Undergraduate Research

The School of Mathematics at Georgia Tech has a rich tradition for undergraduate research. The projects have been mentored by many different faculty, on topics ranging from fad formation, to random walks, tropical geometry, one bit sensing, extremal graph theory, and convex polyhedra. Our students have published many papers, have won a number of awards, and have been very successful in their graduate school applications. For a sample of the past projects please see below. 

In Summer 2018 there will be several research opportunities available for undergraduates.In particular, there may be projects on the following topics:

  • John Etnyre Colorings of knots
  • Mohammad Ghomi: Geometry of curves and surfaces
  • Caitlin Leverson: Legendrian knots and matrices
  • Wenjing Liao: Machine learning and signal processing
  • Galyna Livshyts: Discrete and convex geometry / Asymptotic and harmonic analysis
  • Dan Margalit: Mapping class groups and polynomials
  • Molei Tao: Numerical optimal control

To complement the research projects, the School of Mathematics will also hold professional development sessions on relevant topics, such as:

  • How to create and present a poster
  • What is graduate school like?
  • Applying to graduate school

Undergraduate researchers will also have access to poster sessions and other activities sponsored by the College of Sciences.

The typical research project lasts approximately 6 weeks, in June and July, although the exact timing is negotiable and can be worked out between students and their mentors. There will be a summer stipend, and there is affordable housing available on campus. More details can be found at the FAQ page.

How to Apply Online

Interested students should apply here. The deadline for applications will be February 28th, 2018. Decisions will be announced by March 31, 2018. If you have any questions about the program, or about undergraduate research in general, please contact Igor Belegradek or Dan Margalit.


Research Experiences for Undergraduates at Georgia Tech

Spring 2018 GT REUs

Mentor Student Topic
Dan Margalit Yihan Zhou (GaTech) Algorithms for Mapping Class Groups
Sung Ha Kang Hyunsu Park (GaTech) Curvature Constraint Path Optimization

Fall 2017 GT REUs

Mentor Student Topic
Dan Margalit, Balazs Strenner Shreyas Casturi (GaTech) Simplifying Curves on Surfaces
Jonathan Chen (GaTech)
Vignesh Raman (GaTech)
Kyle Xiao (GaTech)

Summer 2017 GT REUs

Mentor Student Topic
Doron Lubinsky Andrea Martinez* (GaTech) Orthogonal Polynomials
*The work resulted in this poster
Robin Thomas Rose McCarty* (GaTech) Colin de Verdiere Invariant of Graphs, and the Extremal Function for Bipartite Linklessly Embeddable graphs

*The work resulted in these two papers #1, #2, the research helped Rose secure admission

to the graduate program in the Combinatorics and Optimization Department at the University of Waterloo,

a top program in the field.

Josephine Yu Catherine Chen (GaTech) Matroid Theory and Tropical Geometry**
Nhu Do (Mt Holyoke)
Devraj Duggal (GaTech)
James Anderson* Pseudo-Equivalence Classes of Line Arrangements

*James Anderson's work resulted in this poster

**The work of Chen, Do, and Duggal resulted in this poster

Mohammad Ghomi Nicholas Barvinok* (U Michigan) Unfoldings of Convex Polyhedra
*The work resulted in this paper
Sung Ha Kang Jun Xiang (GaTech) Video and Image Restoration with Atmospheric Turbulence Distortion
Sayem Hoque (GaTech)
Caitlin Leverson Hunter Vallejos* (GaTech) Augmentations of Legendrian Knots and Links
*The work resulted in this poster
Christian Houdre Ken Adams (GaTech) A Computational Study of the Longest Common Subsequences in Random Words
Dan Margalit Libby Taylor (GaTech) The Second Johnson Homomorphism
Matt Baker Regular and Oriented Matroids*
*Libby presented her work at Dalton State College in Fall 2017, presented at the JMM in San Diego and her work resulted in a paper (in preparation)
Jen Hom, Sudipta Kolay Shiyu Liang (Jilin University) Non-left-orderable Surgeries on 1-bridge Braids*
*Shiyu's work resulted in this paper

