#  Research 

 



Our research uses methods and ideas from applied mathematics to address foundational and practical problems across science and engineering. We are first and foremost problem solvers, seeking out challenging phenomena where mathematics (simple or complicated, with large computer simulations or without) can clarify, quantify, and predict the behavior of complex systems.

Over the past decade, our work has continued to draw inspiration from close contact with experiments and emerging technological challenges, while developing unifying theoretical principles. A central thrust of our research is **self-assembly**, where we study how simple components with programmable interactions can reliably organize into complex structures. Building on this foundation, we are increasingly focused on **molecular computing**: the design of molecular and soft-matter systems that harness physical dynamics, non-equilibrium processes, and collective behavior to perform computation. Leveraging advances in synthetic biology, protein engineering, and nanoscale manufacturing, we aim to establish the theoretical design principles that enable molecular systems to solve hard computational problems through massively parallel, physics-driven dynamics, rather than sequential electronic logic.

Complementing this, we have also developed **theoretical and computational models of turbulence and fluid mechanics**, addressing problems ranging from droplet dynamics and particle sedimentation to the structure of turbulent cascades and the role of geometry and boundary conditions in complex flows. Across these areas, our goal is to connect microscopic interactions to macroscopic behavior, using applied mathematics to uncover organizing principles that govern complex physical systems.