I'm an Assistant Adjunct Professor for the Program in Computing at the University of California, Los Angeles, and an NSERC Postdoctoral Fellow. I completed my doctor of philosophy at the University of British Columbia in Vancouver, BC, Canada. Having reached the "other side" in that I'm no longer a grad student has its perks, but like being a grad student, this is only a temporary position and I don't know where I'll be after this.
My main responsibilities include research (see some of my topics of interest below) and teaching programming courses.
I've always enjoyed the applications of math more than the theories, although theory can be both useful and beautiful. I've worked on a variety of applied projects, with a few currently underway - see the research portion of this page for details of the various projects. To be very brief, the problems I'm currently working on are:
- developing predictive models for homeless populations and quantifying emergent properties within the state of homelessness;
- assessing the effectiveness of gang reduction strategies targeted for at-risk youth: Gang Reduction Youth Development (GRYD);
- analyzing Los Angeles Twitter data and looking for spatio-temporal patterns and new means of topic clustering; and
- studying how the flow of viscous suspensions is affected by the concentration of the suspended particles and inclination angle.
These projects combine many fascinating mathematical fields including ordinary and partial differential equations, machine learning, asymptotic analysis (analytic approximation schemes), and numerical analysis (studying how the problems can be coded and accurately solved with a computer). At the end of the day, though, being able to say something about the real world is what motivates me most (although the math is super cool!!!).
I grew up in Winnipeg, Manitoba—the mosquito capital of Canada... also famous for the fantastically cold winters, which I am pleasantly reminded of each year when I go back to see family and friends over the break.
I completed my university education in the beautiful city of Vancouver, British Columbia, with tons of beautiful parks and hiking trails in close proximity. I'll miss Vancouver's stellar public transit system, close proximity to nature, and amazing simultaneous views of the mountains and ocean! I guess the main thing I like about LA so far is the winter (I prefer it to the summer). And the food is pretty good, but public transportation is lacking, so it's hard to get out an enjoy.
I really like hiking and being out in nature. Some other interests include: classical music - many pieces by Beethoven, Vivaldi, Mozart, Bach, Handel, or even very ancient, traditional music; languages (French and I know a little Mandarin); cats (they are such amazing creatures); healthy eating, including organic/raw/vegan foods (I'm almost exclusively vegan these days), green juices, local and sustainable food; and meditation (I am very interested in ancient traditions and their practices and I have been involved as a volunteer in teaching meditation and supporting such endeavours for several years).
I'm also a fan of Piled Higher and Deeper comics (reasonably accurate depictions of what it's like to be a grad student - so many memories...).
Over the years I have worked with small groups of students on research projects. Most of these projects you'll see described elsewhere on this page, but I wanted to highlight these specific projects here. The students have done amazing work and these collaborative projects have been among the most enjoyable experiences I've had in academia. It's really fun to have students getting involved in research.
In order of most distant to most recent:
Through MATH 448, a directed studies course at UBC, I worked with a former student in modelling the effects of surface roughness on superconductors. Our work was published here.
Over the summer of 2016, through the UCLA Math Department REU program, Jeffrey Wong and I worked with a group of students running experiments to study the physics and mathematics of slurry flow.
Through MATH 199 at UCLA, my colleagues David Arnold, Claudia Falcon, and I worked with a team of students to study slurry flows of bi-density mixtures.
Over the summer of 2017 through the UCLA Math Department REU program, I worked with a group of students to study crime in the homeless population. It was a collaboration with the LAPD.
Over the autumn 2017, winter 2018, and spring 2018 quarters, I worked with students in a MATH 199 course to use machine learning and data science tools to study factors that can predict and forecast homeless populations within Los Angeles.
Over the summer of 2018, I helped Omri Azencot to mentor a group of REU students studying the effectiveness of the Gang Reduction and Youth Development program, aimed at reducing risky behaviours in youths deemed at risk for joining a gang.
Over the summer of 2018, I also helped David Arnold and Christian Parkinson to mentor a group of REU students studying Los Angeles Twitter data using various techniques of data science.
I am currently teaching courses at UCLA. Prior to this, I taught for 6 years at UBC.