Summer 2017 GT REU: Mapping Class Groups 

Supervisor: Professor Dan Margalit

Mentors Student Topic
Becca Winarski Sarah Davis** (GaTech) Symmetric Mapping Class Groups and the Symplectic Group*
Laura Stordy (Agnes Scott)
Queena Zhou*** (GaTech)

*The work resulted in this poster which was presented at JMM 2018 Undergraduate Poster Session

**Sara Davis presented the work at Tech Topology Conference, Georgia Tech, Dec 2017

***Queena Zhou was awarded the Spring 2018 Travel President's Undergraduate Research Award

Justin Lanier Santana Afton (William & Mary) Big Mapping Class Groups*
Sam Freedman (Michigan)
Liping Yin (Ga State)

*The work resulted in this poster which was presented by Santana and Sam at MathFest 2017,

for which they received an Outstanding Presentation Award

Balazs Strenner Ian Katz (Gatech) Nielsen-Thurston Classification Algorithms*
Yandi Wu (Berkeley)
Yihan Zhou (GaTech)

*The work resulted in this poster which was presented by Yandi at MathFest 2017 and YMC 2017, and received the Outstanding Presentation Award at MathFest 2017, and the work also resulted in this paper.


Summer 2017 GT IMPACT REU 

Supervisor: Professor Michael Lacey

Mentors Student Topic
Robert Kesler, Scott Spencer Bryson Kagy (GT) One Bit Sensing: Phase Transitions for the RIP Property*
Amadou Buh (Perimeter College at Georgia State University)
Emily Smith (Agnes Scott College)
*The work resulted in this poster and the work was presented at the JMM in San Diego
Andre Souza, Michael Northington Alison Madson (GT) Chaos in Lorentz Attractor
Korynn Claiborne (Alabama State University)
Jade Rice (University of Miami)
Samuel Hood (Morehouse University)
Spring 2017 GT REUs
Professor Student Topic
Sung Ha Kang Sayem Hoque Anisotropic Diffusion and Counting
Fall 2016 GT REUs
Professor Student Topic
Sung Ha Kang Sayem Hoque Anisotropic Diffusion and Counting

Summer 2016 GT REU: Geometric Group Theory

Supervisor: Professor Dan Margalit

Mentors Student Topic
Justin Lanier and Shane Scott Sarah Butchko* (Indiana) Algebraic Geometry and Geometric Group Theory
Ryan Dickmann** (GaTech)
Charles Wang*** (GaTech) Gemetric Combinatorics

*Sarah went on to grad studies at GaTech

**Ryan went on to grad studies at Utah

***Charles Wang won the Robert A. Pierotti Memorial Scholarship and the 2017 Love Family Foundation Scholarship (highest undergraduate award at Georgia Tech), and published two papers paper#1/paper#2. Charles went on to grad studies at Berkeley


Summer 2016 GT IMPACT REU

Supervisor: Professor Christine Heitsch

Mentors Student Topic
Megan Bernstein  Ibrahim Apata (Morehouse College) RNA Folding
*The work resulted in this poster
Heather Smith Ida De Vierno (Georgia Tech) Meanders*
Isabella Nang (Georgia State University)
*The work resulted in this poster
Megan Bernstein  Chelsea Huston (Spelman College) RNA Secondary Structures*
*The work resulted in this poster
Torin Greenwood Jason Kolbush (Georgia Tech) RNA Secondary Structures*
Taylor Strickland (Agnes Scott College)
*The work resulted in this poster
Spring 2016 GT REUs
Mentors Student Topic
Mohammad Ghomi Biao Ma* (Jilin U., China)  
Tianhao Xian** (Jilin U., China)
*Biao went on to graduate school at Iowa
**Tianhao went on to graduate school at Cornell
Matt Baker Yang An* (Xi'an Jiotong University) Canonical Representatives for Divisor Classes on Tropical Curves and the Matrix-Tree Theorem
Yao Wang** (Xi'an Jiotong University) The Bernardi Process and Torsor Structures on Spanning Trees

*Yang's work resulted in this paper, and helped in securing entry to the graduate program at Columbia

**Yao's work resulted in this paper, and helped in securing entry to the graduate program at Princeton

Michael Damron Thomas Koelle* (GaTech) Random Walks and Electrical Networks
*The work resulted in the presentation of this paper and an appointment to be an Undergraduate Research Ambassador
Sung Ha Kang Nick Selby* (GaTech) A Dynamical Model for Color Trend and Fad Formation
Sayem Hoque (GaTech) Anisotropic Diffusion and Counting
Kumbit Hwang (GaTech) Graph Representation and Numerical Algorithm

