|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. This goal has driven mathematical modeling for some time, especially in physics, from well before Newton's time the present day. Models are not perfect and often fail to capture important phenomena. Interestingly, this failure is one of modeling's greatest strengths. When a model is unable to sufficiently describe a particular phenomenon, it sharpens questions for scientists and produces new research directions. This approach has consistently improved our understanding of countless phenomena.
There is, however, one potential limitation. Some models are comprehensive but mathematically complex, requiring computers and long times to simulate. Once the simulation is done, how does one know that the computer produced realistic and accurate results as opposed to something like a bug? Much of my work can be called "dimension reduction", where complex mathematical models are reduced to something simple enough that we can understand them without computers. This approach also allows us to prove beyond a shadow of a doubt that certain behaviors of a model truly exist. For example, a computer might predict that a neuron model shows oscillations. 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
My research questions are contained within neurphysiology and electrophysiology. My neurosphysiology work involves questions regarding the molecular motor transport of vesicles into closed constrictions. In particular, I am working to understand the movement of recycling endosomes into the dendritic spines of mammalian pyramidal neurons. Newer modeling methods such as machine learning can not work effectively because data is very sparse. Current published data includes high-resolution but static EM images as well as low-resolution temporal/spatial data of vesicle movement. High-resolution spatio-temporal data is beyond current techology.
The major constraint is of course the nanometer scale of dendritic spines. Despite technological limitations, it is possible to observe endosome movement. In fact, endosomes not only translocate through the dendritic spine, but may get stuck (corked), or rejected. That is, there is bidirectional movement of the vesicle. To understand how bidirectional motion is possible, we model the vesicle using methods from fluid dynamics combined with models of moecular (myosin) motors.
In electrophysiology I ask how synaptically or electrically coupled neurons synchronize or phase-lock. Understanding precisely how bursting neurons synchronize or desynchronize through the bursting phase is a long-term goal. The theory I use and develop applies to many different types of systems that exhibit periodicity, such as heart rhythms (or arhythmias), central pattern generating neurons in simple neural circuits, special chemical and biochemical reactions, and the synchronization of cortical neurons in pathological phenomena like epilepsy.Research Summary for the Aplied Mathematician
My training is in applied dynamical systems with a focus on oscillators or systems on periodic boundaries. The systems I consider are often smooth, but sometimes of Filippov-type with transverse crossings (sliding is hard!). I use some perturbation theory (regular, sometimes singular) with a healthy dose of numerical bifurcation theory to understand how coupled oscillators may change phase-locked states. Books such as Kuznetsov, Ermentrout and Terman, and Izhikevich are my foundation. I am especially interested in extending the theory of weakly coupled oscillators to the case of strong coupling for general networks of n-dimensional oscillators.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)