he discovered a number of properties of chaotic attractors. Comeau is currently (Spring 2002) enrolled in an Independent Study course with Young and Cowieson. The topic for this course is the mathematical theory of fractals.