*Nick Selby won the Best Oral Presentation Award, 11th Annual Undergraduate Research Symposium, CoS, Spring 2016

Fall 2015 GT REUs
Mentors Student Topic
Sung Ha Kang Kumbit Hwang* (Gatech) Graph Representation and Numerical Algorithm
Chris Kwan (GaTech) Data Clustering and K-means
Sayem Hoque (GaTech) Analysis of Applied Physiology Wheel Chair Data
*Kumbit Hwang won the Best Junior Undergraduate Award, SoM, Spring 2016
Igor Belegradek Zixin Jiang* Smoothness of Minkowsi Sum and Generic Rotations
*The work resulted in this paper, and Zixin went on to grad school at Berkeley
Summer 2015 GT REUs
Mentors Student Topic
Kirsten Wickelgren Brandon Boggess* Splitting Varieties for Cup Products with Z/3-Coefficients
*The work resulted in this publication

Summer 2015 GT IMPACT REU:

Applied and Computational Mathematics plus Computational Science and Engineering

​Supervisors: Professor Sung Ha Kang and Professor Haomin Zhou

Mentors Student Topic
Christina Frederick Rosahn Bhattari (Georgia State University) Numerical Analysis
Jamese Lewis (Spelman College)
Austin Little (Morehouse College)
Maryam Yashtinin Veronica Fulton* (Spelman College) Image Processing
Michael Mbaba (Morehouse College)
Rachel Shore (Agnes Scott College)
*Veronica F Fulton received the 1st Place Oral Presentation Award, April, 2016 Spelman College Research Day.
Spring 2015 GT REUs
Professor Student Topic
Sung Ha Kang Sayem Hoque (GaTech) Analysis of Applied Physiology Wheel Chair Data
Fall 2014 GT REUs
Professor Student Topic
Mohammad Ghomi Alena Kim (Alabama School of Fine Arts)  
Leonid Bunimovich Soek-Joo Chae (GaTech) Social Networks*
*The work resulted in this paper
Spring 2014 GT REUs
Professor Student Topic
Sung Ha Kang Chenxing Wang (Xi'an Jiotong University) Total Variation, Heat Equation and Edge Detection Using Mumford-Shah Functional
Lin Li (Xi'an Jiaotong University)
Summer 2013 GT REUs
Professor Student Topic
Yuri Bakhtin Andrew Travis Rogers Invariant Distributions for Systems with Random Switchings
Jeff Geronimo Andrew Pangia Toeplitz Matrices and Bivariate Orthogonal Polynomials
Mohammad Ghomi Arun Jambulapati (U. Tennessee) Foldability of Prismoids
*Arun went on to Stanford Graduate School in Mathematics
Spring 2013 GT REUs
Professor Student Topic
Sung Ha Kang Tyler Cox* (GaTech) Heart Flow Simulation Using RKHS
*Tyler Cox won the Undergraduate Award, SoM, Spring 2013
Summer 2012 GT REUs
Professor Student Topic
Yuri Bakhtin Gautam Goel* Burgers Equation with Random Forcing
*Gautam won the Goldwater Scholarship and went on to grad school at Cal Tech
Ernie Croot Nicholas Dunn Improving the Performance of Algorithms to Solve the Knapsack Problem
Wilfrid Gangbo Ross Granowski* Boundedness Properties of Michell Trusses
*Ross independently submitted this paper, and Ross went on to grad school at Princeton
Mohammad Ghomi Andrew McCullough Polyhedral Approximation of Surfaces and the Gauss-Bonnet Theorem
*Andrew was accepted to the GaTech Mathematics Graduate Program
Klara Grodzinsky Andrea Crews Determining the Most Beneficial Teaching Style: PLUS Leaders vs. TAs
Doron Lubinsky Nguyen Vy Universality Limits for Arcs of the Unit Circle
Dan Margalit Peter Woolfitt Entropy Versus Word Length
