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VIGRE
at the Undergraduate Level
At the undergraduate level, our goal is to attract more students
into the mathematical sciences broadly construed. The following
programs will enhance recruitment of undergraduates, enrich their
educational experience, and allow them to make contact with mathematical
research in the junior and senior years:
- Special Pre-research Courses to prepare undergraduates to participate
in research projects.
- Research experiences (REU) for undergraduates, including summer
research internships.
Vigre funds also partially support the Mathematics-Education
Internship Program and the Mathematics
Content Program for Teachers.
Student Comments on their Research Experiences
Research
Experiences - Summer 2007:
| Mentor(s) |
Student(s) |
Title of Paper |
| Andrea Bertozzi, Zhipu Jin, and Rick Huang |
Trevor Ashley |
Boundary estimation and video tracking |
| Martin Short |
Arash Fayz and Ying Vuong |
Crime modelling and data |
| Todd Wittman |
Meiching Fong |
Dimension reduction on hyperspectral images |
| Todd Wittman |
Zhong Hu |
Gradient Free Boundary Tracking |
| Todd Wittman |
Vicknesh Selvam |
Hyperspectral TV Denoising and Inpainting |
| Martin Short |
Kenn Tevin |
Realistic movement of burglars in crime simulation code |
| Thomas Ward |
Rob Glidden |
Gravity driven effect in flowing particle laden thin films |
| Richard Elman |
Keith Merrill |
Gelfand-Schneider Theorem |
| John Garnett |
Jin Du |
The Fourier Transform, Finite Fourier Analysis, Dirichlet's Theorem |
| Robert Brown |
Adam Ericksen and Matthew Stimpson |
Fixed Points on n-valued multimaps of tori |
| William Duke and John Leo |
Hooman Sherkat-Massoom |
Fourier Coefficients of Triangle Functions |
| Alan Laub |
Ilina Sandler |
Numerical Linear Algebra |
| Alan Laub |
Ani Astrian |
Statistical Condition Estimation, Matlab Coding |
| Martin Short |
Megan Miller |
Crime modelling and data |
| Virginia Pasour |
Sudeep Desai |
Crime modelling and data |
| Virginia Pasour |
Brian So |
Effect of Socioeconomic Health on Burglary Hotspots |
| Seshadri R. Thiruvenkadam |
James Von Brecht, David Hwang, Howard Wang, and Aaron Chen |
Video Tracking |
Research
Experiences - Summer 2006:
| Mentor(s) |
Student(s) |
Title of Paper |
| Russ Caflisch |
Jeffrey Hyman |
Report on Monte Carlo Sampling |
| Maria D'Orsogna |
Jon Azose |
Video of crime hotspots on Jeff Brantingham's Website |
| Young-Ju Lee, Xiaobin Niu, Russel Caflisch, and Christian Ratsch, |
Jason Reich |
Lateral and Vertical Segregation in Thin Alloy Films |
| Thomas Ward |
Asher Metchik |
Viscous fluid mixing in a tilted tank by periodic shear |
| Tony Chan and Seshadri R. Thiruvenkadam |
James von Brecht |
Occlusion tracking with Logic Models |
| A. L. Bertozzi, Y. R. Huang, and A. K. Leung |
Vlad Voroninski |
Robotic path planning and visibility with limited sensor data |
| A. L. Bertozzi, Y. R. Huang, and A. K. Leung |
Vlad Voroninski |
A second generation micro-vehicle testbed for cooperative control and sensing strategies |
| Chad M. Topaz and Andrew J. Bernoff |
Wyatt Toolson |
A model for rolling swarms of locusts |
| Carmeliza Navasca |
Ani Asatryan, Vatche Attarian, Abhijeet Joshi, Vlad Voroninski, Meghdi Aboulian, and Krystle McBride |
Implementations of control laws for motion camouflage in a pursuit-evasion system |
| Alex Chen and Andrea Bertozzi |
Meiching Fong and Zhong Hu |
Hyperspectral Imaging |
| James White |
Johnny Hong |
Looking at Manifolds |
| James White |
Matthew Stimpson |
Manifolds, Special Relativity, and a Hint of General Relativity |
| Ronald Miech |
Shaddi Ramezan |
Frequency Distribution of the English Alphabet |
| Robert Brown |
Adam Ericksen and Keith Merrill |
Classification of Endomorphisms of Fundamental Groups of Certain Aspherical Spaces |
| Tony Chan |
Boris Gutman |
3-D Surface Registration via Spherical Cross-CorrelationApplied to Surface Conformal Mapping |
| James Ralston |
Josh Story |
Inverse Spectral Theory |
| Thomas Ward |
Chi Wey |
Particle Laden Flow |
Research
Experiences - Summer 2005:
| Mentor(s) |
Student(s) |
Title of Paper |
| John Garnett |
George Basilio |
