S.U.R.E. Program
Since the spring 2000 semester the Mathematics Department has sponsored a number of summer research experiences (S.U.R.E.) for a selected number of undergraduates math majors. The Summer Undergraduate Research Experience is aimed at advanced undergraduate math students in their junior year. The project ends with a written report and an oral presentation in the beginning of the fall semester.
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 and research topic.
Below are the student reports from previous years.
Summer 2014 The following undergraduate students participated in summer projects:
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  BosukUlam 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 LatticeSampling 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 MorenoVasquez  Hydrogen Delocalization and Vibrational States of Ni(dmg) by a Discrete Variable Method  Dr. Margaret Mandziuk 
Shaofei Sang  Stochastic SelfFolding of Cube from a Two Dimensional Net  Dr. Miranda HolmesCerfon 
Zeyu Shen  Donsker's Theorem and its Extension to Local Time  Dr. Peter Nandori 
Tobias Shin  Instability for HigherOrder SigmaDelta 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 The following undergraduate students participated in summer projects:
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 SleepWake 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, 20042008

Dr. Thomas LaGatta 
Ruida Xie 
The RegimeSwitching 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 The following undergraduate students participated in summer projects:
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 3D 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 
FullPlane 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 nonexistence 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 PredatorPrey Models 
Professor Charles Peskin 
Xiaojun Wu 
Modeling of sleepwake cycle

Dr. Lisa Rogers 
Xu Yan 
Truss Shape Optimization

Dr. Benedikt Wirth 
Jing Ye 
Predictability in ZeroTemperature 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 The following undergraduate students participated in summer projects:
Name  Topic  Research Mentor 
Jack Amadeo 
Computational Model for Particle Diffusion 
Professor Aleksandar Donev 
Jacob Carruth 
The KolmogorovSmirnov Statistic in Goodness of Fit Testing 
Dr. Rachel Ward 
Jiayang Gao 
The Efficiencies of the RootMeanSquare and Power Divergence Statistics for Testing GoodnessofFit 
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 
ZeroTemperature 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 The following undergraduate students participated in summer projects:
Name  Topic  Research Mentor 
Lauren Bandklayer 
On the stability for chaotic
sigmadelta quantization 
Dr. Rachel Ward 
Clement Chan 
Numerical Methods for tracer
sigmadelta 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
GopakumarVafa 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 The following undergraduate students participated in summer projects:
Name  Topic 
Aukosh Jagannath  Further extensions of adiabatic invariant theory for charged particle motion 
Shunxin Jiang 
Random Walks with Correlated Steps 
Stephanie Lewkiewicz  WinnerTakeAll 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: RiskReturn Analysis for RiskAverse 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 The following undergraduate students participated in summer projects:
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 SineGordon 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 Undergraduate Research Experience (S.U.R.E.) and R.E.U. student presenters, October 17, 2008.
Summer 2007 The following undergraduate students participated in summer projects:
Name  Topic  
Charles Hankin  A OneDimensional Dither Mask and Its Discrete Fourier Transform 

Jessica Lin 
A Theory of Induced Dynamics for InfiniteDimensional 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  
Robert Simione 
An Alternative to Least Squares 
Summer 2006 The following undergraduate students participated in summer projects:
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 

Michael Kramer 
Nanocantilever biosensor design and analysis  
Michael Gordon 
Structural strengths of shells in nature  
Julia Spencer 
Dimer models 
Summer 2005 The following undergraduate students participated in summer projects:
Name  Topic  
Anna Mazover  Introduction of tensile strength to seaice 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 nonEuclidean 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 The following undergraduate students participated in summer projects:
Name  Topic  
Thomas Ferriss  Steadystate models of glacial growth  
Mike Greenberg  Applications of algebra to finite geometries  
Shari Eli  Applications of the revenue equivalence problem  
Marco Stillo  Integrateandfire 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 The following undergraduate students participated in summer projects:
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 MonteCarlo 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 The following undergraduate students participated in summer projects:
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  Spiketrain 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 SarneskiHayes  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 3manifolds  
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 (VIGREsupported) 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 coarsegrained 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 largescale 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 discretetime and continuous time models with an emphasis on the formulation of equations and on their numerical solution. Rachel learned about firstorder and secondorder 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 (VIGREsupported) worked with Professor LaiSang 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 onedimensional 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.
David Lorentz (VIGREsupported) was another student in the Mathematical Neuroscience course offered by Professors McLaughlin and Shelley in spring 2001. David then began an undergraduate research project in summer 2001, which continued during the academic year and will continue into summer 2002. The research project involved a study in cortical visual processing of the effects of a slow receptor (NMDA) and its comparison to the much faster AMPA receptor. First, models of the nonlinearity of the NMDA receptor were studied and developed  comparing the accuracy and efficiency of different representations for use in largescale neuronal network models. The work involved literature searches, computational modeling, and postprocessing. David is currently developing an idealized network of simple and complex cells  comparing the relative effects of AMPA and NMDA receptors on the neurons' performance characteristics.
Tim Novikoff (VIGREsupported) was a third student in the Mathematical Neuroscience course offered by Professors McLaughlin and Shelley in spring 2001. Tim also began his undergraduate research project in summer 2001, which continued during the spring semester 2002 into summer 2002. His research project began with a study of the theoretical mechanisms behind the nonlinearity of the NMDA receptor. It then turned to the construction of very idealized models of neuronal networks with both simple and complex cells present, in which the performance of phased averaged networks were compared with that of networks with selective coupling mechanisms which produce inhibition in "pushpull" antagonism to excitation.
Patricia Tong (VIGREsupported) worked with Professor Robert Kohn and two graduate students, Oana Fainarea and Pedro Judice, on a problem of optimal investment strategies using options. Her project addressed the following question: consider an investor who wishes to speculate on a stock by buying call options rather than the stock itself. How should this investor decide which calls  i.e. which strike prices  to buy? In giving this problem a mathematical formulation, Tong was led to read about the BlackScholes theory of option pricing and the Capital Asset Pricing Model of portfolio optimization. But she also learned that the answer did not lie in these standard tools alone. With further modeling, she did find a suitable answer, which she is now writing up (with Kohn's guidance) in a form suitable for publication. Patricia participated in an REU at Worcester Polytechnic Institute during Summer 2002.
Brad Weir worked with Professor Richard Pollack on "Algorithms in real Algebraic Geometry." In fall 2001, Brad worked through the first chapter of the book of the same title. He has digested the Lefschetz principle (quantifier elimination over algebraically closed fields and the associated transfer principle. This spring he will start thinking about problems related to the TarskiSeidenberg principle (quantifier elimination over real closed fields) and the basic topology of semialgebraic sets.
Elizabeth Zollinger (VIGREsupported) worked with Professors Charles Newman of the Courant Institute and C. D. Howard of Baruch College on simulations of certain dependent percolation models arising from interacting particle systems and cellular automata. After a preparatory period in spring 2001, in which Elizabeth learned about percolation and interacting particle systems, the project itself began in summer 2001 and continued in fall 2001 and spring 2002. (Elizabeth received VIGRE support during all these periods.)