Summer Undergraduate Research Experience

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.




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.