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.

The Summer 2013 S.U.R.E. application is now available. Applications will be due by Friday, March 22nd. All applications will be submitted to Beth Markowitz in Room 626, Warren Weaver Hall. You can bring them to her office, leave them in her mailbox on the first floor of WWH or email them to her at beth@cims.nyu.edu

Below are the student reports from previous years.

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

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.)