Picard's Little and Great Theorems |
| Ronald Miech |
Pablo Bert |
A Binomial Identity |
| Tony Chan |
Boris Gutman |
Hippocampal Surface Analysis using Spherical Harmonic Function applied to Surfacr Conformal Mapping |
| T.V. Singh and P. Korambath |
Kathryn Hymes |
Optimization Techniques in a Medical Imaging Statistical Analysis Tool |
| Geoffrey Mess |
Jenny Lam |
Differential Topology |
| Mark Hansen and Robert Gould |
Aromalyn Magtira |
Disability Due to Alcohol Consumption |
| Dimitri Shlyakhtenko |
Jesus Oliver |
Entropy Approximations and Hausdorff Dimension |
| James Ralston |
Andrew Sanders |
Phase Portrait Analysis of General Predator-Prey Models |
| Chris Anderson and Christian Ratsch |
Jianliang Zhang |
Probability Study of a KMC Simulation in Expitaxial Growth |
| J. Ostroy |
Hao Zhou |
Utility Function with Gross Substitute Condition |
| Andrea Bertozzi and Marc Droske |
Ruchi Varma |
Generating Vector Fields for Images |
Research
Experiences - Summer 2004:
| Mentor(s) |
Student(s) |
Title of Paper |
| Ronald Miech |
Teng Gao |
Some Numerical Results for the 2D Lorentz
Lattice Gas Model |
| Peter Petersen |
Christopher Lyons |
Normal maps of minimal surfaces |
| Kartik Prasanna |
Sean Rostami |
Composition of Binary Integral
Quadratic Forms |
| Ker-Chau Li |
Shannon Stock |
Scouting Genes in C. elegans
Heat Shock Data |
| Ronald Miech |
Alexander Leung |
Survey of Pension Funding Methods:
Private Sector Pension Plans in U.S. |
| Esedoglu, Vese and Chan |
Tal Sansani
Raymond Taylor |
Various Methods in Digital Image
Segmentation |
| Gregory Hjorth |
Marcus Vasquez |
Topological Groups |
| Bryan Ellickson |
Mahdi Raghfar |
Application of the Capital Asset Pricing
Model in the Banking Industry |
| Chad Topaz |
Catherine Beni |
Network Spreading of Epidemics |
| Andrea Bertozzi |
Bao Nguyen |
Virtual Attractive-Repulsive Potentials for
Cooperative Control of Second Order Dynamic Vehicles on the Caltech MVWT |
| Andrea Bertozzi |
David Tung |
Experimental Implementation of an Algorithm
for Cooperative Searching of Target Sites |
| Andrea Bertozzi |
Chung Hsieh |
Experimental Validation of an Algorithm for
Cooperative Boundary Tracking |
Research
Experiences - Summer 2003:
| Mentor(s) |
Student(s) |
Title of Paper |
| Kovchegov/Miech |
Teng Gao |
Some Numerical Results for the 2D Lorentz Lattice Gas Model
|
| T. Liggett |
Andrew Hanh
Vytas Baskauskas |
Integral Forms with Polynomial Functions |
| P. Roberts |
Xin Jia |
Methods for Two-Point Boundary Value Problems
|
| R. Brown |
Ryan Rowe
Jason Wang |
Simplifying Small Scale liner
programming problems: Stricly Intercepts |
| R. Miech |
Juan Romero
Jennifer Lai
Adriana Contreras
Karina Hernandez |
Adventures with Randomly Generated Numbers
|
| B. Ellickson |
Thomas Chen |
Searching for Stochastic Volatility
to Incorporate in Capital Asset Pricing Model |
| J. Garnett |
Christopher Lyons |
Analytic proof of the prime number theorem
|
| G. Hjorth |
Isaac Goldbring |
On the Independence of the Continuum Hypothesis
|
| C. Anderson |
Jessica Baumwoll |
Compression Using Discrete Cosine Transform |
| Belin and Wong (Miech) |
Shannon Stock |
HLA-DRB1 Genotype Associations in a
Recent-Onset Rheumatoid Arthritis Inception Cohort |
| J. Ralston |
Matthew Kucera |
Snell's Law and the Wave Equation |
| Belin and Wong (Miech) |
Ryan Rosario |
Types and Doses of HLA Type Alleles
and Their Effect on Severity and Susceptibility of Rheumatoid Arthritis
|
| A. Garfinkel |
Diana Tran |
The Interation of Maps of the Interval:
The Key to Sudden Cardiac Death |
Research
Experiences - Summer 2002:
| Mentor(s) |
Student(s) |
Title of Paper |
York Marahrens
(Assistant Professor of Human Genetics) |
Elena Allen |
Chromosomal Context Identifies
Two Categories of Allelically Excluded Genes
(submitted to Science as a full length paper)
|
|
Bryan Ellickson
(Professor of Economics<) |
Franco Armando |
A Study of the Top Capitalization
Stocks Using the CAPM Model |
|
James Ralston
|
Isaac Goldbring |
On the Success of the
Competitive Exclusion Principle |
|
Don Blasius
|
Piper Harris |
Schoof's Algorithm for
Counting Points on an Elliptic Curve
|
|
Don Blasius
|
Sarah Hipschman |
