I am very interested in working with students who want to pursue an undergraduate or master's thesis. My training is broadly in applied mathematics with my doctoral research in the area of calculus of variations, differential geometry, continuum mechanics, and applied analysis. However, as an applied mathematician, I have a very broad range of interests. Below you will find descriptions of current and past projects I have mentored. In the past I used to include a list of potential projects I could mentor. However, in some sense I have found this to be constraining. Generally, if your interests lie within the intersection of science, mathematics, and modeling then I am more than happy to work with you to develop a project that overlaps with both of our interests. I would love to hear about your ideas!
Master's Students
- Steven Liao (2023-Present): Noise induced tipping in a bear-bull market model
Undergraduate Students
- Riley Justman (2024-Present): Modeling spread of opinions in social media
Master's Students
- Qiyue (Clare) Zhang (2022-2024): Noise Induced Transitions in the Swift-Hohenberg Equation
- Grace Hofmann 2022: Noise Induced Tipping in Networks of Neurons.
- John Turnage 2021-2022: Controllability of a Rolling Disk on Surfaces of Revolution
- Nick Corak 2019-2020: Stability and Formation of Hurricanes
- Max Rezek (2018-2019): The Formation of Singularities in Non-Euclidean Plates
- Jessica Zanetell (2017-2018): Tipping Points in Stochastically Perturbed Filippov Systems
Undergraduate Projects
- Emily Foley (2023-2024): Spatiotemporal Chaos and Tipping in the Forced Sine-Gordon Equation
- Shelby Horth (2023-2024): Phase Shaping of Images
- Xuan (Kelsy) Fei 2022-2023: Predicting the Most Probable Path for Tipping in Arctic Sea Ice
- Zhengdao (Jack) Liu 2022-2023: Chaos Game on Non-Convex Domains
- Ashley Peake 2021-2023: Polarization in Online Opinion Dynamics
- Malindi Whyte 2021-2023: Opinion Formation on an Adaptive Network
- CURM 2021-2022: Mathematical Modeling of COVID-19 Dynamics
- Hannah Scanlon 2019-2021: Spread of Infectious Diseases on Adaptive Networks
- Grace Hofmann 2020-2021: Spiral Waves in the Belousov–Zhabotinsky reaction
- Kevin Buck 2019-2020: Spread of Infectious Diseases, Vaccination and Opinion Formation
- Elizabeth Dicus (2019-2020): Mathematical Modeling of Sex Trafficking
- Addie Harrison (2019-2020): Reaction Diffusion Equations and Pattern Forming Systems
- Addie Harrison (2018): Human Visual Tracking and Image Formation
- Hanwen Wang (2018-2019): Most Probable Tipping Events in Stochastic Differential Equations
- Brady Gales (2017-2019): Regularization of the Head Injury Criterion Functional
- Dylan King (2017-2018): Energy Driven Pattern Formation
- Elizabeth Wallace (2017-2018): Wolves vs. Sheep
- Christopher Grimm (2015-2016): Brachistochrone Problem in an Inverse Square Field
- Ragna Eide (2015-2016): Spread of Infectious Diseases on Adaptive Networks
- Ekaterina Kryuchkova (2014-2016): Modeling Crowd Dynamics
- Mackenzie Simper (2015): Metastable Systems