Research

My research mainly focuses on Whitney-type extension problems and their applications. At the basic level, these problems ask for efficient ways to extend a function defined on some subsets of $\mathbb{R}^n$ obeying certain constraints. See this expository article by Charles Fefferman for an overview of Whitney problems and related topics.


Papers

  1. (with G.K. Luli and K. O'Neill) Smooth selection for infinite sets, in preparation.

  2. (with C. Fefferman and G.K. Luli) $C^2$ interpolation with range restriction, submitted, 2021. Preprint

  3. (with G.K. Luli and K. O'Neill) On the shape fields finiteness principle, to appear in International Mathematics Research Notices, 2021. Preprint

  4. (with G.K. Luli) Algorithms for nonnegative $C^2(\mathbb{R}^2)$ interpolation, Advances in Mathematics, 385:107756, 2021. DOI Preprint

  5. (with G.K. Luli) $C^2(\mathbb{R}^2)$ nonnegative extension by bounded-depth operators, Advances in Mathematics, 375:107391, 2020. DOI Preprint

  6. (with G.K. Luli) Nonnegative ${C}^2(\mathbb{R}^2)$ interpolation, Advances in Mathematics, 375:107364, 2020. DOI Preprint

  7. Nonnegative Whitney Extension Problem for ${C}^1(\mathbb{R}^n)$, 2019. Preprint


Engineering papers

  1. (with K. Xu et al.) A Transfer Function Approach to Shock Duration Compensation for Laboratory Evaluation of Ultra-High-G Vacuum-Packaged MEMS Accelerometers, IEEE 32nd International Conference on Micro Electro Mechanical Systems (MEMS), 676--679, 2019.
  2. (with K. Xu et al.) Micromachined integrated self-adaptive nonlinear stops for mechanical shock protection of MEMS, Journal of Micromechanics and Microengineering, 28:064006, 2018.
  3. (with K. Xu et al.) Micromachined integrated shock protection via a self-adaptive nonlinear system, 19th International Conference on Solid-State Sensors, Actuators and Microsystems (TRANSDUCERS), 524--527, 2017.

Conferences and Workshops

I am one of the organizers of the 14th Whitney Workshop and the Student Run Analysis&PDE seminar at UC Davis.


Upcoming

Past
Seminars