Publications:

Uniqueness of Clifford Torus with Prescribed Isoperimetric Ratio (with Jingmin Chen)(pdf)(Earlier version with discussion on the general uniqueness problem (see Page 1-4))

Numerical Methods for Biomembranes: Conforming subdivision versus Non-conforming PL methods
(with Jingmin Chen, Patrick Brogan, Robert Kusner, Yilin Yang and Andrew Zigerelli)(pdf)(software)

Numerical Methods for Biomembranes based on PL Surfaces (with John Patrick Brogan and Yilin Yang)(pdf)(Proof of Proposition 1)

A Flexible C^2 Subdivision Scheme on the Sphere: with application to biomembrane modelling
(with Jingmin Chen and Sara Grundel)(pdf)(bibtex entry)(spinnable 3D figures in matlab .fig format)

Approximation of Scattered Manifold-Valued Data
(with Phillip Grohs and Markus Sprecher)(pdf)(bibtex entry)

Smoothing Nonlinear Subdivision Schemes by Averaging
(with Tom Duchamp and Gang Xie)(pdf)(bibtex entry)

On a New Proximity Condition for Manifold-Valued Subdivision Schemes
(with Tom Duchamp and Gang Xie)(pdf)(bibtex entry)

A Necessary and Sufficient Proximity Condition for Smoothness Equivalence of Nonlinear Subdivision Schemes
(with Tom Duchamp and Gang Xie)(pdf)(bibtex entry)(supplementary material)(talk)

Single Basepoint Subdivision Schemes for Manifold-Valued Data: Time-Symmetry without Space-Symmetry
(with Tom Duchamp and Gang Xie)(pdf)(bibtex entry)(talk)(Hindsight)

Invariance Property of Proximity Condition in Nonlinear Subdivision
(with Gang Xie)(pdf)(bibtex entry)(Hindsight)

On Donoho's Log-Exp Subdivision Scheme: Choice of Retraction and Time-Symmetry
(with Esfandiar Nava-Yazdani)(pdf)(bibtex entry)

Flexible C2 Subdivision Scheme for Genus Zero Surfaces
(with Sara Grundel)(pdf)

Approximation Order Equivalence Properties of Manifold-Valued Data Subdivision Schemes
(with Gang Xie)(pdf)(bibtex entry)

Smoothness Equivalence Properties of General Manifold-Valued Data Subdivision Schemes
(with Gang Xie)(pdf)(bibtex entry)(Maple spreadsheet suggesting the breakdown of smoothness equivalence of Donoho's single basepoint log-exp scheme)

Smoothness Equivalence Properties of Interpolatory Lie Group Subdivision Schemes
(with Gang Xie)(pdf)(bibtex entry)

Smoothness Equivalence Properties of Manifold-Valued Data Subdivision Schemes based on the Projection Approach
(with Gang Xie)(pdf)(bibtex entry)

How Data Dependent is a Nonlinear Subdivision Scheme?
--- A Case Study based on Convexity Preserving Subdivision
(pdf)(ps)(bibtex entry)

Jet Subdivision Schemes on the k-Regular Complex
(with Yonggang Xue and Thomas Duchamp)(pdf)(bibtex entry)(Project Page)

Honeycomb and k-fold Hermite Subdivision Schemes
(with Yonggang Xue)(pdf)(ps)(bibtex entry)

Face-based Hermite Subdivision Schemes
(with Bin Han)(pdf)(ps)(bibtex entry)

Smoothness Analysis of Nonlinear Subdivision Schemes of
Homogeneous and Affine Invariant Type
(with Gang Xie) (pdf)(ps)(bibtex entry)

 Non-Interpolatory Hermite Subdivision Schemes
(with Bin Han and Yonggang Xue)(pdf)(ps)(bibtex entry)

Continuous M-Estimators and their Interpolation by Polynomials
(with Jong-Shi Pang)(pdf)(ps)(bibtex entry)(Matlab Code)

Design of Hermite Subdivision Schemes aided by  Spectral Radius Optimization
(with Bin Han and Michael Overton)(pdf)(ps)(bibtex entry)

Multivariate Refinable Hermite Interpolants
(with Bin Han and Bruce Piper)(pdf)(ps)(bibtex entry) 

An Improved Vertex Caching Scheme for 3D Mesh Rendering
(with Gang Lin) (pdf)(IEEE Tanscactions on Visualization and Computer Graphics, Vol 12, No. 4, 2006)

On the Regularity Analysis of Interpolatory Hermite Subdivision Schemes
(pdf)(ps)(bibtex entry)

Nonlinear Pyramid Transform Based on Median-Interpolation
(with David Donoho)(pdf)(ps)(bibtex entry) 

Interpolation of Medians
(with Tim Goodman) (pdf)(ps)(bibtex entry)

Smooth Multiwavelet Duals of Alpert Bases By Moment-Interpolating Refinement
(with David Donoho, Nira Dyn & David Levin) (pdf)(ps)(bibtex entry)

Research supported by NSF grants CCR 9984501 (CAREER Award), DMS 0542237, DMS 0915068, DMS 1115915, DMS 1522337, DMS 1913038.

I am currently recruiting students to work under my NSF project on understanding the geometry of large-scale optimization methods, with applications to various scientific and engineering problems. Please feel free to contact me if interested.

Teaching:

Winter 2021: Math 449: Mathematical Finance
Fall 2020: Math 538: Manifolds

Spring 2020: Math T690: Methods of Nonlinear Optimization

Spring 2019: Math 305: Introduction to Optimization

Winter 2018:
Math 312: Probability and Statistics II

Fall 2017:
Math 311: Probability and Statistics I

Spring 2017:

Math T680: Topics in Geometry

Math 521: Numerical Analysis II

Math 520: Numerical Analysis I

Drexel links:

Term Master Schedule

Final Schedule

Intructional Media Services

MathSciNet

Refereed Conference Papers:

Cutting Corners on the Sphere
(pdf)(ps)(bibtex entry)

On a Linearization Principle for Nonlinear p-mean Subdivision Schemes
(with Gang Xie)(pdf)(ps)(bibtex entry)

Robust Nonlinear Wavelet Transform based on Median-Interpolation
(with David Donoho)(pdf)(ps)(Asilamor '97)

Approximation Order/Smoothness Tradeoff in Hermite Subdivision Schemes
(pdf)(ps)(bibtex entry)(code)

Deslaueriers-Dubuc: Ten Years After
(with David Donoho) (pdf)(ps)(bibtex entry)

Denoising of Electron Tomographic Reconstructions from Biological Specimens
(with Arne Stoschek & Reiner Hegerl) (pdf)(ps)(Proc. of ICASSP 97, Pg. 2793-2796) (my image denoising gallery)