From the Edge of Space with High Altitude Balloons to Planet Earth with Partial Differential Equations. Meet PIMS PDF, Elizabeth Carlson.
by Ruth A. Situma, PIMS Program and Communications Manager.
PIMS PDF at the University of Victoria Elizabeth Carlson, has been in Victoria, BC, for only a week and is settling into the west coast feel. She grew up in Helena, Montana, was homeschooled, attended Carroll College in her hometown (in her words the “best undergraduate institution I have ever encountered”), and graduated with a major in mathematics and a minor in physics in 2016. She got her Masters in 2018 and Ph.D. in 2021 at the University of Nebraska — Lincoln, where for the last three of those years she was a National Science Foundation (NSF) Graduate Research Fellow. She spent the last two years of her Ph.D. at Los Alamos National Laboratory applying her theoretical research in the real-world setting of climate science, in particular oceanography. In this feature, Elizabeth tells us a little bit about her research and work-life balance as she settles in Victoria, BC.
You have moved from a liberal arts college, taken part in an interesting National Aeronautics and Space Administration (NASA) research program, and now moving into your first postdoctoral position. How has your research progressed over the course of these projects?
My research is in fluid dynamics, focusing on the well-posedness of systems of partial differential equations (PDEs) and numerical computations and analysis in fluid dynamics. My work has been directly tied to the core of what drives my passion for research: the rigor of theoretical mathematics provides deeper insights into observations of the physical world, and observations provide intuition for directions to explore in theoretical mathematics. My interest in this research area was first sparked in my coursework and in my first internship. Attending a liberal arts college, my coursework incorporated class projects into all the lower-level mathematics courses (calculus, differential equations, and linear algebra). My class project for multivariable calculus studied wind vector fields and high altitude balloons, and I listed this project as a qualification for applying for the Montana Space Grant Consortiums’s Balloon Outreach, Research, Exploration And Landscape Imaging System (BOREALIS) internship program. The course projects had improved my research self-efficacy and positively impacted my experience in the BOREALIS program, where I learned a myriad of interdisciplinary skills (coding in webpage languages such as PHP, Javascript, HTML, and C++, field work, some engineering, etc) while modeling the current wind vector field in real-time using data from our scientific instruments instead of vague forecasts. This internship spawned my interest in fluid dynamics, which directly impacted both my undergraduate senior thesis and my doctoral dissertation.
For my doctoral work, I have been studying data assimilation, a collection of methods that uses observed data to inform a mathematical model when the initial condition is not known. I have investigated the application of one particular data assimilation algorithm to dynamical systems and the insights it provides into the behavior of these equations. Specifically, I have investigated analytical bounds on error in the context of incorrect parameters, sensitivity of systems of equations to the choice of parameters, well-posedness and convergence of a nonlinear version of the algorithm, and have implemented the algorithm in the context of real-world models. I have 5 papers on this topic (2 published and 2 submitted in high-quality journals, 1P preprint), and am involved in an ongoing research group in this area.
I will be continuing with this line of research as I venture into new research territory during my postdoc with Dr. David Goluskin at the University of Victoria. Dr. Goluskin and I are currently studying energy stability using sum of squares techniques and semidefinite programming, although we are and will be exploring many related research topics. It will require a lot of the same techniques I have studied and adapted over the years, but there are many new techniques and ideas I am learning. In fact, one of the main reasons I chose to accept this postdoc was because of the opportunity it provided to sharpen and expand my existing skillset, in addition to the fact that the project uses both theoretical and applied mathematics to gain insight into the problems.
Aside from my research, I am also very passionate about teaching done right. I became highly engaged with mathematics in my first calculus course where I finally understood how math applied to the real world. Accordingly, I have become very passionate about active learning and teaching students why I love math. This caused me to not only take advantage of the unique pedagogical opportunities at my graduate institution but also to breathe life back into the undergraduate math modeling competitions hosted there.
We are heading into full-time classes at many universities. Each of us needs to remember to take care of both mental and physical health. In what ways do you unplug and focus on your health and wellbeing?
I really enjoy hiking, martial arts, playing piano, and doing Bible studies. Martial arts is very effective in helping me completely detach from work as it requires total mental and physical focus. Once going to a martial arts class actually forced me to fully detach, I was able to figure out how to do that while off doing my other hobbies.
Elizabeth Carlson will be speaking at the PIMS Emergent Research Seminar Series, September 29, 2021 at 9:30AM Pacific. Details on her talk (Using Observations to Accurately and Efficiently Model Turbulent Flows: Parameter Recovery, Sensitivity Analysis, Nonlinear Data Assimilation Algorithms, and a Real-World Implementation) can be found here.