The courses I teach and have taught are listed below:
- PIC 10B, Winter Quarter 2019
- PIC 40A, Winter Quarter 2019
- PIC 10B, Spring Quarter 2019
- PIC 40A (programming for the internet), Autumn Quarter 2018, UCLA
- Math 199 (modelling homeless population dynamics - continued), Spring Quarter 2018, UCLA
- PIC 10B (intermediate programming, C++), Spring Quarter 2018, UCLA
- Math 199 (modelling homeless population dynamics - continued), Winter Quarter 2018, UCLA
- PIC 10B (intermediate programming, C++), Winter Quarter 2018, UCLA
- Math 199 (modelling homeless population dynamics), Autumn Quarter 2017, UCLA
- PIC 10B (intermediate programming, C++), Autumn Quarter 2017, UCLA
- Math 142 (mathematical modelling), Summer Session C 2017, UCLA
- PIC 10A (intro to programming, C++), Spring Quarter 2017, UCLA
- Math 199 (experiments with polydisperse particle-laden flow), Spring Quarter 2017, UCLA - co-instructed with David Arnold and Claudia Falcon
- Math 142 (mathematical modelling), Winter Quarter 2017, UCLA
- PIC 10B (intermediate programming, C++), Winter Quarter 2017, UCLA
- Math 142 (mathematical modelling), Autumn Quarter 2016, UCLA
- PIC 10B (intermediate programming, C++), Autumn Quarter 2016, UCLA
- Math 142 (mathematical modelling), Summer Session C 2016, UCLA
- PIC 40A (programming for the internet), Spring Quarter 2016, UCLA
- PIC 10A (intro to programming, C++), Spring Quarter 2016, UCLA
- PIC 10A (intro to programming, C++), Winter Quarter 2016, UCLA
- PIC 10A (intro to programming, C++), Autumn Quarter 2015, UCLA
- Math 105 (integral calculus for commerce and social sciences), Term 2, Winter 2014-2015, UBC.
- Math 448 (directed studies in mathematics), Summer 2014, UBC.
- Math 215 (ordinary differential equations), Term 2, Winter 2013-2014, UBC.
- Math 104 (differential calculus for commerce and social sciences), Term 1, Winter 2012-2013, UBC.
- Math 105 (integral calculus for commerce and social sciences), Term 2, Winter 2011-2012, UBC.
- Math 103 (integral calculus for life sciences), Term 2, Winter 2010-2011, UBC.
- Math 101 (integral calculus for physical sciences), Term 2, Winter 2009-2010, UBC.
Letters of Recommendation:
I feel I should include a short word on writing letters of recommendation. Some things to keep in mind if you ask me to write a letter:
- You may be better off getting a letter from a tenured faculty member with years of established research instead of myself. Getting a letter from someone well-known has its advantages.
- I need several weeks' notice, ideally a month or two. The less time I have, the lower the quality of letter I may be able to write for you and the more likely I will need to decline.
- I can only write a strong academic letter for a student who earned EITHER an A or A+ in a course I have taught; the story is different for students I mentor in research. Without an A or A+, I cannot use statements such as "top of the class", "mastered the material", etc.
- It wouldn't hurt if I knew who you were! Don't stay anonymous. Hopefully I will have spoken to you in person at least a few times in the course.
- I need as much information from you as possible: unofficial transcript copies, CV/resume, any/all personal statements you are including in your application, a detailed description of what you are applying for, any deadlines, etc.
- Due to FERPA guidelines, I need you to send me a letter granting full permission to disclose information from your academic records (transcript information, course grades, GPA, etc.) to the intended recipients, a list of intended recipients (this could be a description of the type of positions/programs you are applying to), and the purpose of the letters. In addition, you must provide your signature at the bottom. You can mail, fax, or email this to me, but the letter granting consent must clearly address all of these items or I will not be able to write anything for you.
Other Education Stuff
Math Education Resources wiki
I was contributor and administrator for the Math Education Resources wiki. This project began as an online database of past UBC Math Exams with hints and solutions, and has steadily expanded to a more complete online learning resource with questions by topic and interactive features. Currently we're doing an education study on the effectiveness of the wiki.