Elliptic Curves and the
Mordell-Weill Theorem |
|
Paul Roberts
|
Matthew Kennedy |
Stability
of a Mushy Layer |
Ronald Miech
|
Phuong Le
Hayato Ono |
Ozone Depletion and Ultra
Violet Radiation |
Daniel Krashen
(VIGRE Assistant Professor of Mathematics) |
Daniel Lindsey |
Finding Grobner Bases for an
Ideal in a Multivariable Poly Ring |
Rita Cantor
Adj Assoc Professor
Human Genetics |
Isaac Mayhew |
Bioinformatics Lab Aide |
Bryan Ellickson
Professor of Economics |
Michael Montgomery |
A Moving Beta Analysis of the
S & P 500 |
Ronald Miech
|
John Pastor
Sarah Hipschman |
An Introduction to Bifurcation
Through Differential Equations |
| Ronald Miech |
Marla Mattensen
Hsien Liang Tseng |
Why Knot? How Knot Theory
Applies to the Analysis of Enzymatic Action on DNA |
Ronald Miech
|
Janelle Rodriguez
Jiji Varghese |
Some Promising Models for
the Population Dynamics of Parasitemia of Malaria |
Don Blasius |
Michael Slawinski |
Commutative Algebra |
| Chris Anderson |
Derek Urwin |
Adaptive Selection of Data
Points for Higher Order Approximation Techniques |
Rodolfo DeSapio
|
Jeremy Werner |
A Theorem on Invariance of
the Domain |
Research
Experiences - Summer 2001:
| Mentor(s) |
Student(s) |
Title of Paper |
| Ted Gamelin |
Jamar London, I-Shen Lai |
Buckyballs and Mathematics |
| Ricardo Perez-Marco |
Haiming Chu,
Luke Zheng, Phillip Buendia |
Second Degree
Polynmial Iteration modulo m |
| Ricardo Perez-Marco |
Tony Kim |
Henon Attractor |
| Christoph Thiele |
Julia Nudel |
A Polytope |
Kirby Baker
Doreen DeLeon |
Andrew Pappin |
Genetic
Algorithms and Annealing |
| Russel Caflisch |
Cheng Ly |
Analysis
of a qubit system |
| Jon Rogawski |
Shadi J. Jahangir |
Comparison
of Public Keys |
| Richard Elman |
Michael VanValkenburgh |
Transcendental Numbers |
| Kefeng Liu |
Linmei Cao |
Geometry |
Research
Experiences - Summer 2000:
| Mentor(s) |
Student(s) |
Title of Paper |
| Russ Caflisch |
Steve C. Hill |
Automatic Mesh refinement for
the island dynamics/level method |
| Russ Caflisch |
Jennifer Garcia |
Computational studies of kinetic
Monte Carlo and level set |
| Peter Petersen |
Edward Mi Fan |
Geometry of Polyhedra |
Peter Petersen
|
Xiaopeng Hu |
Geometry of Polyhedra |
| Peter Petersen |
Kim Nhat Ha |
Geometry of Polyhedra |
| James Ralston |
Mitra Afshani |
Geometric Optics and Energy Transfer
in Reflections |
| Christoph Thiele |
Carole E. Akl |
1D Schroedinger Operators |
Luminita Vese
Tony Chan |
Roya Furmuly |
Matching of objects in dimension one by energy
minimization |
|
Luminita Vese
Tony Chan |
Narineh Movsessian |
Matching of objects in dimension
one by energy minimization |
These undergraduate research experiences play a key role in exposing students
to research topics early in their studies.
2004 Research Project with CalTech Multi-Vehicle Wireless Testbed
Sample publications from undergrad research:
- C. Hsieh, Z. Jin, D. Marthaler, B. Nguyen, D. Tung, A. Bertozzi, and R. Murray,
"Experimental validation of an algorithm
for cooperative boundary tracking"(2004) submitted to the
American Control Conference 2005
- D. Tung, B. Q. Nguyen, C. H. Hsieh, Y. L. Chuang, Z. Jin, L. Shi, D. Marthaler,
A. L. Bertozzi, and R. M. Murray, "Experimental
implementation of an Algorithm for Cooperative Searching of Target Sites"
(2004) submitted to the American Control Conference 2005
- B. Q. Nguyen, Y-L Chuang, D. Tung, C. Hsieh, Z. Jin, L. Shi, D. Marthaler,
A. L. Bertozzi, R. M. Murray, "Virtual
attractive-repulsive potentials for cooperative control of second
order dynamic vehicles on the Caltech MVWT" (2004) submitted to the
American Control Conference 2005
- C. Ratsch, Jennifer R. Garcia, "Effect of Edge Diffusion
for Growth on a Vicinal Surface" (2002)
- C. Ratsch, M. Gyure, R. Caflisch, F. Gibou, M. Petersen, M.
Kang, Jennifer R. Garcia, and D. Vvedensky, "Level-Set
Method for Island Dynamics in Epitaxial Growth"(PDF File),
Phys. Rev. B 65, 195403 (2002)
View
Student Comments:
Learn more about students and their undergraduate research experiences.
Post-doctoral
| Graduate | Undergraduate
| Research Clusters | Lecture
Series | UCLA Math Vigre Program
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