Winter 2020, Fall 2019, Winter 2017, Fall/Winter 2016, Fall 2015.
MATH 100 - Calculus I
MATH 102 - Applied Linear Algebra
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
Flow charts for differential equations.
Online Research Talks
Pigeon lake health advisory .
Harmful cyanobacteria bloom .
My research interests lie in the areas of Mathematical ecology, and in particular within the framework of Ecological Stoichiometry.
My most recent projects include studying cyanobacteria dynamics in eutrophic freshwater lakes. Cyanobacteria blooms often only form a few times per year in more temperature regions, such as Alberta, Canada. For this reason, studying the long term dynamics of cyanobacteria models might not yield sufficient information with regards to management strategies. Furthermore, by studying the short term dynamics we are able to uncover driving mechanisms behind each aspect of bloom formation and collapse.
Cyanobacteria model simulation .
Fast-slow analysis of cyanobacteria dynamics .
I am also interested in how socio economic factors, such as anthropogenic nutrient inputs and social pressure to limit pollution can be coupled to the cyanobacteria dynamics and the resultant implications. Under various social pressure regime shifts can occur. That is, a human population may transition between being high polluters and low polluters based on social pressure and concern for the algal blooms.
Possible cyanobacteria equilibrium for a given amount of social pressure .
In addition I am mathematically studying competition between phytoplankton species under various incident light scenarios. Furthermore, we consider a niche differentiation of phytoplankton species. This is an approach to mathematically the explain the
paradox of the plankton
and show that robust coexistence of several species is possible when they are able to utilize different wavelengths.
Coexistence region for various advection rates of two competing phytoplankton species that absorb different wavelengths. .
Please see my publications for more information on these projects.
- Image from: https://globalnews.ca/news/2867098/blue-green-algae-bloom-spotted-in-pigeon-lake-despite-communitys-best-efforts/ (2020)
- Image from: https://myhealth.alberta.ca/alberta/pages/blue-green-algae.aspx (2020)
- M. Heggerud, H. Wang, M. A. Lewis, Transient dynamics of a stoichiometric cyanobacteria model via multiple-scale analysis.
SIAM Journal on Applied Mathematics (Accepted for Publication) (2020)
- In a paper to be submitted soon
- C. M. Heggerud, C. M., Wang, H. & Lewis, M. A.
Transient dynamics of a stoichiometric cyanobacteria model via multiple-scale analysis. SIAM J. Appl. Math. 80, 1223–1246 (2020).
- C.M. Heggerud and K.Q. Lan, Local stability analysis of ratio-dependent predator-prey models with
predator harvesting rates.
Applied Mathematics and Computation 270: 349-357 (2015)
- A. Peace, P. C. Frost, N. D. Wagner, M. Danger, C. Accolla, P. Antczak, B. W. Brooks, D. M. Costello, R.
A. Everett, K. B. Flores, C. M. Heggerud, R. Karimi, Y. Kang, Y. Kuang, J. H. Larson, T. Mathews, G. D.
Mayer, J. N. Murdock, C. A. Murphy, R. M. Nisbet, L. Pecquerie, N. Pollesch, E. M. Rutter, K. L. Schulz,
J. T. Scott, L. Stevenson, H. Wang, Stoichiometric Ecotoxicology for a Multisubstance World.
BioScience: biaa160, https://doi.org/10.1093/biosci/biaa160 (2021).
C. M. Heggerud, K.-Y. Lam, H. Wang, Coexistence of phytoplankton species based on niche
differentiation in absorption spectrum.
H. Wang, P. V. Garcia, S. Ahmed, C. M. Heggerud, A mathematical comparison of the Monod and
Droop forms for resource based population dynamics.
C. M. Heggerud, H. Wang, M. A. Lewis, Coupling the socio-economic and ecological dynamics of
J. Xu, P. Ramazi, C. M. Heggerud, M. A. Lewis, R. Zurawell, C. Loewen, R. Vinebrooke, H. Wang, A
Baysian network approach to understanding and predicting cyanobacteria blooms.
A link to my Google Scholar page.
Click here if you can not view the PDF.
I am an outdoor enthusiast born and raised on a farm south of Edmonton, Alberta. I've always enjoyed the outdoors, and am passionate about nature. My main adventures include down hill skiing, ski touring, sport climbing, hiking and backpacking. After completing my undergraduate degree at Ryerson University, my (now) wife and I moved back to Alberta so that I could pursue a PhD in applied mathematics 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.
Title: Ph.D. Candidate Lewis Research Group and Hao Wang Research Group
Office: CCIS 1-092, Department of Mathematical and Statistical Sciences, University of Alberta ᐊᒥᐢᑿᒌᐚᐢᑲᐦᐃᑲᐣ / Amiskwacîwâskahikan / Edmonton, Treaty 6 territory
Christopher M. Heggerud
University of Alberta
Canada T6G 2G1