Timothy Roberts
I am a William H Kruskal Instructor at the University of Chicago's Department of Statistics. My research focuses on dynamical systems and the use of geometry in their analysis, particularly in biological and ecological contexts. My current projects include pattern formation in model of drylands vegetation, and what the formation of patterns might tell you about ecosystem resilience,
I am originally from Sydney Australia, where I received a BSc (Advanced Maths) from the University of Sydney. I then completed my PhD in 2024 at the Division of Applied Mathematics, Brown University under the supervision of Bjorn Sandstede.
Last Updated: June 3, 2026.
Research Projects
My research interests focus on understanding the formation of spatiotemporal patterns in spatially extended systems. I use geometric and dynamical systems techniques such as invariant manifold theory, singular perturbation theory, spectral theory and analysis, to address questions of existence, stability and selection of patterns.
My current work focusses on understanding the formation of patterns in drylands vegetation that form due to limited water resources. I am pursuing a number of projects in various contexts including:
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Stability and selection of 2d stripe patterns on heterogeneous sloped topography
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Existence and stability of 2d spot patterns on flat terrain
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Selection of patterns in a pulsed-precipitation model of vegetation that takes storm variability into account
Recent Activities
Summer 2026:
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(Upcoming) Attending "Order and Function in Complex Systems Conference" at the University of Minnesota Twin Cities
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(Upcoming) Organizing a minisymposium at SIAM Mathematics of Planet Earth in Cleveland OH, MS17
The Mathematics of Resilience: Dynamics, Robustness and Tipping, with Katherine Slyman -
Organizing a minisymposium at SIAM Nonlinear Waves in Montreal, MS25 The dynamics of localized patterns, with Paul Carter
Spring 2026:
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Presenting a poster at the ICERM Workshop: "Nonlinear Waves: From Theoretical and Computational Advances to Experimental Observations"
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Speaking at Work-in-progress Seminar at NITMB
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Speaking at AMS Sectional Meeting at Boston College in the Special Session on Nonlinear Dynamics with a Focus on Tipping and Resilience
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Instructor for MATH18600 Mathematics of Quantum Mechanics
Winter 2026:
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Instructor for STAT28200/CAAM31405 Dynamical Systems with Applications
Fall 2025:
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Speaker: UIUC HADES Seminar
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Instructor: CAAM31470 Applied Complex Analysis
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Co-organizer: Computation and Modeling Seminar - UChicago