Potential Projects
Contact me if any of these topics interest you! We can talk further about potential research questions in these areas and what the project would entail. Each of these projects involves analyzing differential equations (ODEs or PDEs) and most can involve data analysis, depending on your interest.
Climate modeling:
Climate modeling:
- Modeling the reversibility of sea ice
- Modeling global permafrost melt and permafrost explosions
- Modeling diverse racial representation in professional fields
- Bifurcations in differential equations with piecewise-smooth vector fields
- Resilience of food trade networks to climate change-related impacts
- Life cycle models of food and their environmental impact
Past Student Projects
Jump to:
Survival Estimation
Permafrost
Food networks
Gender and professional hierarchies
Opioid epidemic
Periodically-forced cusp normal form
White Nose Syndrome epidemic
Survival Estimation
Permafrost
Food networks
Gender and professional hierarchies
Opioid epidemic
Periodically-forced cusp normal form
White Nose Syndrome epidemic
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Analyzing trends in ground-level ozone
Keily Hart (St Mary's U '24) Honor Thesis: commons.stmarytx.edu/honorstheses/36 2nd place poster award (SET), St. Mary's Research Showcase 2024 Keily analyzed several decades’ worth of ground-level ozone readings in six of the largest metropolitan areas in Texas, using data from the United States Environmental Protection Agency (EPA). Keily identified trends in these readings using the Jonckheere-Terpstra test, a rank-based nonparametric hypothesis test. |
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Applications of survival estimation under stochastic order to cancer: The three-sample case
Sage Vantine (St Mary's U '24) Honor Thesis: commons.stmarytx.edu/honorstheses/37 Sage adapted methodologies from one-sample and two-sample cases of survival estimation under stochastic ordering to the more complex scenario of a three-sample case. Sage investigated four different estimators applied to data representing the relative survival rates of various racial groups affected by eight different types of cancer, and evaluated the performance of each estimator in terms of bias and mean square error. |
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Permafrost melt and the Budyko Energy Balance Model
John Nguyen (U Minnesota '20), Aileen Zebrowski (U Minnesota '17) Co-mentored with Richard McGehee Publication: SIAM Undergraduate Research Online, 14 (2021), doi.org/10.1137/20S1353344. John and Aileen modified the classic Budyko energy balance model to include a 'permafrost line' and studied how the permafrost line and snow line recede towards the North Pole as global mean temperature increases. They quantified the amount of melted permafrost using current estimates of the permafrost line and some assumptions about the structure of permafrost, and cross referenced the results of their model with other climate model simulations. |
Resilience of the international beef trade network
Yuqing Wang (U Minnesota '20), Brandon Freeman (Wake Forest U '20)
What is the potential effect of extreme weather on global food trade networks? How has this changed over time as the network evolves and climate change impacts weather? Yuqing and Brandon investigated the network structure of the international beef trade and how tropical cyclones are changing over time, as well as data-driven methods of analyzing and modeling this question.
Yuqing Wang (U Minnesota '20), Brandon Freeman (Wake Forest U '20)
What is the potential effect of extreme weather on global food trade networks? How has this changed over time as the network evolves and climate change impacts weather? Yuqing and Brandon investigated the network structure of the international beef trade and how tropical cyclones are changing over time, as well as data-driven methods of analyzing and modeling this question.
Agent-based model of gender bias and homophily in professional hierarchies
Jennifer Ai (U Minnesota - UMTYMP '19), Jake Berran (U Minnesota - UMTYMP '19), Mitchel VonEschen (U Minnesota - UMTYMP '19)
Jennifer, Jake, and Mitchel created agent-based models of movement up levels of positions in a theoretical company. Their models investigated the balance of aspects of this process, such as bias in hiring and self-seeking behavior in applicants (homophily), and the effect of different distributions of random behavior in both of these aspects.
Jennifer Ai (U Minnesota - UMTYMP '19), Jake Berran (U Minnesota - UMTYMP '19), Mitchel VonEschen (U Minnesota - UMTYMP '19)
Jennifer, Jake, and Mitchel created agent-based models of movement up levels of positions in a theoretical company. Their models investigated the balance of aspects of this process, such as bias in hiring and self-seeking behavior in applicants (homophily), and the effect of different distributions of random behavior in both of these aspects.
Comparison of models of the opioid epidemic
Thomas Cushing (U Minnesota '19)
Thomas learned about dynamical systems by reproducing the results of a compartmental model of the opioid epidemic.
Thomas Cushing (U Minnesota '19)
Thomas learned about dynamical systems by reproducing the results of a compartmental model of the opioid epidemic.
Dynamics of the cusp normal form with periodic forcing
Mark Pekala (U Minnesota - UMTYMP '18), Antonia Ritter (U Minnesota - UMTYMP '18)
Mark and Antonia conducted a dynamical systems analysis of a variation on a classical dynamical system, particularly its bifurcation structure and how hysteresis in the system changes with parameters.
Mark Pekala (U Minnesota - UMTYMP '18), Antonia Ritter (U Minnesota - UMTYMP '18)
Mark and Antonia conducted a dynamical systems analysis of a variation on a classical dynamical system, particularly its bifurcation structure and how hysteresis in the system changes with parameters.
Spread of White Nose Syndrome in bat networks
David Li (U Minnesota - UMTYMP '18), Grace O'Brien (U Minnesota - UMTYMP '18)
White Nose syndrome is a fungal disease increasingly affecting bat populations in the U.S.. David and Grace investigated a network-based model for the spread of infection.
David Li (U Minnesota - UMTYMP '18), Grace O'Brien (U Minnesota - UMTYMP '18)
White Nose syndrome is a fungal disease increasingly affecting bat populations in the U.S.. David and Grace investigated a network-based model for the spread of infection.
