My research is in applied dynamical systems. I am interested in understanding the dynamics of mathematical models in ways that can lend insight into both their scientific application and dynamical systems theory.

Mathematically, I use tools from differential equations (ODEs and PDEs), networks, and stochastic processes to understand bifurcation and tipping point behavior. Frequently the dynamical systems I analyze are piecewise-smooth, which leads to fascinating mathematical phenomena like non-uniqueness and discontinuity-induced bifurcations.

I enjoy working with mathematical models of all types. I primarily work with models that relate to mathematical geophysics and climate. I am also interested in human and food dynamics, especially as they relate to issues of equity and climate change. My work with students has included all of these areas, as well as mathematical epidemiology and theoretical dynamical systems. If you're interested in working with me, check here for a list of potential topics and previous projects students have worked on - or send me a message if you have an idea you'd like to investigate.

Mathematically, I use tools from differential equations (ODEs and PDEs), networks, and stochastic processes to understand bifurcation and tipping point behavior. Frequently the dynamical systems I analyze are piecewise-smooth, which leads to fascinating mathematical phenomena like non-uniqueness and discontinuity-induced bifurcations.

I enjoy working with mathematical models of all types. I primarily work with models that relate to mathematical geophysics and climate. I am also interested in human and food dynamics, especially as they relate to issues of equity and climate change. My work with students has included all of these areas, as well as mathematical epidemiology and theoretical dynamical systems. If you're interested in working with me, check here for a list of potential topics and previous projects students have worked on - or send me a message if you have an idea you'd like to investigate.

## Mathematical geophysics

In the Earth system, several feedbacks are considered important to understand in the context of potential climate change. Two of these feedbacks are the sea ice - albedo feedback and the permafrost - carbon feedback. With my collaborators, I have worked to deepen our understanding of the dynamics of these feedback processes in the context of planetary energy balance, as well as related questions in the areas of application.
Sea IceAnalysis of an Arctic sea ice loss model in the limit of a discontinuous albedo, K Hill, DS Abbot, M Silber, (2016).Estimating The Sea Ice Floe Size Distribution Using Satellite Altimetry: Theory, Climatology, and Model Comparison, C Horvat, et al. (incl. K Hill), (2019). PermafrostHeat conduction through permafrost and its potential for explosive behavior, K Hill and R McGehee, (2018), preprint. |

## Piecewise-smooth systems

Many geophysical models include dynamics defined in a piecewise-smooth manner, to account for a 'switch' or sudden change in a state or of expected behavior. For example, the dynamics of water change depending on whether it is in a liquid or frozen state. My work in this area focuses on implications of the switching manifold on system dynamics. Piecewise-smooth climate dynamicsCharacterizing tipping in a stochastic reduced Stommel-type model in higher dimensions, C Budd, P Glendenning, K Hill , R Kuske, (2016).Analysis of an Arctic sea ice loss model in the limit of a discontinuous albedo, K Hill, DS Abbot, M Silber, (2016). Smooth vs. piecewise-smooth dynamicsMost probable transition paths in piecewise-smooth stochastic differential equations, K Hill, J Zanetell, JA Gemmer, (2022), to appear.Persistence of saddle behavior in the nonsmooth limit of smooth dynamical systems. J Leifeld, K Hill, A Roberts, (2015), preprint. |

## Social dynamics

Many professional hierarchies exhibit gender inequality to some extent, and even across several levels in the hierarchy. My collaborators and I constructed a minimal dynamical systems model and analyzed potential long-term behavior of a hypothetical hierarchy as job applicant homophily (self-seeking) and hiring committee bias vary.
Mathematical model of gender bias and homophily in professional hierarchies, SM Clifton, K Hill, AJ Karamchandani, EA Autry, P McMahon, G Sun, (2019). |