*Peter went on to grad school at UGA
Tom Morley Roger Mercanti A Study of Roll over - A Combinatorial Game
Doug Ulmer Sam Kim Elliptic Curves, Group Representations, and Lattices
Xingxing Yu Qiqin (Jill) Xie Kuratowski's Theorem
Sung Ha Kang Tyler Cox (GaTech) Cardiac MR Image Segmentation Using Reproducing Kernel Hilbert Spaces and Total Variation Minimization
Fall 2011 GT REUs
Professor Student Topic
Sung Ha Kang Joshua Liu (GaTech) Partial Segmentation and Tracking
Summer 2011 GT REUs
Professor Student Topic
Silas Alben Brittany Smith Optimal Crawling of a Three-link Snake
Matt Baker Melanie Dunn Tropical Implicitization
Jean Bellissard Jon Paprocki Applications of Cuntz-Krieger Algebras to BPS State Counting
Ernie Croot Sean Murphy Hidden Markov Models and Speech Recognition
Jeff Geronimo Howard Tong One and Two Variable Orthogonal Polynomials
Christine Heitsch David Esposito Improved RNA Secondary Structure Prediction Using Stochastic Context Free Grammars 
Christine Heitsch Stephen Nanney Analyzing Optimality Criterion for RNA Secondary Structures Prediction
Plamen Iliev Andrew McCullough Spectral and Self-dual Properties of Krawtchouk Polynomials
Michael Lacey Ross Granowski Toward a Geometric Estimate of the Haar Coeffcients for the Periodically Shifted Halton-Hammersley Set in Four Dimensions
Anton Leykin/Josephine Yu Henry Duong Numerical computation of tropical curves
Doron Lubinsky Trevor Loranger Polynomials that are Biorthogonal to a Fixed Set of Exponentials
Tom Morley Kathleen Sickler Variations on Chomp
Prasad Tetali David Hollis Classical Questions in Computational Complexity Theory, with Focus on Circuit Complexity for Bipartite Matching and Other Problems
Doug Ulmer Mahadi Osman Purity of Gauss and Jacobi sums
Spring 2011 GT REUs
Professor Student Topic
Sung Ha Kang Jacob Yongtaik Mok (GaTech) Biological Particle Tracking Algorithms
Summer 2010 GT REUs
Professor Student Topic
Silas Alben Michiel Shortt Some Interesting Variants on the Thomson Problem
Matt Baker Melanie Dunn Plotting Tropical Curves
Igor Belegradek Melanie Stam* Families of Hyperplanes in the Real and Complex Hyperbolic Plane
*Melanie went on to grad school at Cornell
Jean Bellissard James (Greg) Douthit Computation of the Spectrum of the Fibonacci Hamiltonian Using Bloch Theory
Jean Bellissard Jonathan Paprocki Phason Modes in Quasicrystals
Leonid Bunimovich Mark Bolding Rewiring in Dynamical Networks
Ernie Croot David Hollis Deterministic Methods to Find Primes
David Lowry
Jeff Geronimo Philip Benge Parameters Associated with Bivariate Bernstein-Szego Measures
Plamen Iliev Michael Qin Admissible q-Difference Operators in Two Variables
Tom Morley John Cummings Computations in combinatorial games
Prasad Tetali Harrison Brown Graph Homomorphisms and a Graph Polynomial Conjecture
Xingxing Yu Michelle Delcourt Sum-set Bounds on Graphs
Sung Ha Kang Elisa Trejo (GaTech) Data Clustering and Mathematics
Kevin Lewis* (GaTech) Anisotropic Diffusion and Imaging
MRI and Ultrasound and Transforms
*Kevin Lewis won the PURA Award (President's Undergraduate Research), Spring 2011
Spring 2010 GT REUs
Professor Student Topic
Sung Ha Kang Trevor Siu (GaTech) Imaging System and Medical Imaging
Summer 2009 GT REUs
