URA Research Project Ideas
What follows is a list of some of the project topics that faculty members in the department of mathematics have suggested as suitable for undergraduate research projects. Students who wish to participate can register and receive credit for an independent study or may be able to obtain URA funding to get paid to work on these projects.
Details of the project requirements will be worked out between the faculty supervisor and the student. Some of these projects require little background and are suitable for freshmen or sophomores, while others require knowledge of linear algebra, ordinary differential equations, or group theory. This list is by no means exclusive: any student with a particular interest in some area of research is encouraged to seek out a faculty supervisor. Students are encouraged to contact the URA Program Coordinator for help finding a suitable faculty research mentor.
Looking for examples of undergraduate research? The Honors College maintains a repository of past honors thesis submissions; use the Advanced Filters to search by discipline (Mathematics or Statistics & Data Science). It may also be helpful to look at past MathFest Student Papers, as well as SUnMaRC abstracts.
Students participating in undergraduate research for credit must submit a proposal form through the math academic office. Stop by the window at Math 108 once you have lined up your project advisor and topic.
Project ideas list is not exhaustive  there are additional faculty who are interested in working with undergraduates that have not provided information to us.
If a project has not been updated in a long time, check the professor's homepage to see what they have been working on most recently. Research areas tend not to change drastically.
Name  Research Area(s)  Prerequisites  Honors Thesis?^{*}  URA for Credit?  URA for Pay?**  Last Updated 

Numerical Simulation of Waves in Optics, fluids and solids. 
introductory numerical analysis, basic physics/optics and computer programming. 
Yes 
Yes 
No 
9/7/2021 

statistical mechanics, artificial intelligence, computer graphics 
ability to program  Yes  Yes  No  8/16/2022  
Karl Glasner  Pattern formation on graphs; view description.  ODEs, Linear Algebra, experience with MATLAB. Ideally one or more of: Graph Theory (math 443), Dynamical Systems (math454), PDEs (math456), Numerical Methods (math475)  Yes  Yes  Ask 
1/17/2017 
Karl Glasner  Dynamics of self assembly at the nanoscale; view description.  ODEs, some experience with MATLAB. Ideally one or more of: Dynamical Systems (math454), PDEs (math456), Numerical Methods (math475).  Yes  Yes  Ask 
1/17/2017 
Developing computer software to visualize abstract geometries and polyhedral geometries (like the dodecahedron). Study of differential equations that deform arbitrary embeddings of graphs into "nice" embeddings for graphs. 
Basic linear algebra, differential equations. Topology can be a plus, but not necessary. General mathematical sophistication. Some computer science/programming background is a plus. 
Yes 
Yes 
Yes 
9/17/2012 

Mainly number theory, although I have worked with undergrads on a variety of topics outside of number theory.  None  Yes  Yes  No  8/25/22  
Analysis of partial differential equations (PDE) and/or ordinary differential equations related to PDE  Math 313, Math 355, perhaps a bit of coding, Math 425 is a plus  Yes  Yes  Ask  8/16/2022  
Geometry: Study the space of three and four point configurations on the (projective) plane.

good command of Linear Algebra 
Yes 
Yes 
Ask 
1/3/2017 

Tom Kennedy  Selfavoiding random walks. More detail at : math.arizona.edu/~tgk/undergrad_research_s19  Math 464. Some programming experience would be helpful, but not required.  Yes  Yes  Yes  12/2/2018 
Nonlinear dynamics; Monte Carlo methods; machine learning.

Minimum prerequisites are the calculus sequence, linear algebra (313), and differential equations (254 or 355). Some probability (363 or higher) a bonus, and 464 and/or 454 would be great but not required. Programming ability or willingness to learn by doing a must.  Yes  Yes  Maybe  9/2/2021  
Computational Group Theory; 
413 Linear Algebra or 
Yes 
Yes 
Maybe 
9/18/2012 

Random matrix theory (general theory, modeling applications)  Undergrad probability sequence, measure theory (intro level), basic coding (e.g., MATLAB, python, Julia)  Yes  Yes  No  8/25/22  
Douglas Pickrell  (On sabbatical in 2022  not available). power series identities; conformal mappings  linear algebra, complex variables.  Yes  Yes  Maybe  9/7/2021 
Walter Piegorsch  Statistical inference; Quantitative risk analysis  MATH 466; DATA 467  Yes  Yes  No  9/2/2021 
Robert Sims  Mathematical Physics; also see Dr. Sims' website  Linear Algebra and Differential Equations  Yes  Yes  No  8/16/2022 
Doug Ulmer  Number theory, algebraic geometry, possibly cryptography.  Abstract algebra required. Some geometry and/or complex analysis would be helpful.  Yes  Yes  Yes  9/2/2021 
Aparna Upadhyay  Group Theory; Representation Theory, Combinatorics  Math 313, Math 323, Math 415A  Yes  Yes  No  9/9/2022 
Shankar Venkataramani  Differential equations and modeling physical phenomena; Geometry and applications; Problems in Complex analysis 
Math 254/Math 355 (for Differential equations); Math 323 (for all the problems); MATH 425 (for Complex analysis). 
Yes  Yes  Yes  9/12/2014 
Weinan Wang  Fluid dynamics; Partial Differential Equations; COVID19 related PDE models  Real analysis; advanced partial differential equations  No  Yes  Ask  8/16/2022 
Hang Xue  Number Theory, Representation Theory  solid background in linear algebra and abstract algebra  Yes  Yes  No  8/16/2022 
*Honors Thesis MATH 498H credit available to students in the Honors College.
**Restrictions may apply. Ask the individual faculty member for details.