Courant Institute New York University FAS CAS GSAS

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. To apply for this program please click here to find the application.

Below are the student reports from previous years.

Summer 2015 The following undergraduate students participated in summer projects:

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 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 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 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 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 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 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 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 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 The following undergraduate students participated in summer projects:

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

SURE 2010

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 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
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 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 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 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
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
Nano-cantilever 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 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 The following undergraduate students participated in summer projects:


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 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 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 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 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.

David Lorentz (VIGRE-supported) 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 large-scale neuronal network models. The work involved literature searches, computational modeling, and post-processing. 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 (VIGRE-supported) 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 "push-pull" antagonism to excitation.

Patricia Tong (VIGRE-supported) 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 Black-Scholes 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 Tarski-Seidenberg principle (quantifier elimination over real closed fields) and the basic topology of semialgebraic sets.

Elizabeth Zollinger (VIGRE-supported) 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.)