About

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.

My research interest lies in the applications of differential geometry, including physical modeling, partial differential equations and numerical methods. The approach has been applied to fluid mechanics and geometry processing. 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. With backgrounds in both numerical analysis and discrete differential geometry, I also develop computation tools for practical applications.

One of the main 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.


Honors and Awards

  • 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

News

  • Oct 6, 2017. Talk on Geometric Clebsch Variables at SFB Workshop "DGD Days", Raitenhaslach, Germany
  • Sep 24, 2017. Talk on Geometric Clebsch Variables at Geometry Workshop at Obergurgl, Obergurgl, Austria
  • Aug 3, 2017. Conference presentation on Inside Fluids: Clebsch Maps for Visualization and Processing at SIGGRAPH technical papers, Los Angeles, California
  • July, 2017. Employed as a post-doctoral researcher at math department at TU Berlin.
  • Jun 16, 2017. Graduated as a PhD, Caltech.
  • May 23, 2017. PhD thesis defended.
  • Apr 6, 2017. Invited talk on Schrödinger's Smoke at the applied math at UT Austin, Texas.
  • Mar 27, 2017. Invited talk on Schrödinger's Smoke at Indiana University, Bloomington, Indiana.
  • Feb 22, 2017. Invited talk on Incompressible Schrödinger Flow at Los Alamos National Laboratory, New Mexico.
  • Dec 22, 2016. Invited talk on Fluid Simulations with Hopf Fibration at National Taiwan University and National Chiao Tung University, Taiwan.
  • Oct 19, 2016. Colloquium talk on Fluid Simulations by Incompressible Schrödinger Flow at math department, UCLA, California.
  • Sep 7, 2016. Invited talk on Schrödinger's Smoke at computer graphics group, TU Berlin.
  • Aug 18, 2016. Invited talk on Schrödinger's Smoke at Weierstrass Institute for Applied Analysis and Stochastics (WIAS), Berlin Germany.
  • Aug 11, 2016. Invited talk on Schrödinger's Smoke at KTH Royal Institute of Technology, Stockholm, Sweden.
  • Jul 26, 2016. Conference presentation on Schrödinger's Smoke at SIGGRAPH Technical Papers, Anaheim, California.
  • Jul 12, 2016. Colloquium talk on Incompressible Schrödinger Flow at Berlin International Graduate School in Model and Simulation based Research (BIMoS), Berlin.
  • Apr-Sep, 2016. Visiting research at TU Berlin.
  • Apr 6, 2016. Invited talk on Schrödinger's Smoke at UC Irvine, California.
  • Jan 26, 2016. Talk on Close-to-Conformal Deformation of Volumes at Oberwolfach Mathematical Research Institute, Oberwolfach, Germany.
  • Aug 11, 2015. Conference presentation on Close-to-Conformal Deformation of Volumes at SIGGRAPH Technical Papers, Los Angeles, California.