Research Experience and Interests
- Homelessness (current): Los Angeles, along with many major cities, has a huge homeless problem. Right now there are over 50,000 homeless people in Los Angeles, and the problem is very complicated. There is little understanding as to the mechanisms that yield such high rates of homelessness and how individual characteristic traits influence the outcome of homeless individuals. For over a year now, I've been studying this problem from a number of different angles, which is leading to three rather different research problems: firstly, by collaborating with the Los Angeles Police Department and analyzing arrest records, we are discovering hidden demographics within the homeless population. Secondly, by combining data such as median household income and various proxies for commerce that can be obtained for distinct geographic regions, along with annual homeless counts imputed by the Los Angeles Homeless Services Authority, it seems possible to predict, at least approximately, how the homeless population will evolve on small spatial scales known as census tracts. The main techniques used have included: topic modelling, mixture of Gaussians for clustering, and artificial neural networks. Lastly, from a more theoretical perspective, I have been working to develop a partial differential equation that models the evolution of the homeless population density. The equation is a nonlocal, nonlinear reaction-advection-diffusion equation. I have been working to prove the well-posedness of the model, ensuring that as a mathematical model it yields physically sensible results (finite total populations, non-negativity of the population -- all the stuff that really should be true if the model equation can approximate reality in a meaningful way).
- Fluid Flows (current): There are a vast array of interesting phenomena that emerge in studying the flow of viscous fluids, based on the concentration of particles that may be in suspension and the inclination angle. I'm wrapping up some work on time scale analysis of thin-film viscous suspensions, but the field is full of open, unanswered problems. With colleagues, we have begun to study suspensions with multiple components.
- Gang Reduction and Youth Development (GRYD) (current): The GRYD program schedules after-school programs and other supportive interventions for youths who are deemed at risk for joining gangs. We are provided with surveys the participants take, roughly every 6 months, with the surveys asking questions that attempt to measure the participant's attitudes and inclinations towards risky behaviours such as violence or lack of family contact. By modelling the responses as a dynamical system and using Dynamic Mode Decomposition (DMD), we have been able to analyze modes of growth and periodicity within the responses. DMD has also given us a means of predicting future risk-levels with comparable performance to a shallow neural network.
- Twitter Data (current): Twitter is a popular social network where users "tweet" short stories, comments, or ideas. The tweets themselves have a well-defined time, but also may include geotagging information such as the location the tweet was made. The amount of things one can do with this data is almost unlimited. We have focused upon dynamically clustering the tweets into topics and using the topics and information within the text of a tweet to infer a user's location information. We also found it is possible to predict the time/location of a "current event" by studying the frequency of tweets over space and time along with their corresponding topics.
- Osteogenesis Imperfecta VI: OI type 6 is a severe form of brittle bone disease where patients have bones that are both very soft (due to delayed mineralization) and very brittle (due to over mineralization). Researchers of the disease suspect an abnormally low concentration of a protein known as PEDF is responsible for the disease. Through an industrial workshop in Montreal, a group of us began to study the process of bone mineralization and the potential role of PEDF with mathematical models. Our work is very preliminary, but our current model qualitatively predicts the delayed bone development of OI type 6 patients if these patients have a decreased concentration threshold of calcification-inhibiting enzymes necessary for bone development. Here are slides from our oral report.
- Nutrient Absorption: Biological processes governing digestion and nutrient assimilation are complex, and mathematical modelling can yield deep, qualitative insights into how the various processes work together when, as with many biological systems, only few quantitative relationships are known.
- Electrodialysis: Some modern plans for water filtration systems that purify salt water and those that can reduce the waste water of fracking use electrodialysis as a means to pass ions through selectively permeable membranes with the help of an electric potential gradient. I was involved in simulating the system under various settings, employing a combination of asymptotics and numerics. A paper that combines the theoretical work with experiment is here.
- Superconductors: A superconductor, when in the Meissner state expels magnetic fields from its interior. Very near its surface, there is an exponential decay in field strength that is predicted by the London equation, a special limit of the Ginzburg-Landau equations, provided the surface is flat. In the superconductivity literature, the assumption of a flat interface was taken for granted, but due to experimental measurements of a non-exponential decay in field strength near the surface of a superconductor, experimentalists asked the question of whether small-amplitude perturbations could have an effect on the field profile. This paper presents the results of the analysis undertaken in trying to answer the question. The previous work was extended by using experimental measurements of the superconducting surfaces in the simulations, and the results can be found here.