Professor Student Topic
Silas Alben Leo Chen Stability of an Elastic Sheet with Vortices
Reginald McGee Optimizing a Fin Ray for Strength
Yuri Bakhtin Dustin Burns  
Ernie Croot Nathaniel Chen Number of Problems About Whether Certain Sets Contain
Arithmetic Progressions
William Drobny Counting the Number of Lines that Intersect an n x n Lattice
in Exactly k Points
Christine Heitsch Joshua Anderson Discrete Mathematics Applied to mRNA Codon Variation and Folding Kinetics
Plamen Iliev Hau Chan Orthogonal Polynomials Satisfying Second-order Difference Equations
Doron Lubinsky John Reinhardt Second and Higher Order Differential Equations Associated with Orthogonal Polynomials
Henry Matzinger Vladimir Kolesov Analysing Responses to a Questionnare by Using Decision Trees
Tom Morley Ben Sirb Investigations in Game Theory
Prasad Tetali Aisha Arroyo G-Parking Functions of Special Graphs
Maria Westdickenberg
Sung Ha Kang 
Jing Cui* (Agnes Scott College) Anisotropic Diffusion and the Perona-Malik Scheme
Chuya Guo* (Agnes Scott College) Numerical Methods for Isotropic and Non-isotropic Diffusion, Including Total Variation Denoising
Tarik Trent (Emory University) Shock Filter and Variational Models for Image Deblurring, Including the Case of Non-isotropic Blur Kernels
Janatta Washington (Spelman College) Principal Component Analysis, SVD and Image Analysis
Yingfei Yi Racheal Lunde Modeling, Simulation, and Analysis of Chemical Reactions with Applications to Cell-biology
*Not funded by NSF grants
Summer 2008 GT REUs
Silas Alben Daniel Yancey Effect of Fin Shape on the Dynamics of Flexible Rubber Fins in a Flow Tunnel
Josh Anderson Collective Motions of Magnetic Swimmers
Kevin Spears (math/bio) Modeling Synchronous and Metachronal Swimming of Krill
Matt Baker Stefan Froehlich Brill-Noether Theory for Graphs
Daniel Connelly Green's Functions for Mandelbrot-like Sets
Yuri Bakhtin Spencer Nettleton Directed Polymers in Random Environment
Igor Belegradek Cindy Phillips* Complex Hyperbolic Plane in Cylindrical Coordinates about the Real Hyperbolic Plane
*Cindy went on to grad school at U Arizona
Johan Belinfante William Drobney Zorn's Lemma
Luca Dieci Abhishek Pandey Exploration of the Deterministic and Stochastic Van Der Pol Equation
Christine Heistch Nicole Larsen Enumerating Pseudoknotted RNA Structures
Doron Lubinsky Nicholas McKibben Sanders Curious q-series on the Unit Circle
Tom Morley Patrick Brandt Markov Chains and Music
Prasad Tetali Robert Glenn On Sampling Spanning Trees with no Broken Circuits
Hao Min Zhou/Shui-Nee Chow Fei He Computations of Stochastic Different Equations for Oscillators
Summer 2007 GT REUs
Ernie Croot Aisha Aroyo Develop Basic Integer Factoring Algorithms
Jonathan Eisen Improve Upon More Basic Integer Factoring Methods
John McCuan Arthur J. Friend
Rob Ward
Exotic Capillary Tubes (ordinary differential equations, physics and mean curvature)
Prasad Tetali Brian Benson G-parking Runctions and Acyclic Orientations of Graphs
Fall 2006 GT REUs
Mohammad Ghomi Arthur J. Friend* (GaTech)  
*Arthur went on to obtain his PhD from Stanford
Summer 2006 GT REUs
Matt Baker Dragos Ilas On the Abel-Jacobi Map from a Graph to its Jacobian
Ander Steele* Carmichael Numbers in Number Rings

