|My roommates got a puppy. Her name is sky. She is not mine, but she is like family.|
Research Summary for the Layman
I like to say that if we understand something, we should be able to make predictions. Lots of mathematical modeling has been done with this goal in mind. The power of modeling also comes from its failure. When a model is unable to sufficiently describe a particular phenomenon, it sharpens the question for scientists and mathematicians and produces new research questions. This approach is powerful and has consistently improved our understanding of countless phenomena. However, there is one potential limitation. Some models are comprehensive but incredibly complex, requiring computers and long times to simulate. Once the simulation is done, how does one know that the computer is showing them sommething realistic as opposed to a bug? Much of my work can be called "dimension reduction", where I take complex models and reduce them to something simple enough that we can understand them without computers. This approach also allows us to use classic mathematical theory established over the course of centuries to prove beyond a shadow of a doubt that certain behaviors of a model truly exist. For example, a complicated model of a neuron simulated using a computer might show oscillations in the membrane potential for certain parameters. By using a simplified or reduced version of the model, we can prove mathematically that such a solution is possible. If we prove that it does not exist, the oscillations must be a result of computer errors.Research Summary for the Scientist
I pursue questions in neurphysiology and electrophysiology. My neurosphysiology work involves the molecular motor transport of vesicles into closed constrictions, in particular into dendritic spines in mammalian pyramidal neurons. Newer modeling methods used in machine learning can not work effectively because data is very sparse. We have access to published data of detailed but static EM images, or we have decent temporal resolution of vesicle movement with low spatial resolution, but researchers are unable to measure dynamic mechanisms in detail. We use methods from fluid dynamics to understand how vesicles exhibit bidirectional motion into and out of spines. In electrophysiology, I pursue questions in coupled oscillators such as coupled bursting neurons. In particular, understanding precisely how bursting neurons synchronize through the bursting phase is a long-term goal. I am also beginning to pursue questions in strongly-coupled oscillating neurons and how some neurons may be suppressed in simple networks.Research Summary for the Aplied Mathematician
My training is in applied dynamical systems with a healthy dose of numerical bifurcation theory. Books such as Kuznetsov, Ermentrout and Terman, and Izhikevich were my foundation. I am especially interested in extending the theory of weakly coupled oscillators to the case of stronger coupling. I am using phase response curves and isostables to this end.About Me
I'm mostly from Madison, Wisconsin (see left, image credit Wikipedia). I am originally from Seoul, South Korea, but because my Dad was a diplomat, we moved shortly thereafter to a random sequence of English-speaking countries. I've lived in the US since the second grade. I went to middle school and high school in Madison, WI. I went to college in Cleveland and received my BS and MS in applied math at Case Western Reserve University. No, it is not a military school, it is named after the Western Reserve, which is territory that includes most of Northeastern Ohio. The "Case" part comes from the Case Institute of Technology (CIT) which merged with Western Reserve University in the 70s. At the time, both universities were top-tier research institutions with CIT second only to Cal Tech.
For my PhD I went to the University of Pittsburgh. The city has a similar story to Cleveland, but generally fared better. Here, I had the distinct pleasure of working with my advisor Bard Ermentrout. He is great. I also hold the rest of my thesis committee in high regard: Rob Coalson, Brent Doiron, and Jon Rubin.
I used to play a lot of shows but have mostly retired from music as a hobby. I still play my instruments occasionally, and the main part of my repertoire includes guitar (since 2002) and ukulele (since 2015). I've replaced music with more visual arts including pottery (since 2015) and drawing (since 2017). See below for some of my work, which I will continue to improve upon for the forseeable future.
(click images to enlarge)