Undergraduate Research Project Topics
This page contains a list of possible research project topics provided by members of the department who may be interested in supervising undergraduate research students in the near future. This includes undergraduate research awards and MATH 498 projects. This list is not exhaustive. Other department members not listed here may also be interested in supervising undergraduate students; see the research interests on the list of department faculty members. Department members who would like to add, delete or edit their entry on this page should contact Jon Noel.
| Name | Topic |
| Research in undergraduate math education. | |
| Analytic aspects of probability and stochastic processes, including Stein's method and its generalizations. | |
| Statistical ecology or population health: projects typically involve simulation studies or Bayesian modelling using R software with applications to fisheries, ecology, or health. | |
| Combinatorial structures related to graphs, set families, matrices and permutations. | |
| Mathematical logic (including model theory, set theory, and computability theory) and its applications to problems concerning topology and operator algebras. Most projects involve only a subset of these topics, and prior experience with mathematical logic is not required. | |
| Heath Emerson | C*-algebras and Representation Theory of Groups. Topics in Mathematical Finance. |
| Structural and algorithmic aspects of graph theory | |
| Graph theory, algorithms and complexity, discrete-time graph games, math in sports, and math education. A sample project is to determine conditions under which it is possible to generate all systems of distinct representatives (SDRs) of a set system so that consecutive SDRs differ in the representative of one set. Equivalently, determine conditions under which the graph whose vertices are the SDRs and two of them are adjacent if they differ in the representative of one set has a Hamilton cycle. | |
| Projects involve the development and application of statistical methods to neuroscience and brain imaging data. Students may work on problems related to functional connectivity, high-dimensional data analysis, or Bayesian modeling of complex signals. | |
| Biostatistics, Spatial Statistics, Bayesian Statistics, Bioinformatics and Health Applications. | |
| Discrete Math with connections to probability, analysis, computer science, optimization and statistical physics. Specifically, maximization and minimization problems involving the number of small "patterns" in large graphs, tournaments, permutations, etc. | |
| Can supervise students interested in dynamical systems or probability. | |
| Probability theory, Statistical mechanics, Mathematical physics, Coding theory | |
| The algebraic theory of quadratic forms is an elegant and well-established subfield of algebra that aims to investigate the classification of quadratic forms (i.e., homogeneous polynomials of degree 2) over general fields. Over the real or complex numbers, the classification problem is rather trivial, but over fields of greater arithmetic complexity the situation becomes much more interesting, revealing deep connections to a number of fundamental topics in contemporary algebraic geometry, including algebraic groups and homogeneous varieties, algebraic cycles and K-theory, motives and motivic homotopy theory. The study of quadratic forms, as well as closely related algebraic structures such central simple algebras and hermitian forms, therefore represents a beautiful and concrete access point to the forefront of modern algebra and algebraic geometry. | |
| Statistics. |