*Ander independently published this paper based on his REU research, and

won GaTech Sigma Xi Undergraduate Research Award in 2006

Johan Belinfante Lee Martie GOEDEL
Shui-Nee Chow D. Andrew Brown Study of Control of a Nonlinear System Modeling a Terrorist Attack
John Etnyre Gokhan Civan* Invariants Derived from the Contact Homology Eifferential Graded Algebra
*Resulted in this publication
Mohammad Ghomi Robert Vincent DeMarco* The Four Vertex Theorem and the Extension of its Converse to the Sphere
Brian Nakamura** Alexandrov's Conjecture

*Robert went on to work for the NSA

**Brian went on to obtain his PhD from Rutgers

Lew Lefton Darshan Bryner The Homology of 17-Crossing Knots: A Computational Approach to Knot Theory
Doron Lubinsky Beth Hart Rodrigues formulae for biorthogonal polynomials
John McCuan Steven Britt
Laura Stilz
A Mathematical Framework for Paper Folding
Tom Morley Garrett Thompson Searching for Periodicity in the Game of Officers
Emanuel Indrea Markov Chains and Traffic Analysis
Robin Thomas Masanori Koyama An Algebraic Approach to a Graph Choosability Problem
Yang Wang Brian Benson An Analysis of the Three Hat Problem
Summer 2005 GT REUs
Matt Baker Ander Steele Carmichael Numbers in Abelian Extension Fields
Matt Baker Matthew Tanzy Minimizing the Effective Resistance Energy on a Graph
Johan Belinfante Claudia Huang Automated Reasoning Assistant GOEDEL and Peano's Arithmetic
Ernie Croot Brian Williams Small roots of polynomials modulo squarefree numbers
Brian Swanagan Determining Lower Bounds for Differences of Powers of 2 and 3 Using Pade Approximations
Jeff Geronimo Nick Cotton Numerical Analysis of an Epsilon-Difference Equation
C. Houdré, L. Peng Alexander Block Credit Risk Modeling
Lew Lefton Darshan Bryner Parallel Computing in Various Mathematical Algorithms
Yingjie Liu Carina Saxton Simulation of Plankton Ecosystem Dynamics in Oceans
Doron Lubinsky Ioana Soran Orthogonal and Biorthogonal Polynomials
John McCuan Alan Diaz A Geometric Method for Measuring the Structure of Optical Fibers
Peter Mucha A. J. Friend A Local Community Detection Algorithm for Weighted Real-world Networks
Tom Trotter Bill March On-line Coloring of Interval Graphs
Yang Wang Charles Martin Basic Digit Sets: Investigations and Applications
Summer 2004 GT REU
Shui Nee Chow Caroline Seabrook 
Stephanie Chung
Pattern Formation
Ernie Croot Bayazid Sarkar Fermat Numbers
John McCuan Jeffrey Elms Soap Films in Corners
Mason Porter
Leonid Bunimovich
Julie Bjornstad 
Alexie Dachevski
Mathematical Biology
Dana Randall Brittany Hughes Markov Chains
Robin Thomas Matt Perry Topics in Graph Theory
Hou Min Zhou Robert Pruvenok Image Processing
Mohammad Ghomi James Krysiak (Penn State)  
Zachary McCoy (Penn State)
Summer 2003 GT REUs
Shui-Nee Chow/Mason Porter Jeremy Corbett Numerical Work in Spatial Temporal Chaos
Michael Lacey Brandon Luders
Alex Charis
Additive Number Theory
Peter Mucha Casey Warmbrand Political Network Theory
Thomas Callaghan Football Network Theory
Mason Porter Steven Lansel Computer Simulation of Billiard Systems
Robin Thomas Michael Abraham Topics in Graph Theory
Summer 2002 GT REUs
Peter Mucha Michael Abraham Small World Networks, on the Bewoulf Cluster
John McCuan Roberto Lopez
Jeffery Elms
ACE Lab, Electrostatics
John Pelesko Ryan Hynd ACE Lab, Electromagnetics
Joe Landsberg Erika Norenberg Morse Theory
Joe Montgomery Degenerate Gauss Maps on Algebraic Varieties
Johan Belinfante David Eger Artificial Intelligence
Xingxing Yu Jeremy Barrett Algebraic and Topological Aspects of Graphs
Prasad Tetali David Skoog Random Codes
Margaret Symington Andy Wand* Contact Topology
*Andy is currently a professor at Glasgow
Anthony Yezzi Ganesh Sundaramoorthi Electrostatics Charge, Image Segmentation
Prasad Tetali Boris Kerzhner Random Codes
Summer 2001 GT REUs
Evans Harrell Clark Alexander Convex Geometry
Chris Heil Nick Bronn Time Frequency Analysis
Michael Lacey Nick Bronn Sets avoiding Arithmetic Progression
Prasad Tetali Blair Dowling Elliptic Curves, Cryptography
Brendan Nagle Erika Norenberg Hypergraphs
Johan Belinfante Tack Soo Im Automated Reasoning