- Mass Spectrometry: A mass spectrometer separates atoms and molecules based on their mass. This has applications in detecting heavy metal or radioactive contaminants in air or water supplies. At a recent problem solving workshop, a group of us worked in collaboration with PerkinElmer on creating a new method of mass spectrometry that allows for continuous measurements of concentrations, without the costly use of magnetic fields. We found that it may be possible to create an electric field configuration that causes periodic oscillations dependent upon mass, which would allow for different chemical species to be separated spatially or detected with Fourier analysis. Our article on the problem is found here.
- Nuclear Fusion: Magnetized target fusion is a relatively new idea for producing conditions for hydrogen fusion on earth. The essence of the idea is to confine a plasma in a magnetic field and compress it by an intense pressure-focused pulse so that it yields a high enough particle density and pressure for fusion to take place, releasing energy. A local Canadian research company has a design of such an apparatus that they are currently working on engineering: the plasma is found in an empty region of a vertical central cylindrical axis of a sphere of molten lead-lithium. Pistons deliver an immense pressure on the outer walls of the spherical lead-lithium region, with the pressure growing in magnitude as it reaches the plasma, causing it to compress to a very small radius. Simulating this design requires a careful interplay of plasma physics and fluid dynamics, and reasonable modelling skills. My research interest here is in developing a suitable model, performing numerical simulations for the hyperbolic conservation laws, and doing asymptotic analysis to estimate the influence of various factors on the reactor performance qualitatively and analytically. Here is a paper covering some of the numerical aspects and here is a paper covering some of the asymptotic estimates. Another paper outlining a study of the instabilities associated with asymmetric implosions can be found here.
- Gas Diffusion in Fuel Cells: Fuel cells are costly to build, and developing accurate techniques to simulate their performance beforehand is essential in minimizing production costs. Unfortunately, there are many complex processes that take place within a fuel cell, one of the most important processes is gas diffusion. Those in industry who work with numerical simulations are often puzzled as to what formulation to adopt for gas diffusion: Fick (a simple gradient flow often formulated with a single Fick diffusion coefficient) or Maxwell-Stefan (a complex flow rate that depends upon the concentration gradients of all other species and experimentally determined binary diffusivities). The research I have been involved with on this topic was in studying the two formulations in a simple one-dimensional model of a PEMFC gas diffusion layer. Through nondimenzionalization, and a two-term formal asymptotic expansion, the two models provide nearly identical predictions. Furthermore, Fick diffusion is really a special limit of Maxwell-Stefan diffusion and in many industrial applications, the simpler Fick formulation can be used with reasonable precision. A paper explaining these results has been submitted to Heat and Mass Transfer.
- Malaria Management: Recently, a fungus has been discovered that could help reduce malaria-prevalence in endemic regions. The fungus infects mosquitoes, but instead of killing them like a pesticide, it kills the malaria that they carry and could transmit to humans. One biological question that arises is, if this fungus is used, should it be engineered to also kill mosquitoes? A few colleagues and I came up with a model of how this fungus could be used in combating malaria, and through studying a model system of ODEs numerically and analytically, we demonstrated that under certain assumptions on the mosquito carrying capacity and growth rate, the fungus should be engineered to have minimal virulence to mosquitoes to have an optimal effect in reducing malaria. Under other assumptions on the carrying capacity, different behaviour can be observed. Our paper has been published by Malaria Journal.
Papers, Proceedings, Theses, etc.
- Conversion of Saline Water and Carbon Dioxide into Value-Added Chemicals by Electrodialysis (2017, published in Journal of CO2 Utilization), in collaboration with Saad Dara, Joseph English, Arman Bonakdarpour, Brian Wetton, and David Wilkinson.
- Assessment of the Effects of Azimuthal Mode Number Perturbations upon the Implosion Processes of Fluids in Cylinders (2017, published in Physica D).
- Effect of Surface Roughness on the Magnetic Field Profile in the Meissner State of a Superconductor (2016, published in Journal of Superconductivity and Novel Magnetism), in collaboration with Ching-Yang Fang (Alex) and Rob Kiefl.
