Current projects:

• Compact modeling of semiconductor devices
  Collaborators: Henok Abebe, Ellis Cumberbatch, Uno Shigeyasu
• Solitary elastic waves in a heterogeneous medium
  Randy LeVeque and I investigated how elastic waves in a heterogeneous medium support solitary wave behavior.

• Multiple-scale homogenization for the initial-boundary value problem for hyperbolic conservation systems with rapid spatial fluctuations
  When hyperbolic conservation laws involve large, rapidly fluctuating quantities, the natural solution technique is multiple-scale homogenization. Although the initial-value problem has been well-studied, a general theory for initial-boundary value problems using the method of multiple-scales is missing. This work is under the supervision of Jirair Kevorkian.
  Here is a copy of my thesis.
  

Previous projects:

• Nutational movement of plant cotyledons
  Please see this awesome video. Worked with Mele Sato and James Moore, summer of 2004 and 2005, respectively.
• Dynamics of modelocking optical fiber lasers
  One way to generate stable solitons along an optical fiber is by taking advantage of the nonlinearity of its polarization rotation. In our model, a train of solitons is trapped in a optical fiber ring with a polarization control. Our goal is to understand the dynamics of this optical system, governed by a coupled pair of nonlinear Schrodinger equations. Arnold Kim and I are working with Kristin Spaulding, Nathan Kutz and David Muraki.
• Issues relating to turbulent combustion (a.k.a. turbulent reacting flows). My advisors for this work were James Riley and George Kosály from the Department of Mechanical Engineering at the University of Washington.
  
• Factorization of almost-periodic matrix functions, a joint effort with Ilya Spitkovsky from the College of William and Mary. See "Almost periodic factorization of certain block triangular matrix functions" in Mathematics of Computation.