*Postdoctoral researcher in Mathematics at TU Berlin.*

I am a postdoctoral researcher in Mathematics at Technische Universität Berlin, geometry research group (Discretization in Geometry and Dynamics).

I received my PhD (2017) in Applied and Computational Mathematics at California Institute of Technology advised by Professor Peter Schröder. Prior to the PhD study, I received a master (2012) and bachelor (2011) degree in Mathematics at National Taiwan University.

With backgrounds in both *numerical analysis* and *differential geometry*, I study the interplay among differential geometry, algebraic topology, differential equations, and computational mathematics. This includes physical modeling in geometric language, and discretization methods that preserves structures in their continuous analogs. The research direction has given successful and novel applications in fluid dynamics, geometry processing, as well as classical numerical PDE challenges such as absorbing boundary conditions in wave computations.

A main theme in this research area is to study the structure in a system in the language of *fiber bundles* and their *connections* (a.k.a. gauge theory). Although the problems mostly originate from classical mechanics and computer graphics, the modeling approach often reveals their intriguing relations to condensed matter physics, field theory, and quantum mechanics. New insights are learned by the methods of differential geometry and algebraic topology.

One of the focuses in the PhD study and there after is on fluid dynamics and its relation to the Schrödinger equation. Beyond the long-known Madelung's hydrodynamic form of quantum mechanics, we discover an underlying geometric structure involving *Clebsch variables* and *prequantum bundles*, which enable a new way of looking at incompressible fluid and conservation laws. Schrödinger formulation greatly reduces the nonlinearity in fluid equations, and has been turned into practical vortex-capturing numerical schemes for fluid simulation.

My teaching interests and experiences include stochastic processes, complex analysis, ordinary and partial differential equations, discrete differential geometry, numerical analysis, mathematical softwares and visualization.

Besides academic interests, I am also an amateur Houdini programmer, drawing artist and classical pianist.

- SAP Young Researcher Grant at the 6th Heidelberg Laureate Forum, 2018.
- Ben P.C. Chou Doctoral Prize in IST
*(for outstanding dissertations in the broad area of information science and technology)*, 2017. - W. P. Carey & Co. Prize (
*for outstanding doctoral dissertations in applied mathematics)*, 2017. - Microsoft Graduate Teaching in CMS Prize
*(awarded to a graduate student for outstanding teaching and course development in computing and mathematical sciences)*, 2017