- Electric Ion Dispersion as a New Type of Mass Spectrometer (2015, published in Mathematics-in-Industry: Case Studies), in collaboration with Iain Moyles and Kevin Ryczko.
- Asymptotic Estimation for Minimal Plasma Radius in a Spherically Symmetric Magnetized Target Fusion Reactor Model (2015, published in SIAM Journal on Applied Mathematics)
- From Exam to Education: The Math Exam/Educational Resources wiki (2015, published in PRIMUS), in collaboration with Carmen Bruni, Christina Koch, Bernhard Konrad, Iain Moyles, and William Thompson.
- Investigation into Fusion Feasibility of a Magnetized Target Fusion Reactor (2014, published in Journal of Fusion Energy), in collaboration with Sandra Barsky and Brian Wetton.
- A Comparison of Fick and Maxwell-Stefan Diffusion Formulations in PEMFC Cathode Gas Diffusion Layers (2015, published in Heat and Mass Transfer), in collaboration with Brian Wetton.
- Assessing the optimal virulence of malaria-targeting mosquito pathogens: a mathematical study of engineered Metarhizium anisopliae (2013, published in Malaria Journal), in collaboration with Bernhard Konrad, Anja Gumpinger, Jielin Zhu, and Daniel Coombs.
- Mathematical modelling of the effect of surface roughness on magnetic field profiles in type II superconductors (2013, published in Journal of Engineering Mathematics), in collaboration with Brian Wetton and Rob Kiefl.
Papers in Progress
- Fast time dynamics of particle diffusion for viscous suspension flow in an inclined channel
- Arrest records reveal hidden demography of homelessness
- Using local geograhic features and fluctuations to predict changes in the visible homeless population of Los Angeles
- A Partial Differential Equation Model for the Homeless Population
- Modelling the Effects of Surface Roughness on Superconductors (2012, published in muSR 2011 proceedings), in collaboration with Brian Wetton and Rob Kiefl: a compact summary of our detailed paper studying surface roughness of superconductors.
- Doctoral Thesis (2015): Investigation into the Feasibility and Operation of a Magnetized Target Fusion Reactor : Insights from Mathematical Modelling
- Masters Thesis (2010): Asymptotic and Numerical Modeling of Magnetic Field Profiles in Superconductors with Rough Boundaries and Multi-Component Gas Transport in PEM Fuel Cells
- Honours Thesis (2008): Computation of Gluon Scattering Amplitudes in N=4 SYM Gauge Theory via AdS-CFT Duality
Talks, Posters, Conferences, and Proceedings
- 2017 - UCLA Math Undergraduate Students Association Professor Talk
- 2017 - CAIMS 2017 in Halifax
- 2017 - SoCal Fluids 2017 in San Diego
- 2016 - CAIMS 2016 in Edmonton
- 2016 - UCLA Applied Math Colloquium
- 2015 - Slides from my PhD Defense Presentation
- 2014 - Math Department Colloquium
- 2014 - Undergraduate Math Colloquium
- 2014 - Fields-MPrime Industrial Problem Solving Workshop in Toronto. Here's our group presentation.
- 2014 - PIMS YRC 2014 in Vancouver: organizer.
- 2014 - IAM seminar retreat in Vancouver: oral presentation.
- 2013 - Simon Fraser University, Applied Math Colloquium in Burnaby: oral presentation on modelling nuclear fusion.
- 2013 - Centre de Recherce Mathematiques Industrial Problem Solving Workshop in Montreal.
- 2013 - IAM Seminar Retreat in Vancouver: oral presentation.
- 2012 - CAIMS 2012 Annual Meeting in Toronto, Ontario: oral presentation.
- 2012 - UBC Math Undergraduate Colloquium at UBC: oral presentation on industrial modelling for fuel cells and nuclear reactors.
- 2011 - Applied Mathematics, Modeling and Computational Science Conference in Waterloo, Ontario: oral presentation
- 2011 - ICIAM 2011 in Vancouver, BC: poster presentation
- 2011 - 12th International Conference on Muon Spin Rotation, Relaxation and Resonance in Cancun, Mexico: poster presentation
- 2011 - PIMS YRC 2011 in Vancouver, BC: oral presentation.
- 2011 - IAM Seminar Retreat 2011: oral presentation.
You can read my CV here (April 2017).