Teaching

Instructor Experience

University of California, Davis

MAT 21A - Differential Calculus

Fall 2022 ( Sample syllabus here)

TA Experience

University of Alberta

MATH 201 - Differential Equations

Winter 2020, Fall 2019, Winter 2017, Fall/Winter 2016, Fall 2015.

MATH 100 - Calculus I

Fall 2018

MATH 102 - Applied Linear Algebra

Winter 2019

Toronto Metropolitan University

MATH 131 - Modern Mathematics

Fall 2014, Winter 2015

Guest Lectures

IUSEP July 2019

Lecture on perturbation theory at the University of Alberta

MATH 570 Winter 2019

Lecture on Enzyme Kinetics: slow manifold and perturbation analysis at the University of Alberta

Research Interests

Keywords

  • Transient Dynamics
  • Empirical dynamical modelling
  • Ecological Stoichiometry
  • Resource explicit population dynamics
  • Dynamical systems

My research is at the intersection of Mathematics and Ecology. Using mathematical tools, I aim to answer important ecological questions that arise from societal, cultural, economic and environmental concerns.

Currenly, I am interested in the study of transient dynamics from both the mathematical and ecological perspectives. In particular, I am studying how we can utilize the existed dynamical systems literature to predict transient behavior in ecological data using empirical dynamical modelling as a tool.

In my PhD work I studied various mathematical and ecological aspects of phytoplankton dynamics: using dynamical systems and singular perturbation theory to uncover the driving ecological mechanisms behind algal bloom dynamics, using game theory and bifurcation theory to understand the complex interaction between humans and aquatic environments, and using spatial modeling and monotone dynamical systems theory to offer insights towards the observed diversity of phytoplankton species via niche differentiation in the light spectrum.

Recorded Research Talks

Interesting figures

This video shows how a chaotic attractor can be reconstructed using delayed coordinates. That is, the dynamics of the full model are similar to the dynamics of the just a single dimension realized at different times. This stems from Taken's theorem and is the foundation of Empirical Dynamical Modelling.
A sample of transient dynamics induced by a changing environment. This example shows rate, or phase induced tipping, where a system undergoes no bifurcation but certain environmental parameters change fast enough causing the dynamics to leave the stable limit cycle and enter another attracting region. See publication [9] and preprint in progress.
Using singular perturbation theory to offer a mechanisitic explanation of the observed transient dynamics in phytoplankton dynamics(right). The left figure shows that transient dynamics occur due to a transition between two attracting manifolds. One represent light limiation, the other nutrient limitation. Details in publication [2]
Shows the regime outcome for given social norm costs of a model that couples human interaction with a network of lakes. Humans chose to either cooperate or defect to reduce lake pollution based on economic and social costs. A high cooperation regime results in a lower abundance of phytoplankton. The figure shows parameter values such the each node is in an high cooperation or low cooperation regime. The mixed cooperation regime is where some nodes are highly cooperative and others are not. See publication [4]
Shows the coexistence region of two phytoplankton species for light. Treating light as a continuous rescource we consider niche differentiation in the light spectrum allow for more robust coexistence. When the niches are significantly different coexistence occurs. See publication [10]

Please see my publications for more information on these projects.

Publications

A link to my Google Scholar page. If you cannot access any of these papers on your own please do not hesistate to request one directly from me.

Click here if you can not view the PDF.

CV

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About Me

Professional Life

I am currently a postdoctoral reasearcher at the University of California, Davis under the supervision of Alan Hastings in the Department of Environmental Science and Policy. My research is mathematical in nature but has real applications in general ecology. I am currently on the job market. After completing my undergraduate degree at Toronto Metropolitan University, I moved back to Alberta to receive my PhD in applied mathematics (Mathematical Ecology) at the University of Alberta under the supervision of Mark Lewis and Hao Wang. Please reach out if you would like to know more about me and my research.

Personal Life

I am an outdoor enthusiast born and raised on a farm south of Edmonton, Alberta, Canada. I've always enjoyed the outdoors, and am passionate about nature. My main adventures include down hill skiing, ski touring, sport climbing, hiking and mountain biking as well a general enjoyment of the outdoors with my wife and kids. I currently live in Davis, California.

Contact Me

Email: cmheggerud[at]gmail[dot]ca or cmheggerud[at]ucdavis[dot]edu
Title: Postdoctoral Researcher
Affiliations: Alan Hastings research lab, Center for Populaition Biology (UC Davis), Department of Environmental Science and Policy (UC Davis), and Department of Mathematics (UC Davis).
Office: Wickson Hall 3059, Department of Environmental Science and Policy, University of California, Davis.
I am a guest on the traditional, unceded land of the Patwin people.