Below is a list of some possible undergrad research projects in our group. The list is current as of August 2019. Note that due to time limitations, I can't start working with students simultaneously on all these projects. This list is to give you an idea of some of the things we work on and help you compare those with your interests and academic background.

Blue crab population dynamics

Blue crabs form the most valuable fishery in the Chesapeake Bay, so there is a lot of interest in predicting their future population. Complications include harvesting/fishing, changing weather/climate, and cannibalism of juvenile blue crabs by adults. A current student has developed a blue crab model and is working on it in the 2019-20 academic year. It may be possible to work with this student to start learning the model and develop your own research questions about blue crabs this academic year, with a more intense time commitment in Summer 2020. For example, a possible research topic is the effect of the parasite Hematodinium on blue crab populations, and how that will change as the climate changes.
Important skills: Knowledge of differential equations (such as from MATH 302 or MATH 345)
Background reading: See Tim Becker's honors thesis for some background and a much earlier version of our model.

Oysters

The Eastern oyster is an important species in the Chesapeake Bay. It is a valuable fishery, oysters filter and clean up the water, and oyster reefs form habitat for other organisms. Oyster populations in the Bay have drastically declined (to about 1% of their historic levels), so there is great interest in restoring oyster reefs. We have been modeling oyster populations for a while but there are still many open questions, especially related to the spatial arrangement of oyster reefs. We have recently been trying to answer some of these questions by analyzing aerial imagery of oyster reefs.
Important skills: Knowledge of differential equations (such as from MATH 302 or MATH 345) and/or knowledge of GIS
Background reading: Jordan-Cooley et al 2011, Rachel Wilson's honors thesis

Stochastic extinction in coupled populations

Biological populations interact with each other across space, and they are also subject to a fluctuating environment. How do environmental fluctuations combine with other aspects to determine a population's vulnerability to extinction? We are trying to answer this using a simplified model inspired by oyster populations.
Important skills: Knowledge of differential equations (such as from MATH 302 or MATH 345), knowledge of a programming language, and willingness to write simulations.
Background reading: Ovaskainen and Meerson 2010

Polio spread and control

Despite vaccination, polio remains endemic in three countries. A proposed treatment strategy is to administer defective interfering particles (DIPs), which are modified viruses that can't cause infection on their own but compete with the wildtype virus for resources. During the initial infection with polio virus, and initial treatment with DIPs, the number of virus particles is small and stochastic effects will be important. How does the infection become established in these early stages, and what is the best strategy for treating with DIPs?
Important skills: Knowledge of a programming language and willingness to write simulations. Knowledge of differential equations (such as from MATH 302 or MATH 345) preferred.
Background reading: Shirogane et al 2019

Opinion dynamics on networks

How do opinions spread through a social network, and when will a population reach consensus? As opinions propagate, the social network structure could change in response to people's opinions. We're interested in opinions that can take a range of continuous values (e.g., a spectrum ranging from more conservative to more liberal) rather than just binary opinions (e.g., Republican/Democrat).
Important skills: Initially: Knowledge of a programming language, willingness to write simulations, and interest in digging deep into published literature about opinion models. Later: One possible research direction would benefit from familiarity with partial differential equations (from MATH 442 or various physics classes)
Background reading: Xinyu Zhang's honors thesis

One lane bridges

Using the Boltzmann distribution, it's theoretically possible to predict the behavior of systems that are in equilibrium with their environment. However, there isn't a corresponding general theory for systems that are out of equilibrium. Most of the real world (e.g., all living things) exists far from equilibrium, so there is great interest in understanding nonequilibrium systems. One way is by studying simple toy models and trying to predict how they behave. We want to study a nonequilibrium toy model based on traffic across one lane bridges.
Important skills: Knowledge of statistical physics (such as from PHYS 403), knowledge of a programming language, and willingness to write simulations. Background reading: This model is a variant of the asymmetric simple exclusion process (ASEP). See Shaw et al 2003 for a different example of an ASEP variant, this one motivated by protein synthesis.